Mat

237 School of Physical Sciences

Date: 22/2/2009

Shah Jalal University Of Science & Technology, Sylhet, BangladeshSchool of Physical Sciences

Department of Mathematics.Syllabus of B. Sc. (Hons) degree for the session 2008-2009 to 2011-2012

The B.Sc. (Hons) courses in Mathematics will comprise the courses on Mathematics, Physics, Statistics, Computer Science, English and Bangla. The course is spread over four academic years. Each year is divided into two semesters. Final examinations are held at the end of each semester and also there are in course examinations. A student has to complete at least 140 credit hours of courses successfully to obtain the B.Sc. Honors degree. A student will be given two extra years to complete his/her B.Sc. degree. A student has to complete at least 40 credit hours in one year programme.

There will be a distribution of marks for a course in class participation, assignments and mid-semester examination and final examination for which the distribution of marks is as follows:

Class participation : 10%Assignment & mid-semester examination : 20%Final examination : 70%

The grading system consists of letter grading, corresponding Grade Point Average (GPA) will be awarded as follows:

Numerical Grade Letter Grade Grade Point80% and above A+ 4.0075% to less then 80% A 3.7570% to less then 75% A- 3.5065% to less then 70% B+ 3.2560% to less then 65% B 3.0055% to less then 60% B- 2.7550% to less then 55% C+ 2.5045% to less then 50% C 2.2540% to less then 45% C- 2.00 less then 40% F 0.00Incomplete X

Absence from the final examination will be considered incomplete. The distribution of courses for respective academic years and semesters is given below along with the detail of the courses.

Course PlanFour (4) Years B. Sc. (Hons) Courses

Session : 2008-09 to 2011-12

Session : 2008-09First Year: First Semester

Course No. Course Title Hours/ WeekTheory + Lab

Credits

MAT-111 Fundamentals of Mathematics 3 + 0 3.0MAT-112 Basic Algebra 2 + 0 2.0MAT-113 Calculus I 4 + 0 4.0STA-101 Principles of Statistics 3 + 0 3.0BAN-101/ENG 101 Bengali Language/English Language 2 +0 2.0BAN-102/ENG 102 Bengali lab / English Lab 0+2 1.0MAT-119 Viva Voce 0 + 0 2.0Total = 14 + 2 =16 17.0

Department of Mathematics 238

Session : 2009-10First Year: Second Semester


Credits

MAT-121 Linear Algebra 3 + 0 3.0MAT-122 Calculus II 3 + 0 3.0PHY-101 Mechanics, Properties of Matter and Waves 3 + 0 3.0STA-102 Probability and Probability Distribution 2 + 0 2.0ENG-101/ENG 103 English Language/ Advance English 2 + 0 2.0ENG-102 /ENG- 104 English Lab/ Advance English Lab 0 + 2 1.0MAT-129 Viva Voce 0 + 0 2.0Total = 13 +2 =15 16.0

Session : 2009-10Second Year: First Semester

Course No. Course Title Hours/WeekTheory + Lab

Credits

MAT-211 Vector and Tensor Analysis 3 + 0 3.0MAT-212 Differential Equations I 3 + 0 3.0MAT-213 Calculus III 4 + 0 4.0PHY-201M Heat, Thermodynamics and Optics 3 + 0 3.0CSE-203E Introduction to Computer Language 2 + 0 2.0CSE-204E Introduction to Computer Language Lab 0 + 6 3.0MAT-219 Viva Voce 0 + 0 2.0Total = 15 + 6=21 20.0

Session : 2009-10Second Year: Second Semester


Credits

MAT-221 Real Analysis I 3 + 0 3.0MAT-222 Complex Analysis 3 + 0 3.0PHY-203M Electromagnetism and Modern Physics 3 + 0 3.0STA-201 Mathematical Statistics 3 + 0 3.0CSE-213E Data Structure 3 + 0 3.0CSE-214E Data Structure Lab 0 + 3 1.5MAT-229 Viva Voce 0 + 0 2.0Total = 15 + 3=18 18.5

Session : 2010-11Third Year: First Semester


Credits

MAT-311 Real Analysis II 3 + 0 3.0MAT-312 Discrete Mathematics 4 + 0 4.0MAT-313 Statics 2 + 0 2.0MAT- 314 Dynamics 2+0 2.0CSE-301E Algorithm 3 + 0 3.0CSE-302E Algorithm Lab 0 + 3 1.5MAT-319 Viva Voce 0 + 0 2.0Total = 14 + 3=20 17.5


Session: 2010-11Third Year: Second Semester


Credits

MAT-321 Theory of Numbers 3 + 0 3.0MAT-322 Abstract Algebra 3 + 0 3.0MAT-323 Hydrodynamics 3 + 0 3.0MAT-324 Mathematical Methods 3 + 0 3.0MAT-325 FORTRAN Programming 2 + 0 2.0MAT-325 L FORTRAN Programming (Lab) 0 + 2 1.0MAT-329 Viva Voce 0 + 0 2.0

Total = 14 + 2=16 17.0

Session : 2011-12 Fourth Year: First Semester


Credits

MAT-411 General Topology 3 + 0 3.0MAT-412 Lattice Theory and Boolean Algebra 3 + 0 3.0MAT-413 Numerical Analysis 3+ 0 3.0MAT-413 L Numerical Analysis ( Lab ) 0 + 2 1.0MAT-414 Mathematical programming 2 +0 2.0MAT-414 L Mathematical programming ( Lab ) 0 + 2 1.0MAT-415 Classical Mechanics 3 + 0 3.0MAT-416 Mathematics Practical Lab-1 0 + 3 1.5MAT-419 Viva Voce 0 + 0 2.0

Total = 15 + 4=19 19.5

Session : 2011-12 Fourth Year: Second Semester


Credits

MAT-421 Differential Geometry 3 + 0 3.0MAT-422 Theory of Groups 3 + 0 3.0MAT-423 Differential Equations II 3 + 0 3.0MAT-424 Advanced Mathematical Methods 3 + 0 3.0MAT-425 Numerical Methods for Boundary Value Problems 2 + 0 2.0

MAT-425 L Numerical Methods for Boundary Value Problems (Lab) 0 + 4 2.0

MAT-426 Mathematical Modeling in Biology 3 + 0 3.0

MAT-427 Mathematics Practical Lab-2 0 + 3 1.5MAT-428 History of Mathematics 3+0 3.0CSE-333 Database System 3 + 0 3.0CSE-334 Database System Lab 0 + 6 3.0CSE-335 Operation System 3 + 0 3.0CSE-336 Operation System Lab 0 + 6 3.0MAT-429 Viva Voce 0 + 0 2.0Total = 24 + 18 35.0

(Students have to complete minimum 16 credits)

Total Credits : 17.0 + 16.0 + 20.0 + 18.5 +17.5 + 17.0 + 19.5 + 16.0= 141.5


Detailed SyllabusMajor Courses in details

MAT-111 FUNDAMENTALS OF MATHEMATICSTheory: 3 Hours/Week, 3 Credits

Sets: Elementary idea of set, subsets, power set of a set, product set. Basic set operations and related theorems on sets, Venn diagrams, countable and uncountable sets, cardinality of a set. Real Number system: set of natural numbers, rational numbers, irrational numbers and real numbers along with their geometrical representation, idea of open & closed interval, product set of real numbers and their geometric representation, Idea of absolute value of real number. Axioms of real number system and their application in solving algebraic equations. Equation and Inequality: Elementary idea of law of inequality, solution of equations and inequalities. Relations and Functions: binary relations, reflexive, symmetry anti-symmetry and transitive relations, Pictorial representations of relations, properties of relation. Variable of a set, functions of a variable, domain and range of a function Polynomial, graph of single polynomial functions, exponential, logarithmic, trigonometric functions and their graphs, algebra of functions, inverse of functions and its graph. Vertical line test for a function and test for symmetry of functions, test for continuity of a function from its graph. Complex Number system: Geometrical representation and properties. Books Recommended :

1. Seymour Lipschutz: Set Theory2. R. David Gustafson & Peter D. Frisk: Functions and Graphs3. Earl W. Swokowski: Calculus with Analytic Geometry4. George B. Thomas Jr. & Ross L. Finney: Calculus with Analytic Geometry

MAT-112 BASIC ALGEBRATheory: 2Hours/Week,2 Credits

Introduction : Definitions and identities of trigonometric and hyperbolic functions with their inverses, Demoivre’s Theorem and its application. Summation of series (algebraic and trigonometric): Arithmetic and geometric series, method of difference and C + i S method (for trigonometric series), Inequalities: Inequalities involving mean, inequalities of Weirstrass, Cauchy, Tchebyshev, Holder and Minskowski. Theory of equations: Polynomials and division algorithms, fundamental theorem of algebra. multiple roots, transformation of equations, relations between roots and coefficients. Descarte’s rule of signs, symmetric functions of the roots. solutions of cubic and biquadratic equations. Sturm’s theorem.

Books Recommended:1. Lipschutz, S : Set Theory and Related Topics2. Bernard & Child : Higher Algebra3. Spiegel, M. R. : Vector Analysis

MAT-113 CALCULUS ITheory: 4 Hours/Week, 4 Credits

Two-dimensional geometry: Set of coordinates for a plane, straight line in a plane. increments, distance of two lines, slope of a line, tangent and normal on a curve, pair of straight lines, basic properties of Circle, Parabola, Ellipse and Hyperbola. Change of coordinates and axes, invariant. General equation of second degree, Reduction of general equation of second degree to standard form and identification of Conic. Polar and parametric equations of conic., poles, polars, chords in terms of middle points, director circle, eccentric angles and conjugate diameters of conic. Functions: limit and its properties of functions, continuity of functions. Derivative of Functions: Intermediate forms and L’Hospital rules, successive differentiations and Leibnitz Theorem. Integration: Introduction, Indefinite integrals, applications, determining constants of integration, basic integration formulas, integration by parts, products and powers of trigonometric functions, even powers of sine’s and cosines, trigonometric substitutions, partial fractions. Definite integrals, calculating areas as limits, the fundamental theorems of integral calculus, integration by substitution, differentials, rules for approximating definite integrals.

Books Recommended:1. Thomas and Finney: Calculus and Analytic Geometry2. J. Stewart, Calculus3. Swokowski, E. W.: Calculus with Analytic Geometry4. Smith, C.: The Analytical Geometry of Conic Sections


MAT-121 LINEAR ALGEBRA Theory: 3 Hours/Week, 3 Credits

Matrix: Introduction to matrices, addition and multiplication of matrices, determinant of matrix, H. sc. typs adjoint and inverse of a matrix, elementary row operations and echelon forms of matrix, rank, row rank, column rank of a matrix and their equivalence, use of rank and echelon form in solving system of homogeneous and non-homogeneous equations. Vector space and subspace over real numbers and direct sum, linear combination, linear dependence and independence of vectors, basis and dimension of vector space, quotient space and isomorphism theorems. Linear transformations, kernel, rank and nullity, matrix representation, change of basis, eigenvalues and eigenvectors, characteristic equations and Caley-Hamilton theorem, diagonalization of matrices, similar matrices, canonical forms. Orthogonal and Hermitian matrices, inner product, orthogonal vectors and orthonormal basis, Gram-Schmidt orthogonalization process, bilinear and quadratic forms.

Books Recommended:1. Hamilton, A. G.: Linear Algebra2. Anton, H. and Rorres, C. Elementary Linear algebra with Applications.3. Kolman, B.: Elementary Linear Algebra4. Nering, E. D.: Linear Algebra and Matrix Theory5. Lipschutz, S.: Linear Algebra

MAT-122 CALCULUS IITheory: 3 Hours/Week, 3 Credits

Applications of derivatives: Curve sketching, the significance of the first derivative, increasing & decreasing functions, concavity and point of inflection, asymptotes and symmetry, maxima and minima. involute, evolute, envelop. Rolle's theorem, Mean Value theorem, Taylor’s Theorem in different forms, Maclaurin Series and their application for the expansion of functions, extending the Mean Value theorem to Taylor’s formula, estimating approximate errors. Applications of definite integrals: Area between two curves, calculating volumes by slicing , volumes modeled with shells and washers, length of a plane curve, area of a surface of revolution, average value of a function, moments and centre of mass, evaluation of improper integrals. Gamma and Beta functions, reduction formulas. Transcendental functions: Derivatives of trigonometric functions and related integrals, the natural logarithm and its derivative, graph of exponential and logarithmic functions. Applications of exponential and logarithmic functions. Hyperbolic function: Derivatives and integrals, hanging cables, polar coordinates, graphs of polar equations, polar equations of conic and other curves, integrals.

Books Recommended:1. Thomas and Finney: Calculus and Analytic Geometry2. Swokowski, E. W.: Calculus with Analytic Geometry3. Spiegel, M. R.: Advanced Calculus 4. Stewart, J. Calculus

MAT-211 VECTOR AND TENSOR ANALYSISTheory: 4 Hours/Week, 4Credits

Vectors: Vectors in the plane, Vectors in space, vector algebra, Dot and Cross products of vectors, Vector differentiation: Vector and scalar fields, directional derivatives, gradient, divergence, curl and Laplacian operator. Vector integration: Line, surface and volume integrals, theorems of Green, Gauss and Stokes and their applications . Curvilinear Coordinates, Concept of Tensors: Transformation of coordinates, covariant and contravariant tensor. Conjugate tenso,Associate tensor. Fundamental operations on tensors.Fundamental operations on tensors: conjugate tensor, associate tensor, christoffel symbols, covariant differentiation . Parallesism and geodesics. Riemann- Christoffel Tensor, curvature tensor, tensor and Bianchi identity.

Books Recommended:1.Thomas and Finney: Calculus and Analytic Geometry2. Swokowski, E.W. Calculus with Analytic Geometry3. Spiegel, M.R. Advanced Calculus4. Spiegel, M.R. Vector Analysis and and Introduction to Tensor Analysis5. Lass, H. Vector and Tensor Analysis6. Spain, B.: Tensor Calculus

MAT-212 DIFFERENTIAL EQUATIONS ITheory: 3 Hours/Week, 3 Credits

Introduction to differential equations. Ordinary differential equations and their solutions: Ordinary differential equations of first order and first degree, ordinary differential equations of 1st order but of higher degree, initial value problem, orthogonal


trajectories, general solution of linear ordinary differential equations (homogeneous and non-homogeneous) with constant coefficients, methods of undetermined coefficients and variation of parameters, reduction of order, solution in series, simple cases of non-linear differential equations, system of linear ordinary differential equations. Partial differential equations of the 1st order: Langrange’s method (linear first order PDE), Charpit’s method( used for non-linear 1st order PDE), total differential equations of three variables.

Books Recommended:1. Ayres, F.: Differential Equations2. Piaggio, H. T. H.: Differential Equations3. Forsyth: Differential Equations4. Ross, L.: Introduction to Differential Equations5. Boyce and D’Prima: Differential Equations

MAT-213 CALCULUS IIITheory: 4 Hours/Week, 4 Credits

Coordinates in three dimensions: Different systems of coordinates and transformations of coordinates, direction cosine, direction ratios, planes and straight lines in three dimensions, general equation of second degree in three variables, reduction to standard forms and identification of conicoids, sphere, cylinder, cone, ellipsoid, paraboloid and hyperboloid. Curve tracing: Polar Coordinate systems and tracing the curves using the ideas of Calculus. Partial derivatives: Functions of two or more variables, limits and continuity, partial derivatives, chain rule, gradients, directional derivatives and tangent planes, higher order derivatives, partial differentials, linear approximation and increment estimation, maxima, minima and saddle points, Lagrange multipliers, exact differentials, Taylor’s theorem. Multiple integrals: Double integrals, areas and volumes, physical applications, changing to polar coordinates, triple integral in rectangular coordinates, physical application in three dimensions.

Books Recommended:1. Smith, C.: An Elementary Treatise on Solid Geometry.2. Bell, R. J. T.: An Elementary Treatise on Coordinate Geometry of Three Dimension.3. Stewart, J. Calculus4. Thomas and Finney: Calculus and Analytic Geometry5. Swokowski, E. W.: Calculus with Analytic Geometry

MAT-221 REAL ANALYSIS ITheory: 3 Hours/Week, 3 Credits

Real number system: The completeness axioms and and Dedekind’s axioms. Limit points of a set of real numbers, Bolzano-Weierstrass theorem. Sequence of real numbers: Definition, convergence of a sequence, subsequence, monotonic sequence bounded sequence, Cauchy sequence, Cauchy criteria for convergence of sequences. Infinite series: Concept of sum and convergence, series of positive terms, alternating series, absolute and conditional convergence, tests for convergence. Continuity: Limits and continuity of functions with their properties, uniform continuity, Heine-Borel theorem, differentiability of functions, Rolle’s theorem, Intermediate value theorem, Darboux theorem, Mean value theorem, Taylor’s theorem with remainder in Lagrange’s and Cauchy’s forms, expansions of functions. Power series: Interval and radius of convergence, differentiation and integration of power series, Abel's continuity theorem. Riemann integrals: Definition of Riemann integration, Riemann integration with related theorems, conditions for integrability, fundamental theorem and mean value theorem of integral calculus, Riemann-Stieltjes integrals: definitions, necessary & sufficient conditions, some other properties.

Books Recommended:1. Rudin, W.: Principle of mathematical analysis2. Apostol, I.: Mathematical Analysis3. Bartle,: Real Analysis4. Marsden, J.E. and Hoffman, M.J. Elementary Classical Analysis5. Burkill,J. G.: A First Course in Mathematical Analysis

MAT-222 COMPLEX ANALYSISTheory: 3 Hours/Week, 3 Credits

Complex variables: Geometry of the complex plane, elementary functions of a complex variable (including the general power and the logarithm). Limit, continuity and differentiability of functions of a complex variable, analytic functions and their properties, harmonic functions, meromorphic function and entire functions. Complex integrals: Line integral over rectifiable curves, Cauchy’s theorem for simple contours, Cauchy’s integral formula, theorems of Liouville and Morera, fundamental theorem of algebra. Zeros, singularities, poles, and residues. Taylor’s and Laurent’s series, expansion of functions. Cauchy’s


residue theorem, Rouche’s theorem, the maximum modulus principle, evaluation of real integrals by contour integrations. Conformal mappings: bilinear transformations and their properties.

Books Recommended:1. Churchill and Brown: Complex variables and Applications2. Stewart and Tall: Complex Analysis3. Spiegel, M. R.: Complex Variable4. Copson, E. I.: Theory of Function of Complex Variables

MAT-311 REAL ANALYSIS IITheory: 3 Hours/Week, 3 Credits

Metric space, neighbourhood at a point, open and closed sets, cluster points, closure, interior and boundary points. Compact sets & Connected sets: Compact sets, locally compact sets and related theorems; connected sets, locally connected sets, pathwise connected sets and related theorems, continuity and compactness, continuity and connected sets. Sequences in metric space: convergent and Cauchy sequence, completeness, Banach fixed point theorem with applications, sequence and series of functions, pointwise and uniform convergence, differentiation and integration of series. Continuous functions on metric space: Boundedness, intermediate value theorem, uniform continuity. Functions of several variables: Linear transformations, differentials, the inverse function theorem, the implicit function theorem, the rank theorem, Jacobian. Contraction mapping theorem. Introduction to Lebesgue’s integral.

Books Recommended:1. Rudin, W.: Principle of mathematical Analysis2. Apostol, I.: Mathematical Analysis3. Phillips, E. G.: Course of Analysis4. Spiegel, M. R.: Real Variables

MAT-312 DISCRETE MATHEMATICS Theory: 4 Hours/Week, 4 Credits

Number Systems: Numbers with different bases, their conversions and arithmetic operations, normalized scientific notation,. Logic : Introduction to logic, elements of logic, conditional propositions and logical equivalence, quantifiers, method of proofs, mathematical induction, recursion and iteration. Boolean algebra: Boolean algebra, Boolean operations, Boolean functions and expressions, Application of Boolean Algebra: logic gates, minimization of Boolean expressions, Karnaugh maps, Karnaugh map algorithm. Graphs: Introduction: The bridges of Königsberg, representing graphs and graph isomorphism, connected graph, planar graph, path and circuit, shortest path algorithm, Eulerian path, Euler’s Theorem, graph coloring. Application of Graphs: Trees, tree traversal, trees and sorting, cryptology coding, decoding, encoding. Huffman code, error correcting codes, Hamming code. spanning tree, minimum spanning trees: Kkruskal’s algorithm. Modeling Computation: Languages and grammars, Finite State Machine, language of Finite State Machine, accepted and non-accepted Finite State Machine, Turing Machine.

Books Recommended: 1. Rosen, K.H.: Discrete Mathematics and its application, McGraw-Hill International edition (4th edition) 1999 2. Biggs, N. L.: Discrete Mathematics, Clarendon press. Oxford (2nd Print.) 19873. Cameron, P. J. & J. H. Van Kint: Graph Theory, Coding Theory and Block Designs C.U.P 1974. Bose, R. C. and B. Manvel: Introduction to Combinatorial Theory J. Willey 1984

MAT-313 STATICSTheory: 2 Hours/Week,2 Credits

Introduction: Fundamental concepts and principles of Mechanics. Statics of particles: Addition of forces, resultant of several concurrent forces, resolution of a force in components, equilibrium of a particle in plane and in space. Rigid bodies: Moment of a force and a couple. Equilibrium of rigid bodies: Reactions at supports and connections of a rigid body in two dimensions. Centroid and centre of gravity: Centre of gravity of two and three dimensional bodies, centroids of areas, lines and volumes, determination of centroid by integration. Moments of inertia: Moments and products of inertia, determination of moment of inertia by integration, radius of gyration, parallel axis theorem, principal axis and principal moments of inertia. Method of virtual work: Work of a force, principle of virtual work and its application, potential energy, potential and equilibrium, stability and equilibrium, catenary. Books Recommended:

1. Beer, F. P. and Johnston, E. R.: Vector Mechanics for Engineers: Statics2. Synge and Griffiths: Principle of Mechanics3. Loney, S.L.: Statics4. Chatterjee, P.N: Statics


MAT-314 DYNAMICSTheory: 2 Hours/Week,2 Credits

Kinematics of particles: Mechanical vibrations: Simple harmonic motion, application of the principle of conservation of energy, motion under a central force and conservative central force, principle of impulse and momentum, impulsive motion. System of particles: Applications of Newton’s laws to the motion of a system of particles, effective forces, linear and angular momentum of a system of particles, conservation of momentum and energy for a system of particles, work energy principles. Kinematics of rigid bodies: Translation, rotation, velocity, acceleration and plane motion of a particle relative to a rotating frame, Corilis acceleration. Plane motion of rigid bodies: Equations of motion for a rigid body, motion of a rigid body in two dimensions, Euler’s equation of motion of a rigid body about a fixed point.

Books Recommended:1. Beer, F. P. and Johnston, E. R.: Vector Mechanics for Engineers2. Synge and Griffiths: Principle of Mechanics3. Beer, F. P. and Johnston, E. R.: Vector Mechanics for Engineers: Dynamics4. Khanna, M.L: Dynamics5. Chorlton, F.: Text Book of Dynamics

MAT-321 THEORY OF NUMBERSTheory: 3 Hours/Week, 3 Credits

Divisibility and greatest common divisors, arithmetic in Z, prime numbers and perfect numbers, fundamental theorem of arithmetic and its consequences, division algorithm, Congruence, least residue theorem, Fermat’s Theorem, Euler’s Theorem and Wilson's Theorem, solutions of congruence, Lagrange’s theorem of congruence, Chinese remainder theorem, arithmetic functions and their properties, multiplicative functions, Zeta function and its relation with arithmetic functions. Quadratic residues and non-residues, Law of quadratic reciprocity. Legendre symbol, Some Diophantine equations and their solutions, representation of integers by sum of two squares or four sum squares, solution of the equation z 2 = x2 + y2. Selberg’s proof of the prime number theorems.

Books Recommended:1. Apostol: Theory of Numbers2. Chowdhury, F. and Chowdhury, M.R.: Essentials of Number Theory3. Niven and Zucherman: Theory of Numbers4. Hunter, J..: Number Theory5. Hardy, G. H. and Wright, E. M.: Theory of Numbers

MAT-322 ABSTRACT ALGEBRATheory: 3 Hours/Week, 3 Credits

Permutations of a set: Equivalence relation and residue classes modulo n. Groupoids, monoids and semigroups. Groups, subgroups, orders of elements in a group, Cyclic group, Multiplication of subgroups, Cosets and Lagrange’s Theorem: Normal subgroups, quotient (factor) groups, Centre of a group, permutation groups, Homomorphism, isomorphism & automorphism of groups with related theorems & problems, Cayley’s theorem, Generalized isomorphism theorem, Centralizer and normalizer of an element/subset in a group.

Rings, different types of rings, subrings. Ideals, prime, maximal and minimal ideals, principal ideals with related theorems. Idempotent and nilpotent ideals, sum and direct sum of ideals, factor rings.. Integral domain and field with related theorems and problems, Characteristic of a field. Homomorphism and isomorphism of rings with related theorems and problems, Rings of functions.

Books Recommended:1. Herstein, I, N.: Topics in Algebra2. Dean, R. A.: Elements of Abstract Algebra3. Paley, H. and P. M. Weicheel: A First Course in Abstract Algebra4. Printer, C. C.: A Book of Abstract Algebra5. Baumslag and Chandler: Theory and Problems of Group Theory6. John B. Fraleigh : A First Course in Abstract Algebra


MAT-323 HYDRODYNAMICSTheory: 3 Hours/Week, 3 Credits

Introductory motion: Physical dimension, stream lines and path lines, hydrodynamic pressure, Bernoulli’s theorem, adiabatic expansion. Equation of motion: Equation of continuity, equation of motion of inviscid liquid and Bernoulli’s equation, steady motion and conservative forces, circulation and Kelvin’s theorem, vorticity, irrotational motion and velocity potential, the energy equation, kinetic energy and Kelvin’s minimum energy theorem. Two dimensional motion: rate of change of vorticity, stream function and pressure equation, streaming motions, complex potential and complex velocity, stagnation points, circle theorem, motion past a cylinder, Joukowaski transformation, Blasius theorem. Two dimensional source and sink, doublets, combination of source and stream, source and sink of equal strength, source and sink in a stream, the method of image, source outside a cylinder. Vortex motions: Vortex lines, tubes and filaments, rectilinear vortex, circular vortex, and vortex doublets, kinetic energy of a system of vortices, vortex in or outside of a circular cylinder, vortex sheet, single infinite row of vortices and Karman’s vortex street. Three dimensional motions: Three dimensional axi-symmetric motions and Stoke’s stream function, three dimensional sources in a uniform stream, Butler’s sphere theorem, sphere in a stream and moving cylinders. Hydrodynamic waves: Mode of energy transmission, mathematical representation of wave motion and conditions at the free surface, surface waves, speed of propagation and wave length, progressive and standing waves, kinetic energy of waves, group velocity and wave at interface.

Books Recommended:1. Milne-Thompson, L. M.: Theoretical Hydrodynamics2. Chorlton, F. : Fluid Dynamics3. Lamb, H.: Hydrodynamics4. Raisinghania: Fluid Mechanics5. Gupta, P. P.: Hydrodynamics6. Ramsey : Hydrodynamics7. Rutherford, D. E. : Fluid Mechanics

MAT-324 MATHEMATICAL METHODSTheory: 3 Hours/Week, 3 Credits

Fourier series, Fourier integral, Fourier transform and their applications. Laplace transform and its applications in differential equations. Harmonic functions: Laplace equation in different coordinates and its applications. Concepts of singularities and series solutions, Legendre polynomials, Hermite polynomials,Laguerre functions, Bessel function and their properties. Boundary value problems involving second order ordinary differential equations, eigenfunction expansions and Green’s functions. Ideas about Strum-Liouville problems. Linear integral equations : elementary ideas.

Books Recommended:1. Stephenson : Mathematical Methods2. Ross, S. L. : Introduction to Differential Equations3. Courant and Hilbert: Methods of Mathematical Physics4. Churchill, R. V.: Fourier Series and Boundary Value Problems5. Mackies, A. G.: Boundary Value Problems6. Spiegel, M. R.: Laplace Transform 7. Rajput: Mathematical Physics8. P. P. Kanwal : Linear Integral Equations

MAT-325 FORTRAN PROGRAMMING Theory: 2 Hours/Week, 2 Credits

Fortran programming: Computer representation of numbers, source program; object program; interpreter; compiler; editor; FORTRAN instruction cards and coding forms, FORTRAN statements; Variables; constants; elementary control statements: control statements (GO TO); logical IF; compound IF statements; IF-THEN-ELSE construct , Block-IF; (single alternative), case construct (multiple alternative). Loop control statements: The CONTINUE statements; the DO WHILE statements, computed GO TO statement. Forming a Database: Subscripting variables; input/output of arrays in FORTRAN; the DIMENSION and PARAMETER statement. Functions/subroutine/subprograms: Types of sub-programs; arithmetic statement functions (in details); dummy variables; the function subprogram; the subroutine subprogram. equivalence, common and data statements Formal – Statements : I,F,E, A- format-statements;

Books Recommended:1. Kumar: Programming with FORTRAN-772. Francis Scheid: Numerical Analysis


3. Hilderman, F.B.: Introduction to Numerical Analysis4. Noble B.: Numerical Methods Vol. I & II

MAT-325 L FORTRAN PROGRAMMING (Lab)2 Hours/Week, 1 Credits

Syllabus will be designed by course teacher based on MAT-325.

MAT-411 GENERAL TOPOLOGYTheory: 3 Hours/Week, 3 Credits

Topology and Topological space, open sets and closed sets, closure of a set, interior, exterior and boundary, neighborhoods and neighborhoods systems, weak and strong topology, topology of the real line and plane, cofinite and cocountable topology, subspaces, relative topology, bases and subbases for a topology, continuity and topological equivalance, homeomorphic spaces. Metric and normed spaces: Metric topologies, properties of metric spaces, metrizable space, Hilbert space, convergence and continuity in metric space, normed spaces. Countability: First countable spaces, second countable spaces and related theorems. Compactness : Covers, compact sets, subset of a compact space, finite intersection property, Bolzano-Weierstrass theorem, locally compact spaces. Connectedness: Separated sets, connected sets, connected spaces, components, locally connected spaces

and simply connected spaces. Separation axioms: T -spaces, Hausdorff spaces, regular spaces, normal spaces, completely

normal spaces and completely regular spaces. Books Recommended:

1. Simmons, G.F.: Introduction to Topology and Modern Analysis2. Gal, S.: Point Set Topology3. Lipschutz, S.: General Topology4. Kelley,J.L.: General Topology5. Hockling and Young: Topology

MAT-412 LATTICE THEORY AND BOOLEAN ALGEBRATheory: 3 Hours/Week, 3 Credits

Ordered sets: Ordered sets, diagrams, constructing and deconstructing ordered sets, down-sets and up-sets, order preserving map. Lattices and complete lattices: Lattices as ordered sets, Lattices as an algebra, sublattices and convex sublattice of a lattice, product lattice, ideals and filters, prime ideals and maximal ideals, Zorn’s Lemma, complete lattice, chain conditions and completeness, join irreducible elements. Modular, Distributive and Boolean lattices: Modular and distributive lattices and its characterizations; ideals, prime ideals and maximal ideals for modular and distributive lattices, Stone’s separation theorem. Boolean lattice and Boolean algebra. Congruences and lattice homomorphism: Introducing congruence, congruences and diagrams, the congruences lattice, factor lattice, lattice homomorphism and related theorems. Representation: Finite Boolean algebras and power set algebras, finite distributive lattice and finite ordered sets in partnership, Stone’s representation theorem for Boolean algebras, Priestley’s representation theorem for distributive lattices, distributive lattices and Priestley spaces in partnership.

Books Recommended: 1. Balbs, R. and Dwinger, P., Distributive lattices, University of Missouri Press, 19742. Birkhoff, G., Lattice Theory, 3rd edition, Coll. Publ., XXV, American Mathematical Society, 1967.3. Davey, B.A. and Priestley, H.A., Introduction to Lattices and Order, 2nd edition, Cambridge University Press,

2002.4. Grätzer, G., General Lattice Theory, 2nd edition, Birkhäuser Verlag, 1998.

MAT-413 NUMERICAL ANALYSIS Theory: 3 Hours/Week, 3 Credits

Errors in numerical calculations; errors; definitions, sources, examples, propagation error. a general error formula. Root finding: The bisection method, the iteration method, the method of false position, Newton-Raphson method. Methods of interpolation theory: Polynomial interpolation, error in polynomial interpolation, interpolation using Newton’s forward and backward formulas and Newton’s divided difference formula and central difference formula. Starling’s interpolating polynomial, Lagrange’s interpolating polynomial, idea of extrapolation. Numerical integration: Trapezoidal method, Simpson’s methods, Weddle’s method, Romberg’s method, error analysis.


Interpolation: Quadratic and cubic spline interpolation methods. Solutions of systems of linear equations: Gaussian elimination with and without pivoting, iteration method, solution of tri-diagonal system of equations. Numerical solution of ordinary differential equation (IVP): Euler's Method (including modified form) Runge-Kutta method , predictor and corrector method. Boundary value problem: explicit and implicit finite difference method for BVP involving ODE, explicit finite difference method for BVP involving PDE (elliptic, parabolic and hyperbolic).

Books Recommended:1. Francis Scheild: Numerical Analysis2. Hilderman ,F. B.: Introduction to Numerical Analysis3. Noble, B.: Numerical Methods Vol. 1 & II4. Burden, R. L., and Faires, J. D.: Numerical Analysis5. Gerald and Wheatley: Applied Numerical Analysis 6. Smith, G.D.: Numerical solution of Partial Differential Equations7. Jain, M. K.: Numerical Solution of Differential equations

MAT-413 L NUMERICAL ANALYSIS II ( Lab )2 Hours/Week, 1 Credits

Syllabus will be designed by coursed teacher based on MAT-413.

MAT-414 MATHEMATICAL PROGRAMMINGTheory: 2 Hours/Week, 2 Credits

Linear programming: Linear programs, convex set, graphical solution of systems of linear inequalities and linear program, solution of linear program by simplex method, algebraic basis and computational set up, Duality problem-Duality theorem, transportation set problems, assignment problem and simple applications, connection between linear programming and two–person zero-sum matrix game, simple inventory problems. Non-linear programming: Definiteness of matrix, general optimization problem, concave and convex functions, optimization of convex functions, general nonlinear programming problem, tangent plane, regular point, equality constraint, Lagrangian for equality and inequality constraints, Kuhn-Tucker condition, standard extremization problem of convex and concave programming, saddle point.

Books Recommended:1. Haldey, G.: Linear Programming2. Gass, S.I.: Mathematical Programming3. Saaty, T.L.: Mathematical Methods of Operational Research4. Lieberman: Operational Research5. Luenberger: Linear and Nonlinear Programming6. Taha: Operation Research

MAT-414 L MATHEMATICAL PROGRAMMING ( Lab )Lab: 2 Hours/Week, 1 Credits


MAT-415 CLASSICAL MECHANICSTheory: 3 Hours/Week, 3 Credits

Generalized coordinates, Rigid body motion. Motion under no forces, application of Euler’s equation. Keplar’s equation. Lagrange’s equation of motion, ignoration of coordinates, the Routherian function, small oscillation, Hamilton’s equations, contact transformation, Lagrange’s and Poisson’s brackets, Hamilton-Jacobi equations for Hamilton’s principal functions.

Books Recommended:1. Goldstein, H. Classical Mechanics2. Rutherford: Classical Mechanics


MAT-416 MATHEMATICAL PRACTIAL LAB-13 Hours/Week, 1.5 Credits

Syllabus will be designed by course teacher to use MAT Lab/ Mapple for practical problems.

MAT-421 DIFFERENTIAL GEOMETRYTheory: 3 Hours/Week, 3 Credits

Curves in space : Concepts of space curves and their applications, tangent, normal and bi-normal, osculating plane, rectifying plane and normal plane , curvature and torsion , Serret-Frenet formulae, helices, evolutes and involutes. Elementary theory of surfaces : First fundamental form, second fundamental form, Euler’s theorem, Gaussian curvature, mean curvature, the equation of Gauss–Weingarten, the theorem of Gauss and equation of Codazzi, developable surface, minimal surface, rulled surface. Mapping of surfaces: Conformal mapping, geodesic mapping, isometric mapping.

Books Recommended:1. T. J. Willmores : Differential Geometry2. W. Klingenberg : A course in Differential Geometry3. C. E. Weatherburn : Differential Geometry in three dimension

MAT-422 THEORY OF GROUPSTheory:3 Hours/Week, 3 Credits

The class equation of a group: p-groups and related theorems, Cauchy’s theorem, Commutator subgroup, characteristic subgroup, maximal subgroup. Group actions on a set: Double cosets, Sylow’s theorems with applications, groups of order pq, classification of groups of small orders (upto 15). Normal series: Composition series, Jordan-Hölder theorem,Zassenhans’s Butterfly Lemma, Solvable groups, nilpotent groups and related theorems & problems, Directed products of groups with application. Group extension: Splitting extension of groups, Non-abelian group of order p3.Representaion of groups & generalization of Cayley’s theorem, Permutational and matrix representation of finite groups, Maschke’s theorem, Schur’s lemma.Galois Theory.

Books Recommended:1. Hall, M. : The Theory of Groups2. B. Bhattacharya, S.K. Jain & S.R. Paul: Basic Abstract Algebra3. B. Baumslag & B. Chandler: Theory & Problems of Group Theory4. Martin Burrow: Representation Theory of Finite Groups5. W. Ledermann, Introduction to group Character

MAT-423 DIFFERENTIAL EQUATIONS IITheory: 3 Hours/Week, 3 Credits

Group-A: Partial differential equationsTheory of PDEs: Cauchy problem, characteristics, characteristics surface, existence and uniqueness, typical well-posed problems for hyperbolic and parabolic equations, elliptic equations, Dirichlet problem. Variational principles for non-homogeneous problems: Minimum potential energy theorem, quadratic functionals and complementary variational principles. Green’s functions: Influence functions, causal solution, Green’s functions and its properties. Modified Green’s functions.Group-B: Non-linear differential equationsNon-linear DEs-I: Second-order DEs in the phase plane: Phase diagram for the pendulum equations, autonomous equations in the phase plane, conservative systems, the damped linear oscillator and non-linear damping. Non-linear DEs-II: First-order systems in two variables and linearization: The general phase plane, some population models, linear approximation at equilibrium points, the general solution of a linear system, classifying equilibrium points, constructing a phase diagram, transition between types of equilibrium points.

Books Recommended:1. Sneddar : Elements of Partial Differential Equations2. Stakgold : Green’s Functions and Boundary Value Problems3. Roach : Green’s Functions4. Jordan & Smith : Non-Linear Differential Equations5. Struble : Non-Linear Differential Equations6. Snneddon : Partial Differential Equations


MAT-424 ADVANCED MATHEMATICAL METHODSTheory: 3 Hours/Week, 3 Credits

Local Analysis: Approximate solution of linear differential equation (LDE): Classification of singularity of homogenous LDE, asymptotic solution at irregular singular point of homogenous and non homogenous LDE, irregular singularity at infinity, asymptotic solution of LDE for large value of the independent variable.. Perturbation methods: Perturbation theory, regular and singular perturbation theory, perturbation method for linear eigenvalue problems. Global analysis: Boundary layer theory: Introduction to BL theory, mathematical structure of BL, Higher order BL theory, distinguished limits and BLS of thickness 0. WKB theory: The exponential approximation for dissipative and dispersive phenomena, conditions for validity of WKB approximation, WKB solution of inhomogeneous linear equations.

Books Recommended:1. Carl, M. Bender & Steven, A. : Advanced mathematical methods for scientist and Orszag engineers 2. J. D. Cole : Perturbation methods in applied mathematics

MAT-425 NUMERICAL METHODS FOR BOUNDARY VALUE PROBLEMTheory: 2 Hours/Week, 2 Credits

IVP for ODE: Euler’s & modified Euler’s methods, Runge-Kutta method, multi-step method, Adam-Bashforth, Adam-Moulton, higher-order equations and system of DE, stability analysis. Nonlinear system of equations: Fixed points for functions of several variables, Newton’s and quasi-Newton’s methods, steepest descent technique. BVP for ODE: Shooting method for linear and nonlinear problems, finite difference method for linear and non-linear problems, Rayleigh-Ritz method. Numerical solution of PDE: Solution of elliptic, parabolic and hyperbolic PDE by finite difference method, preliminary idea about finite element methods

Books Recommended:1. R L. Burden & J. D. Faires : Numerical analysis; prindle, Weber & Schmidt, Boston2. G. D. Smith : Numerical solution of PDE; oxford University press3. M. K. Jain : Numerical solution of DE; Tata McGraw-Hill, India

MAT-425 L NUMERICAL METHODS FOR BOUNDARY VALUE PROBLEMS (Lab)Lab: 4 Hours/Week, 2 Credits


MAT-426 MATHEMATICAL MODELING IN BIOLOGYTheory: 3 Hours/Week, 3 Credits

Existence and Uniqueness Theory: The Lipschitzs condition, Existence and uniqueness theorem. Graphical Theory (Representation of solution of non-linear differential equation by graphs) : Line element and direction field, The method of isocline. Qualatative theory: Critical points and paths of non-linear system, limit cycles and periodic solution. Stablity theory Mathematical models and stability in Ecology: Single-species growth: (i) Multhusian growth, (ii) Logistic growth (iii) The genearal Autonoumous model (iv) Nonautonomous growth (v) Discrete growth. Two-species population models: (i) predator prey models (ii) competion models (iii) Models of mutualism (iv) The kolmogorov Model. some Three-species population models: Stability versus complexity in Multi-species models. Models with few-species: Limit cycles and time delays.

Books recommended:

1) S.L. ROSS- Differential equations2) J.C. Frauenthal: Introduction to population modelling- 3) H. F. Freedman- Deterministteic mathematical models in population Ecology4) R. M. May- Stability and complexity ni Model Ecosystems.

MAT-427 MATHEMATICS PRACTICAL Lab-2 3 Hours/Week, 1.5 Credits

Syllabus will be designed by course teacher to use MatLab/ Mapple/ Mathematica for practical problems.


MAT-428 HISTORY OF MATHEMATICSTheory: 3 Hours/Week, 3 Credits

A survey of the development of mathematics beginning with the history of numeration and continuing through the development of calculus: Early number systems and symbols. Mathematics in early civilizations. the beginnings of Greek mathematics. The Alexandrian school: Euclid. the Twilight of Greek Mathematics: Diophantus. The first Awakening: Fibonacci. The Renaissance of Mathematics: Cardan and Tartaglia . The mechanical world: Descartes and Newton. Study of selected topics from each field is extended to the 20th century: The development of Probability Theory: Pascal. bernoulli and Laplace. The revival of Number Theory: Fremat. Euler, Euler, And gauss. Nineteenth- Century Contribution: bolyai and Lobachevsky. The Transition to the Twenticth Century: Cantor and Kronecker.

Text: The History of Mathematics- David M Burton

Non-major Courses for other Departments

MAT-101 FUNDAMENTALS OF MATHEMATICS (for ENG)Theory: 2 Hours/Week, 2 Credits

Sets: Elementary idea of set, set notation, set of natural numbers, rational numbers, irrational numbers and real numbers along with their geometrical representation, idea of open & closed interval, subsets, power set of a set, basic set operations and related theorems on sets and venn diagrams. Real Number system: Idea of absolute value of real number. Axioms of real number system and their application in solving algebraic equations. Equation and Inequality: Elementary idea of law of inequality, solution of equations and inequalities. Variable and Functions: Variable of a set, functions of a variable, Polynomial, graph of single polynomial functions, exponential, logarithmic, trigonometric functions and their graphs, domain and range of a function; sum, difference, product, quotient, composition and inverse of functions.

Books Recommended :1. Seymour Lipschutz: Set Theory2. R. David Gustafson & Peter D. Frisk: Functions and Graphs

MAT-101A ALGEBRA (for STA)Theory: 2 Hours/week, 2Credits Complex numbers: Definition of complex numbers and their properties. De-Moivre’s theorem (for integral and rational exponents) and its applications. Inequalities: Cauchy, Chebyshev and Jensen’s inequality. Theory of equations: Polynomials, division algorithm, fundamental theorem of algebra, multiplicity of roots, relation between roots and coefficients of algebraic equations, Descartes rule of signs.

Books Recommended:1. Bernard & Child, Algebra2. 2. Hall & Knight, Higher Algebra3. 3. Rahman M.A. Algebra and Trigonometry4. Shahdullah & Battacharjee, Albegra and Trigonometry

MAT-101B VECTOR ANALYSIS AND TENSOR (FOR PHYSICS)Theory: 3 Hours/Week, 3 Credits

Vectors: Vectors and vector algebraic operations on vectors, null and unit vectors, components of vectors, scalar and vector products of two vectors, angle between two vectors, product of three and four vectors – their applications. Spherical polar and cylindrical coordinate systems – unit vectors and vector component in spherical and cylindrical systems. Vector calculus: Derivative of vectors with respect to scalars, vector operator DEL, gradient, divergence and curl – their physical significance. Outlines of line, volume and surface integrations. Green’s theorem , divergence theorem, Stokes theorem and their applications . Tensors: Definatons of tensors, fundamental metric tensor, covariant and contravariant tensors. Christoffel’s symbols, covariant differentiation of tensors..

Books Recommended:1. Spiegel, M.R. Vector Analysis and and Introduction to Tensor Analysis2. Jaffreys, H. and Jaffreys B: Method of Mathematical Analysis.3. Spain, B.: Tensor Calculus


MAT–101B MATHEMATICS (for Forestry)Theory: 4 Hours/Week, 4 Credits

Matrix: Definition, elementary properties and solution of system of linear equations with the help of matrices. Differential Calculus: limit, continuity, differentiation of functions, partial differentiation, leibniitz’s theorem and its applications, maxima and minima of a function of one variable. Integral Calculus: Methods of integration, integration by parts, definite integral, area and volumes. Vector Analysis: Scalars and vectors, algebraic operations on vectors, Scalar and vector product of two vectors. derivative of vectors with respect to scalars, vector operators gradient, divergence and Curl. Out lines of line, volume and surface integration.

Books Recommended:1. Ayres, F., Matrices2. Kolman, B., Elementary Linear Algebra.3. Thomas and Finney, Calculus and Analytic Geometry4. E. W Swokowski, Calculus with Analytic Geometry5. Speigel M R.: Vector analysis

MAT-101H MATHEMATICS-1 (for Architecture)Theory: 2 Hours/Week, 2 Credits.

PART-A: Differential Calculus- function , limit , continuity, differentiation , successive and partial differentiation, Rolle’s theorem , Mean value theorem, Maxima and minima. .Integral Calculus – Integration by various methods; standard Integrals; Definite Integrals; length of curves; area bounded by plane curves; volumes and surface areas of solids of revolution . PART–B: Co-ordinate geometry of two dimensions - Co-ordinate system, pair of straight lines; circle; tangent & normal at a point on a circle; General equation of second degree.Co-ordinate geometry of three dimensions - distance between points; angle between two straight lines; plan through three points; angle between two planes; straight line through two points. Books Recommended:

1. Thomas and Finney, Calculus and Analytic Geometry2. E. W Swokowski, Calculus with Analytic Geometry3. H. Anton, Calculus4. Rahman & Bhattacharjee; Co-ordinate geometry of two & three dimensions.5. Loney, S. L.: Coordinate Geometry of Two dimensions6. Smith, C.: The Analytical Geometry of Conic Sections

MAT-101S MATHEMATICS (For SOC)Theory: 3 hours/week, 3 Credits

Sets and Algebra: Sets of real numbers, operation on sets, quadratic equations, solving linear equations and inequalities in one variable, exponents and roots, absolute value and inequalities. Linear equations and system of linear equations. The Cartesian coordinate system. Linear functions and their graphs, the slope and equation of lines, system of two linear equations in two unknowns, a traffic flow (Optional). Matrices and Matrix Operations: Matrix and matrix product, system of linear equations, inverse of a square matrix.Linear Programming: Linear inequalities in two variables and linear programming, introduction of graphic approach ,slack variables, the simplex method, the standard maximizing problem. The Derivative: Introduction, limits, continuity, the derivative as the slope of a curve, the derivative as the rate of change, some differentiation formulas, the product and quotient rules, the chain rule, higher order derivatives, implicit differentiation, derivatives of exoibebtuak and integrating functions. Books Recommended:

1.Sanley I Grossman, Applied Mathematics for the Management Life and Social Sciences2. Finney & Thomas, Calculus and Analytic Geometry.

MAT 101Z DIFFERENTIAL CALCULUS AND MATRIX (for PGE)Theory: 3 Hours/ week, 3 Credits

Differential calculus: Differentiation of explicit and implicit functions and parametric equations, sucfessive differentiation of various types of functions, Leibnitz’s theorem, Rolls theorem, Mean value theorem. Taylor’s theorem in finite and infinite forms.


Laclaurin’s theorem in finite and infinite forms, lagrange’s form of remainder, Cauchy’s form of remainder. Expansion of function by differentiation and integration. Partial differentiation. Euler’s theorem. Tangent and normal, subtangent and subnormal in Cartesian and polar coordinates. Deteremination of maximum and minimum values of functions, point of inflexion, its applications. Evaluation of indeterminant forms by L’Hospital’s rule. Curvature, radius of curvature, centre of curvature and chord of curvature. Evolute and involute. Asymptotes, Envelopes, curve tracing.Matrices: Definition of matrix. Different types of matrices. Algebra of matrices. Adjoint and inverse of a matrix. Rank and elementary transformations of matrices. Normal and canonical forms. Solution of linear equations. Quadratic forms. Matrix polynomials. Caley Hamilton theorem and eigenvectors.

Books recommended:1.Thomas and Finney: Calculus and Analytic Geometry2. Swokowski, E. W.: Calculus with Analytic Geometry3. Mohammad and Bhattacharjee: Defferential Calculus4. Spiegel, M. R.: Vector Analysis5.Bell, R. J. T.: An Elementary Treatise on Coordinate Geometry of Three Dimension.6.Rahman and Bhattacharjee: A Text Book on Coordinate Geometry

MAT-102B TRIGONOMETRY, MATRICES, COMPLEX VARIABLE (for PHY)Theory: 4 hours/week, 4 credits

Trigonometry: Complex numbers and functions, De Moiver’s theorem and it’s application, summation of finite trigonometric series, hyperbolic functions. Matrices: Type of matrices, null and unit matrices, algebraic operations in matrices, Determinant of square matrices, Matrix equivalence, adjoint and inverse of a matrix, orthogonal and unitary of a matrices, Linear equations, vector spaces, Linear transformations, similar matrices, Charectiristic roots and vectors, diagonalizations of matrices. Complex Variable: Complex numbers and their properties, functions of a complex variable, limit, continuity, analytic functions, Cauchy – Reimann equations, Cauchy’s theorems, Simple contour integrations.

Books Recommended1. Sarder and Others: Higher Trigonometry2. Ayres, F: Matrices3. A G Hamilton: Linear Algebra4. A Rahman: College Linear Algebra5. M L Khanna: Linear Algebra6. I S Sokolnikoff & R M Redheffer: Mathematics for Physics & Modern Engineering7. KK Kodaira: Introduction to Complex analysis8. H Jaffreys & B Jaffreys: Methods of Mathematical Physics

MAT-102C TRIGONOMETRY, VECTORS AND GEOMETRY (for CHE)Theory: 4 Hours/week, 4 credits

Trigonometry: Complex numbers and functions, De Moiver’s theorem and it’s application, summation of finite trigonometric series, hyperbolic functions. Vector algebra: Scalars and vectors, algebraic operations on vectors, null and unit vectors, components of vectors, scalar and vector products of two vectors, angle between two vectors, product of three & four vectors – their applications, spherical polar and cylindrical coordinate systems - unit vectors and vector components in these systems. Vector Calculus: Derivative of vectors with respect to scalar, vector operators DEL, Gradient, Divergence and Curl – their physical significance, outlines of line, volume and surface integration. Geometry: Locus of a point, equations for straight line, circle, parabola, ellipse and hyperbola, pairs of straight lines, equations for plane and straight line in space, sphere, cylinder, cone & ellipsoid.

Books Recommended1. Sarder and Others: Higher Trigonometry2. Speigel M R.: Vector analysis 3. Smith C.: An elementary treatise on coordinate geometry of three dimension4. Rahman & Bhattacharjee: A Text Book on coordinate geometry5. Harun Ar Rashid: A Text Book on coordinate geometry

MAT-102D MATRICES, VECTOR ANALYSIS AND GEOMETRY (For CSE)Theory: 4 Hours/week; 4 Credits Matrices: Types of matrices, null and unit matrices, algebraic operations on matrices, determinant of a square matrix, matrix equivalence, adjoint and inverse of a matrix, orthogonal and unitary matrices, linear equations, vector spaces, linear transformations, similarity, characteristic roots and vectors, diagonalization of matrices.


Vector Analysis: Scalars and vectors; operation on vectors, Null and unit vectors; components of a vectors, scalar and vector products of two, three and four vectors, their applications; vector components in spherical and cylindrical systems, derivative of vectors, vector operators, Del, Gradient, Divergence and Curl, their physical significance, vector integration, line, surface and volume integrals, Greens’, Gauss’ and Stokes’ theorem and their applications. Geometry: Review of equation of a straight line, circle, parabola, ellipse and hyperbola. Pair of straight lines, General equation of the second degree. Three-dimensional coordinates. Equations for a plane, sphere, cylinder, cone, ellipsoid and paraboloid.

Books Recommended:1. Ayres, F., Matrices2. Kolman, B., Elementary Linear Algebra.3. Speigel M R.: Vector analysis 4. Smith C.: An elementary treatise on coordinate geometry of three dimension5. Rahman & Bhattacharjee: A Text Book on coordinate geometry6. Harun Ar Rashid: A Text Book on coordinate geometry

MAT-102E Geometry, Matrix & Vector Calculus ( for CEP)3 Hours/ Week, 3 Credits

Geometry: Three-Dimensional: Coordinates in three dimensions, locus of a point, equations for straight lines & planes in space, spheres, cylinders, cones, spheroids & ellipsoids. Matrix: Types of matrices, null and unit matrices, algebraic operations of matrices, determinant of square matrix, matrix equivalence. Adjunct and inverse of matrices, orthogonal land unitary matrices, linear dependence and independence of vectors, system of linear equations. Vector Calculus: Scalars and vectors, algebraic operations on vectors, null and unit vectors, Components of vectors, Scalar and vector products of two vectors, angle between two vectors, products of three and four vectors with their applications: spherical, polar and cylindrical coordinate systems, unit vectors and vector components in these systems, derivative of vectors with respect to scalars, vector operators- DEL, gradient, divergence, curl & their physical significance.

MAT-103A CALCULUS ( for STA)Theory: 3 Hours/Week; 3 Credits

Group-A: Differential Calculus. Functions of real variables and their graphs. Limit, Continuty and derivative. Physical meaning of derivative of a function, higher derivatives. Leibnitz’s theorem , Rolle’s theorem , Mean Value theorem ,Taylor’s theorem ,Taylor’s and Maclaurin’s series without proof. Maximum and Minimum of a function , functions of two and three variables , partial and total derivatives, concavity and convexity of a function.Group-B: Integral Calculus. Physical meaning of integration of a function , evaluation of indefinite integral, definition of Reimann integral, fundamental theorem of integral calculus and its application to definite integral double and triple integration , application of integration in finding lengths areas and volumes. Books recommended:

1. Dass &Mukherjeee , Integral Calculu2. Dass &Mukherjeee , Integral Calculus3. Thomas and Finney: Calculus and Analytic Geometry4. Swokowski, E. W.: Calculus with Analytic Geometry5. Tierney, Calculus with Analytic Geometry

MAT-103B CALCULUS AND DIFFERENTIAL EQUATIONS (for PHY)Theory: 4 hours/week, 4 credits

Differential Calculus: Functionof a real variable and their Graphs, limit, continuity and derivatives, Physical meaning of derivative of a function, successive derivative, Leibnitz’s theorem, Rolle’s theorem, Mean value & Taylors theorem (statement only), Taylor’e & Maclaurins series and Expansion of function, Maximum & minimum Values of functions, functions of two and three variables. Partial and total derivative. Integral calculus: Physical meaning of integration, integration as a inverse process of differentiation, definite integral as the limit of a sum and as an area, Definition of Reimann integral, fundamental theorem of integral calculus and its application to definit integrals, reduction formula, improper integrals, double integration, evaluation of areas and volumes by integration. Differential equations: Definition and solution of ordinary differential equations, first order ordinary differential equations, second order ordinary linear differential equations with constant coefficients, initial value problems.

Books Recommended


1. Thomas & finney: Calculus and analytic geometry2. Swokowski E W: Calculus with analytic geometry3. Mohammed & Bhattacharjee: Differential calculus4. Das & Mucharjee: Differential calculus5. Mohammed & Bhattacharjee: Integral calculus6. Das & Mucharjee: Integral calculus7. Ayres, F : Differential calculus

MAT-103C CALCULUS AND DIFFERENTIAL EQUATIONS (for CHE)Theory:3 hours/week, 3 credits

Differential Calculus: Functionof a real variable and their Graphs, limit, continuity and derivatives, Physical meaning of derivative of a function, successive derivative, Leibnitz’s theorem, Rolle’s theorem, Mean value & Taylors theorem (statement only), Taylor’e & Maclaurins series and Expansion of function, Maximum & minimum Values of functions, functions of two and three variables. Partial and total derivative. Integral calculus: Physical meaning of integration, integration as a inverse process of differentiation, definite integral as the limit of a sum and as an area, Definition of Reimann integral, fundamental theorem of integral calculus and its application to definit integrals, reduction formula, improper integrals, double integration, evaluation of areas and volumes by integration. Differential equations: Definition and solution of ordinary differential equations, first order ordinary differential equations, second order ordinary linear differential equations with constant coefficients,solutions by the method of undetermined coefficient and variation of parameter, initial value problems.

Books Recommended1. Thomas & finney: Calculus and analytic geometry2. Swokowski E W: Calculus with analytic geometry3. Mohammed & Bhattacharjee: Differential calculus4. Das & Mucharjee: Differential calculus5. Mohammed & Bhattacharjee: Integral calculus6. Das & Mucharjee: Integral calculus7. Ayres, F : Differential calculus

MAT 103D CALCULUS (for CSE)Theory: 4 Hours/ Week; 4 Credits

Differential Calculus: Funtions of a real variables and their plots, limit, continuity and derivatives, Physical meaning of derivative of a function, Leibnitz Theorem, Rolles Theorem,,Mean value theorem and Taylors theorem (statements only).Taylors and Maclaurins series and expansion of functions,Maximum and minimum values of function, Functions of two or three variables, Partial and total derivatives .

Integral Calculus: Physical meaning of a integration of a function , Integration as an inverse process of differentiation, different techniques of Integration’s, definite integrate as the limit of a sum and as an area, definition of Riemann integrals, Fundamental theorem of integral calculus and its application to definite integral, Improper integral, Reduction formula , improper integrals, Double integration, Evaluation of area and volume by integration.Differential Equations: Definition and solution of Ordinary Differential Equation, First order Ordinary Differential Equation , second order Ordinary Linear Differential Equation with constant coefficients. Initial value problems Books Recommended:

1. Das & Mukherjee; differential Calculus2. Das & Mukherjee, integral Calculus3. J. Edwards; differential Calculus4. J. Edwards; integral calculus5. R.A. Sardar; differential Calculus6. S. L. Ross; Differential equations

MAT-103E DIFFERENTIAL & INTEGRAL CALCULUS (for CEP)Theory: 3 Hours/ Week; 3 Credits

Differential Calculus: Physical meaning of derivative of a function, Higher derivatives, Leibnitz Theorem, Rolles Theorem,,Mean value theorem ,Taylors thorem,Taylors and Maclaurins series , Maximum and minimum values of function, Functions of two or three variables, Partial and total derivatives , Taylors series for multivariable functions, Convexity of a function.Integral calculus: Physical meaning of a integration of a function , Evaluation of a indefinite integral, definition of Riemann integrals, Fundamental theorem of integral calculus and its application to definite integral, Improper integral, Double integration Evaluation of area, volume and revolution by integration.


Books Recommended:1. Das & Mukherjee; differential Calculus2. Das & Mukherjee, integral Calculus3. M.R. Spiegel; Advanced Calculus4. J. Edwards; differential Calculus5. J. Edwards; integral calculus6. R.A. Sardar; differential Calculus7. S. L. Ross; Differential equations

MAT 103F DIFFERENTIAL CALCULUS & VECTOR ANALYSIS (for CEE)Theory: 3 Hours/ week, 3 Credits Differential Calculus: Differentiation of explicit and implicit functions and parametric equations, sucfessive differentiation of various types of funnctions. Leibnitz’s theorem, Rolls theorem, Mean Value Theorem. Taylor’s theorem in finite and infinite forms. Laclaurin’s theorem in finite and infinite forms, lagrange’s form of remainder, Cauchy’s form of remainder. Expansion of function by differentiation and integration. Partial diffferentiation. Euler’s theorem. Tangent and normal, subtangent and subnormal in cartesian and polar coordinates. Determination of maximum and minimum values of functions, point ofinflexion, its applications. Evaluation of indeterminant forms by L’ Hospital’s rule. Curvature, radius of curvature, centre of curvature and chord of curvature. Evolute and involute. Asymptotes , Envelopes, Curve tracing.Vectors: Definitions of vectors Equality of vectors, Addition and multiplication of Vectors, Triple products and multiple products.


MAT 103G DIFFERENTIAL CALCULUS , SOLID GEOMETRY (for IPE)Theory: 4 Hours/ week, 4 Credits

Differential Calculus: Differentiation of explicit and implicit functions and parametric equations, sucfessive differentiation of various types of funnctions. Leibnitz’s theorem, Rolls theorem, Mean Value Theorem. Taylor’s theorem in finite and infinite forms. Laclaurin’s theorem in finite and infinite forms, lagrange’s form of remainder, Cauchy’s form of remainder. Expansion of function by differentiation and integration. Partial diffferentiation. Euler’s theorem. Tangent and normal, subtangent and subnormal in cartesian and polar coordinates. Determination of maximum and minimum values of functions, point of inflexion, its applications. Evaluation of indeterminant forms by L’ Hospital’s rule. Curvature, radius of curvature, centre of curvature and chord of curvature. Evolute and involute. Asymptotes , Envelopes, Curve tracing.and symmetryThree dimensional coordinate geometry : System of coordinates, distance between two points, Sections formula, Projections, Direction cosines and direction ratios. Equations planes and straight lines.


MAT-104F INTEGRAL CALCULUS AND ORDINARY DIFFERENTIAL EQUATIONS (for CEE)Theory: 3 hours/Week , 3 Credits

Integral calculus: Difinition of integration,integration by method of substitution , integration by parts , standard integrals , method of successive reduction. Definite integral ,its properties and use in summing series. Walli’s formulae. Improper integral, Beta and Gamma function. Area under a plane curve in cartesian and polar coordinates , area of the region enclosed by two curves in cartesian and polar coordinates, Trapezoidal rule .Simpson’s rule, Arc length of curves in cartesian and polar coordinates, parametric and pedal equations , intrisic equation. Volumes of solid of revolution Volumes of hollow solid of revolution by shell method , area of surface of revolution .


Differential Equation : Ordinary differential equation and formation of differential equations , Solution of first order differential equations with various method. Solutions of general linear equations of second and higher order with constant coefficients. . Solutions of homogeneous linear equations , applications . Solution of differential equations of the higher order when the dependent and independent variables are absent . solutions of differential by the method based on factorization of the operators.

Book Recommended:1. Thomas and finney ,. Calculus and Analytic Geometry .2. Swokowski , E.W., Calculus and Analytic Geometry3. Mohammed & Bhattacharjee , Integral Calculus .4. Ayres , F., Differential equation5. Edward , J.,Integral Calculus

MAT-104G INTEGRAL CALCULUS AND DIFFERENTIAL EQUATIONS (for IPE)Theory: 3 hours/Week , 3 Credfits

Integral calculus: Difinition of integration,integration by method of substitution , integration by parts , standard integrals , method of successive reduction. Definite integral ,its properties and use in summing series. Walli’s formulae. Improper integral, Beta and Gamma function. Area under a plane curve in cartesian and polar coordinates , area of the region enclosed by two curves in cartesian and polar coordinates, Trapezoidal rule .Simpson’s rule, Arc length of curves in cartesian and polar coordinates, parametric and pedal equations , intrisic equation. Volumes of solid of revolution Volumes of hollow solid of revolution by shell method , area of surface of revolution .Differential Equation : Ordinary differential equation and formation of differential equations , Solution of first order differential equations with various method. Solutions of general linear equations of second and higher order with constant coefficients. . Solutions of homogeneous linear equations , applications . Solution of differential equations of the higher order when the dependent and independent variables are absent . solutions of differential by the method based on factorization of the operators.

Book Recommended:1. Thomas and finney ,. Calculus and Analytic Geometry . 2. Swokowski , E.W., Calculus and Analytic Geometry3. Mohammed & Bhattacharjee , Integral Calculus .4. Ayres , F., Differential equation5. Edward , J.,Integral Calculus

MAT–104T MATHEMATICS (for Tea Technology)Theory: 4 Hours/Week, 4 Credits

Matrix: Definition, elementary properties and solution of system of linear equations with the help of matrices. Differential Calculus: limit, continuity, differentiation of functions, partial differentiation, leibniitz’s theorem and its applications, maxima and minima of a function of one variable. Integral Calculus: Methods of integration, integration by parts, definite integral, area and volumes. Vector Analysis: Scalars and vectors, algebraic operations on vectors, Scalar and vector product of two vectors. derivative of vectors with respect to scalars, vector operators gradient, divergence and Curl. Out lines of line, volume and surface integration.

MAT 104Z INTEGRAL CALCULUS AND ORDINARY DIFFERENTIAL EQUATIONS 3 Hours/Week, 3 Credits

Integral calculus: Definition of integration, integration by method of substitution, integration by parts, standard integrals, method of successive reduction. Definite integral, its properties and use in summing series. Walli’s formulae. Improper integral, Beta and Gamma function. Area under a plane curve in Cartesian and polar coordinates, area of the region enclosed by two curves in Cartesian and polar coordinates, Trpezoidal rule, Simpson’s rule, Arc length of curves in Cartesian and polar coordinates, parametric and pedal equations, intrinsic equation. Volumes of solid of revolution, volumes of hollow solid of revolution by shell method, area of surface of revolution.Differential Equation: Ordinary differential equation and formation of differential equations, solutions of first order differential equations with various method. Solution of general linear equations of second and higher order with constant coefficient. Solutions of homogeneous linear equations, applications. Solutions of differential equations of the higher order when the dependent and independent variables are absent, solutions of differential by the method based on factorization of the operators.


Book Recommended:1. Thomas and finney ,. Calculus and Analytic Geometry2. Swokowski , E.W., Calculus and Analytic Geometry3. Mohammed & Bhattacharjee , Integral Calculus4. Edward , J.,Integral Calculus5. Ayres , F., Differential equation

MAT 109 A LINEAR ALGEBRA (for STA)Theory: 4 Hours/week, 4Credits

Matrix: Definition of a matrix, different types of matrices, addition and multipication of matrices. adjoint and inverse of matrix, Cramer’s rule, application of inverse matrix and Cramer’s rule. Elementary row operations and Echelon forms of matrices, rank, row rank, column rank of a matrix and their equivalenc, use of rank and Echelon forms in solving system of homogeneous and nonhomogeneous equations. Vector space and subspace over reals and direct sum, linear combination linear dependence and independence on vectors, basis and dimension of vector space, quotient space and isomorphism theorems, Linear transformations, kernel, rank and nullity nonsingular transformations and matrix representation , Changes of basis, Eigenvector. eigenvalues, characteristic equations and Cayley-Hamilton theorem. Similar matrices, canonical forms orthogonal and hermitian matrices, inner product, orthogonal vectors and orthonormal bases, Gram-schmidt orthogonalization process. Bilinear and quadratic forms.

Books Recommended:1. Hamilton A.G Linear Algebra2. AYres, F. Matrices3. Kolman B, Elementary Linear Algebra4. Bering E.D Linear Algebra and Matrix Theory5. Lipschutz S, Linear Algebra6. Morris AO, Linear Algebra7.Khanna M I, Linear Algebra8. Rahman M A, College Linear Algerba

MAT- 201 MATHEMATICS (for ECO)Theory: 4Hours/ Week, 4 Credits

Trigonometry: Trigonometric functions and their inter relations, Trigonometric identities.Set Theory: Concepts of sets and subsets , operations on sets, Cartesian products , functions and relations, binary operations on the sets N,Q,R as algebraic systems, equivalence relations, equivalent sets, countable and uncountable sets.Vector Space: Defination, linear sum, inner product space.Calculas: Concept of Integration, ibndefinite and definite integrals, methods of integration, applications from a marginal to total functions, investment and capital formation, consumers and producer surplus.Calculus of Variation: Eeuler’s equation and its application. Differential and Difference equations: Equations of the first and second order, simple cases of linear differential equations with constant, co-efficients, economic applications.

Books Recommended: 1. A.C. Chiang, Fundamental methods of Mathematical Economics( 3rd edition )2. W.J Baumol, Economic dynamics3. W.J. Baumol, Economic theory and Operations Analysis (4th edition)4. A.K. Dixit Optimization in Economic Theory5. P.J. Iamberte Advanced Mathematics for Economists 6. taro Yamane Mathematics for Economists7. E.T.Dowling Mathematics for Economists8. Akira Takayama Mathematical Economics

MAT 201Z VECTOR ANALYSIS AND NUMERICAL ANALYSIS4 Hours/Week, 4 Credits

Vector Analysis: Scalars and vectors, equality of vectors. Addition and subtraction of vectors by scalars. Position vector of a point. Resolution of vectors, Scalar and vector products and multiple products. Application to geometry and mechanics. Linear dependence and independence of vectors. Differentiation and integration of vectors together with elementary applications. Definition of line, surface and volume integrals. Gradient divergence and curl of point functions. Various formulae. Gauss’s theorem, Stoke’s theorem, Green’s theorem and their applications.Numerical Analysis: Interpolation: Simple difference, Newton’s formulae for forward and backward interpolation. Divided differences. Tables of divided differences. Relation between divided differences and simple differences. Newtonís general


interpolation formulae. Lagrangeís interpolation formulae. Inverse interpolation by Lagrangeís formula and by successive approximations. Numerical differentiation of Newton’s forward and backward formula. Numerical integration. General quadrature formula for equidistant ordinates. Trapezoidal rule. Simpsonís rule. Weddleís rule. Calculation of errors. Relative study of three rules. Gaussís quadrature formula. Legendre polynomials. Newtonís Cotes formula. Principles of least squares. Curve fitting. Solution of algebraic and transcendental equations by graphical method. Regula-Falsi method. Newton-Rapson method, Geometrical significance. Convergence of iteration and Newton-Rapson methods. Newton-Rapson method and iteration method for the solution of simultaneous equations. Solution of ordinary first order differential equations by Picardís and Eularís method. Runge-Kuttaís methods for solving differential equation.

Books Recommended1. Speigel M R.: Vector analysis 2. Freeman H, Finite Difference for Actuarial Students3. Francis Scheid: Numerical Analysis4. Hilderman, F.B.: Introduction to Numerical Analysis5. Noble B.: Numerical Methods Vol. I & II

MAT-202C MTHEMATICAL METHODS ( for CHE)Theory:3 Hours/Week, 3 Credits

Matrix: Type of matrix: null and unit matrices, algebraic operations on matrices, determinant of squre matrices, matrices equivalance, adjoint and inverse of a matrix, orthogonal and unitary matrices, linear dependence of vectors, system of linear equations. Complex Variables: analytic functions, Cauchy- Rieman equations, Complex integration. Furier series: Periodic functions, furier series of odd and even functions. Special Functions: Hermite and Bessel equations,Legendre and associated Legendre equations. Laplace transfor,mation.

MAT- 202E Differential Equation and Mathematical Methods (for CEP)3 Hours/Week, 3 Credits

Differential equations: Definition, solution of differential equations, basic theory of linear differential equations, homogeneous differential equations of the 2nd and higher order with constant coefficients, power series solution about ordinary and regular points, non-homogeneous differential equations, solutions by the methods of undetermined coefficients and variation of parameters, Hermit and Bessel equations, Legendre and associated Legendre equations, partial differential equation, liner and non-liner partial differential equations of 1st order. Laplace transforms: definition of lap lace transform, elementary transformations and properties, convolutions, solution of differential equations by lap lace transforms, evaluation of integrals by Lap lace transforms. Fourier series and transformation

MAT 202Z COMPLEX VARIABLES, PARTIAL DIFFERENTIAL EQUATIONS, LAPLACE TRANSFORMATION4 Hours/Week, 4 Credits

Complex Variable : Complex number system, general functions of a complex variable limits and continuity of a function of complex variable and related theorems. Complex differential and the Cauchy, Riemann equations. Mapping by elementary functions. Line integral of a complex function. Cauchy’s integral formula. Kiouville’s theorem. Taylor’s and Laurent’s theorem. Singular points. Residue. Cauchy’s residue theorem. Evaluation of residues. Contour integration. Conformal mapping.Fourier series: Real and complex form. Finite transformation. Fourier integral. Fourier transforms and their uses in solving boundary value problems.Partial Differential Equation: Introduction. Equation of the linear and non-linear first order. Standard forms. Linear equations of higher order. Equations of the second order with variable coefficients.Laplace Transform: Definition. Laplace transforms of some elementary functions. Sufficient conditions for existence of laplace transform. Inverse Laplace transforms. Laplace transforms of derivatives. The unit step function. Periodic function. Some special theorems on Laplace transforms. Partial fraction. Solutions of differential equations by Laplace transform. Evaluation of improper integrals

Books Recommended:1. Churchill: Introduction to Complex Variable and Applications2. Freeman H: Finite Difference for Actuarial Students3. Macrobeat: Complex Variable.4. Spiegel, M.R. Complex Variable5. Stephenson : Mathematical Methods6. Ross, S. L. : Differential Equations7. Spiegel, M. R.: Laplace Transform8. Khanna, M. L. : Partial Differential Equations9. Khanna, M. L. : Laplace Transforms


MAT-204D COMPLEX VARIABLES, LAPLACE TRANSFORM AND FOURIER SERIES(for CSE) Theory: 4 Hours/week; 4 Credits

Complex Variables: DeMoivre’s theorem and its application,Locus problem. Complex numbers and their properties, functions of a complex variable, limits and continuity of a function of complex variable. Analytical functions, the Cauchy-Riemann equations, Cauchy’s theorem, Singularity and Poles, Residues , Simple contour integration, and their uses in solving boundary value problemsLaplace Transformations: Definition of Laplace transform, Laplace transform of different functions, first shift theorem, inverse transform, linearity, use of first shift theorem and partial functions. Transform of derivative, transform of an integral, the Heaviside unit function, the unit impulse function, the second shift theorem, periodic functions, convolutions, solution of ordinary differential equations by Laplace Transform.Fourier Series: Fourier series, Convergence of Fourier Series, Fourier Analysis, Fourier transforms.

Books Recommended:1. KK Kodaira: Introduction to Complex analysis2. H Jaffreys & B Jaffreys: Methods of Mathematical Physics3. Spiegel, M. R.: Laplace Transform4. Khanna, M. L. : Laplace Transforms

MAT-206E Numerical Analysis (for CEP)Theory: 3 Hours/ Week; 3 Credits

Numerical Analysis: Interpolation: Simple difference, Newton’s formulae for forward and backward interpolation. Divided differences. Tables of divided differences. Relation between divided differences and simple differences. Newton’s general interpolation formulae. LaGrange interpolation formulae. Inverse interpolation by Lagrange formula and by successive approximations. Numerical differentiation of Newton’s forward and backward formula. Numerical integration. General quadrate formula for equidistant ordinates. Trapezoidal rule. Weddle rule. Calculation of errors. Relative study of three rules. Solution of algebraic and transcendental equations by graphical method. Regula-Falis methods. Newton- Rap son methods. Geometrical significance. Convergence of iteration and Newton-Rap son methods. Newton-Rapson method and itegration method for the solution of simultaneous equations.

MAT- 207A ADVANCED CALCULUS AND DIFFERENTIAL EQUATIONS (for STA)Theory: 3 Hours/Week, 3 Credits

Group A: Advanced Calculus: Improper Integrals, Gamma and Beta functions, their incompleteness and other properties, functions of several variables and limit and continuity, Taylor’s expansion of such functions, maxima and minima of functions of more than one variables, Lagrange’s multipliers, multiple integrals, jacobians of transformation, Dirichlet integral and its extension, Laplace transformation, concept of Fourier series.

Group B: Differential equations: Definition, solution of differential equations, basic theory of linear differential equations, basic theory of linear differential equation, equation of the first order and their solution, homogeneous differential equations, linear differential equations of the second and higher order and their solution.

Book Recommended: 1. Ayres F, Differential Equations2. Edward, Differential and Integral Calculus3. Maxwell E H G, Analytical Calculus, Vol-II & Vol-II4. Piaggio H TH, An Elementary Treaties of Differential Equations and Their Application5. Ross S L, Differential Equations6. Widder, Advanced Calculus

MAT-207F VECTOR CALCULUS, MATRICES, LAPLACE TRANFORM( for CEE)Theory: 3 Hours/week, 3 Credits

Vector Calculus: Differentiations and integration of vectors togather with elementary applications. Line, surface and volume integrals. Gradient of scalar functions. Divergence and curl of vector functions. Physical significance of gradient, divergence and curl. Stoke’s theorem. Green’s theorem and their applications. Matrices: Types of matrices and algebraic properties. Rank and elementary transformations of matrices. Solution of linear equations by mtrix methods. Linear dependence and independence of


vectors. Quadratic forms, matrix polynomials. Determination of characteristic roots and vectors. Laplace transforms: Definition of Laplace transforms. Elementary transformations and properties. Convolution. Solution of differential equations by Laplace transforms. Evaluation of integrals by Laplace transforms.

Books Recommended:1. Spiegel, M.R. Advanced Calculus2. Spiegel, M.R. Vector Analysis and and Introduction to Tensor Analysis3. Lass, H. Vector and Tensor Analysis4. Ayres, F: Matrices5. A G Hamilton: Linear Algebra6. Spiegel, M. R.: Laplace Transform7. Khanna, M. L. : Laplace Transforms

MAT-207G VECTOR CALCULUS, MATRICES, LAPLACE TRANFORM( for IPE)Theory: 3 Hours/week, 3 Credits

Vector Calculus:Definitions of vectors Equality of vectors, Addition and multiplication of Vectors, Triple products and multiple products. Differentiations and integration of vectors togather with elementary applications. Line, surface and volume integrals. Gradient of scalar functions. Divergence and curl of vector functions. Physical significance of gradient, divergence and curl. Stoke’s theorem. Green’s theorem and their applications. Matrices: Types of matrices and algebraic properties. Rank and elementary transformations of matrices. Solution of linear equations by mtrix methods. Linear dependence and independence of vectors. Quadratic forms, matrix polynomials. Determination of characteristic roots and vectors. Laplace transforms: Definition of Laplace transforms. Elementary transformations and properties. Convolution. Solution of differential equations by Laplace transforms. Evaluation of integrals by Laplace transforms.

Books Recommended:1. Spiegel, M.R. Advanced Calculus2. Spiegel, M.R. Vector Analysis and and Introduction to Tensor Analysis3. Lass, H. Vector and Tensor Analysis4. Ayres, F: Matrices5. A G Hamilton: Linear Algebra6. Spiegel, M. R.: Laplace Transform7. Khanna, M. L. : Laplace Transforms

MAT 208A NUMERICAL METHOD AND COMPLEX VARIABLE (for STA)Theory: 4 Hours/Week, 4 Credits

Group A: Numerical Methods: Interpolation and extrapolation. Shifting operators, difference operators and their relationships. Newton’s interpolation formulae, Lagrange’s formula, Newton’s divided difference formula, central difference formulae (Stirling and Bessel’s) Relationship between divided difference and simple difference. and simple difference. Inverse interpolation formula. Numerical differentiation. Numerical integration by different formulas. Numerical solution of equations by various methods. Convergence of these methods and their inherent errors. Numerical solution of simultaneous Linear equation. solution by determinants by inverse matrices, by iteration and by successive elimination of the unknowns. Group-B Complex functions. elementary single and many valued functions of complex variables. differentiable functions. analytic functions. Cauchy’s theorem for simple contours. Taylor’s theorem. Laurent’S theorem. Liouville’s theorem, different types of singularity, Cauchy,s residue theorem, evaluation of integral by contour integration.

Books Recommended:1. Churchill Introduction to Complex Variable and Applications2. Freeman H, Finite Difference for Actuarial Students3. Macrobeat, Complex Variable.

MAT 209A REAL ANALYSIS (for STA) Theory: 3 Hours/Week, 3 Credits

Sets: Functions, relations,equivalence relations, real valued functions, open set, dense set, countability, compact and connected sets,monotonic class of sets, aditive class of sets. Sequence: Convergence of a sequence, monotonic sequence, upper limit and lower limit. Infinite Series: Concept of sum, series of positive terms, alternating series, absolute and conditional convergence, test for convergence. Limit points, Bolzano-Weierstrass theorem, properties of continuous functions, uniform continuity, Heine-


Borel theorem. Derivatives: Rolle’s theorem, Mean value theorem and Taylor’s theorem with remainder in Lagrange’s and Cauchy’s forms. Expansions of functions. Power series: Interval and radius of convergence, differentiation and integration of power series, Abels’ continuity theorem. Riemann integration: Definition of Riemann integration. Fundamental theorem and mean value theorem of integral calculus. Improper integral and their tests for convergence.

Books rceommended:1. Ruddin, W.: Principle of mathematical analysis2. Aposstal, I.: Mathematical Analysis3. Bartle,: Real Analysis4. Royden,: Real Analysis5. Hobson, E.: The Theory of Functions of Real Variable and Theory of Fourier Series6. Burkill,J. G.: A First Course in Mathematical Analysis7. Binmore, K. G.: Mathematical Analysis

MAT 301F COMPLEX VARIABLE, HARMONIC ANALYSIS AND PARTIAL DIFFERENTIAL EQUATIONS (for IPE)Theory: 4 Hours/week; 4 Credits

Complex Variables: Complex number system, functions of a complex variable, limits and continuity of a function of complex variable and related theorems; complex differentiation and the Cauchy-Riemann equations, Mapping of elementary functions, line integral of a complex function, Cauchy’s integral formula, Liouville’s theorem, Taylor’s and Laurent’s theorem, singular point, residue , Cauchy’s residue theorem, evaluation of residues, contour integration, and their uses in solving boundary value problems.Fourier Series: Real and Complex form, Finite Transformation, Fourier integral, Fourier transforms and their uses in solving boundary value problems.Harmonic Function: Definitions of harmonic functions, Laplace’s equation in cartesian, polar, cylindrical and spherical coordinates, solutions of these equations together with applications, gravitational potentials, due to a ring, steady state temperature, potential inside or outside of a sphere, properties of harmonic functions.Partial Differential equation: Introduction, equations of linear and nonlinear first order standard forms, linear equations of higher order, equations of the second order with variable coefficients. Solution of Bessel’s and Legendre differential equations with properties.

Books Recommended:1. Spiegel, M.R., Complex Variable2. Khanna, M. L., Complex Variable3. Churchill, R. V., Fourier Series and Boundary Value Problems4. Stephenson. Mathematical Methods5. Fraid, S.M., Special Functions6. Ross, S. L., Differential Equations


Detailed Syllabus for Non-Major Courses in details for the Department of Mathematics

CSE-101E INTRODUCTION TO COMPUTER APPLICATIONTheory: 2 Hours/Week, Lab: 2 Hours/Week, 3 Credits

Computer Basis: History and development computer types. Scope of computer Impact of computers on society and technology. Specification of Computers: CPU types, Speed variation, Memory, type size Cache, Storage Media, Hard disk, Floppy disk, CD ROM Multimedia, Printer. Dot matrix Laser, ink jet. Computer Hardware: Digital electronics, CPU. Memory (RAM,ROM). Mass storage devices, I/O Devices(Peripherals) Idea of System Software and Application Software: Function of Operating System, Discussion of different types of Operating System: DOS/Windows, Mac UNIX/XENIX etc. Concept of Formal Language: Different type of computer Languages: Assembly, FORTRAN, Pascal C and C ++ , Artificial Language etc. Purpose and scope of Application Packages: Essential General purpose packages: Word-Processing, Spreadsheet analysis, Database etc. Networking: Different types of networks, network topologies, e-mail, internet. Maintenance. And Troubleshooting: Virus, Power Surge Protection, Disk maintenance. Future Trends: Super Computer, Distributed Computer, Information Supper Highway, Multi-media and virtual reality.

LABORATORY: Operating System: DOS and Windows- students will learn the basics of computer, how to operate them in two basic environments, dos and Windows, Word Processor: Students will learn to use a popular word processor to create a camera ready test file complete with figures, columns and tables. Spread Sheet: Students will learn to use a popular Spread Sheet to maintain a small data base, minor book keeping and statistical and graphical analysis of data.

CSE-203E INTRODUCTION TO COMPUTER LANGUAGE CTheory: 2 Hours/Week, 2 Credits

THEORY: Software: Basic concept and its classification: Overview of programming languages; C-Language: Preliminaries, Program structures, variables and data types in C Input and output Character and formatted I/O; Arithmetic Expressions and Assignment statements; Loops and Nested loops; Decision making; Arrays, functions; Arguments and Local variables, Ceiling functions and arrays. Recursion and recursive functions;Structures within structures. Files functions for sequential and random I/O. Pointers; Pointers and Structures;Pointer and Functions; Pointer and Arrays; Operation and Pointer; Pointer and memory addresses; Operations on Bits; Bit Operation; Bit field; Advance features; Standard and library.

CSE-204E INTRODUCTION TO COMPUTER LANGUAGE LABLab: 6 Hours/Week, 3 Credits

Computer Basics: Students will learn the basic concepts of windows operating system, word processor software, Spread Sheet software, and Presentation software. C-Language: Laboratory works based on theory classes of ECS-205E CSE-213E DATA STRUCTURETheory: 3 Hours/Week, 3 Credits

Internal Data Representation. Specification, representation and manipulation of basic data structures; arrays, records and pointers, linked lists, stacks, queues, recursion, trees, optimal search trees, heaps. Graphs and their application, List and string processing , Searching and Sorting algorithms. Hashing techniques.

CSE-214E DATA STRUCTURE LABLab: 3 Hours/Week, 1.5 Credits

Laboratory works based ECS-207E

CSE-301E ALGORITHMTheory: 3 Hours/Week, 3 Credits

Techniques for analysis for algorithms, standard efficient techniques, divide and conquer, greedy method ,dynamic programming, backtracking, branch and bound, basic search and traversal techniques, Graph algorithms, geometric algorithms, geometric algorithms, parallel algorithms, Algebraic simplification and transformations, Lower bound theory, NP hard and NP complete problems.


CSE-302E ALGORITHM LABLab: 3 Hours/Week, 1.5 Credits

Laboratory works based on ECS-305E

CSE-333 DATABASE SESTEMTheory: 4 Hours/Week, 4 Credits

Introduction: Purpose of Database Systems Data Abstraction, Data Models, Instances and Schemes, Data Independence, Data Definition Language, Data Manipulation Language, Database Manager, Database administrator, Database Users, Overall System Structure, Advantages and Disadvantages of Database Systems. Relationship Entity-Model: Entities and Entity Sets, Relationships and Relationship Sets, Attributes, Mapping Constraints, Keys, Entity-Relationship Diagram, Reducing of E-R Diagram to Tables, Generalization, Aggregation, Design of an E-R Database Scheme. Relational Model: Structure of Relational Database, The Relational Algebra, The Tuple Relational Calculus, The Domain Relational Calculus, Modifying the Database, Views. Relational Commercial Language: SQL, Query-by-Example, Quel. Relational Database Design: Pitfalls in Relational Database Design, Normalization using Functional Dependencies, Normalization using Multi-valued dependencies, Normalization using join Dependencies. File and System Structure: Overall System Structure, Physical Storage Media, File organization, Organization of Records into Blocks, Sequential Files, Mapping Relational Data to Files, Data Dictionary Storage, Buffer Management. Indexing and Gashing: Basic Concepts, Indexing, B+ Tree Index Files, B- Tree Index Files, Static and Dynamic Hash Function, Comparison of Indexing and Hashing, Index Definition in SQL, Multiple Key Access. Query Processing: Query Interpretation, Equivalence of Expressions, Estimation of Query-Processing Cost, Estimation of Costs of Access Using Indices, Join Strategies, Join Strategies for parallel processing, Structure of the query optimizer. Concurrency Control: Schedules, Testing for Serializability, Lock-Based Protocols, Timestamp-Based Protocols, Validation Techniques, Multiple Granularity, Multi-version Schemes, Insert and Delete Operations. Disturbed Database: Structure of Distributed Databases, Trade-off in Distributing the Database, Design of Distributed Database, Transparency and Autonomy, Distributed Query Processing, Recovery in Distributed Systems, Commit Protocols, Concurrency Control, Deadlock Handling.

CSE-334E DATABASE SYSTEM LABLab: 6 Hours/Week, 3 Credits

Laboratory works based on CSE-333E

STA-101 PRINCIPLES OF STATISTICS (for Dept. of Math)Theory: 3 Hours/Week, 3 Credits

Statistics: Its nature and scope. Nature of statistical data. Attributes and variables. Population and sample, collection and condensation of data. Frequency distribution. Graphical representation of data. Measures of location: arithmetic Mean, Median, mode, geometric mean, harmonic mean, quadratic mean, quartiles, deciles and percentiles. Measures of dispersion: range, mean deviation, standard deviation, variance quartile deviation, coefficient of variation, moments and cumulants of a distribution, skewness and kurtosis. Regression and correlation: Bi-variate data. Relationship between the variables Method of least squares, regression line, Correlation and regression coefficients. Rank correlation and correlation ratio.

Books Recommended:1. Hoel P.G.: Introductory Statistics, John Wiley, NY2. Johnston J.: Econometric Methods3. Mostafa M.G.: Methods of Statistics, Bangladesh4. Weatherburn C. E.: A first Course in Mathematical Statistics5. Wonnacott & Wonnacott: Introductory Statistics6. Yule and Kendal: An Introduction to the theory of statistics

STA-201 PROBABILITY AND PROBABILITY DISTRIBUTIONS (for Dept. of Math)Theory: 2 Hours/Week, 2 Credits

Random experiment: sample space. Events. Union and intersection of events. Different types of events, Probability of events. Axiomatic development of probability. Computation of probability. Theorems of total and compound probability. Conditional probability. Bayes theorem. Random variables: Probability function, distribution function, Joint, marginal and conditional probability functions. Mathematical expectation: Expectations of sum and product Conditional expectation and conditional variance. Moments and moment generating functions .Characteristic function Distributions : study of binomial, Poisson, and normal distribution.

Books Recommended:1. Feller W. : Introduction to Probability, Vol-1, 3rd Ed, John Wiley, NY


2. Hoel P.G.: Introduction to Mathematical Statistics, John Wiley, NY3. Hogg R.V. & Craig A..T.: Introduction to Mathematical Statistics, 4th Ed, Macmillan London4. Meyer A. : Probability and statistics, Addison-Wesley, USA5. Mood, Graybill & Boes: Introduction to the Theory of Statistics, Mc.Graw Hill, NY6. Mosteller, R. & Thomas: Probability with Statistical Applications, 2nd Ed, Addison-wesley, USA.7. Ross S.M.: A first Course in Probability, Academic Press, NY

STA-301 MATHEMATICAL STATISTICS (for Dept. of Math)Theory : 3 Hours/Week, 3 Credits

Sampling from normal and non-normal populations. Distribution of various statistics, distribution of linear functions of normal variates, Detailed study of x, t and F-distributions. Concept of estimation. Point estimation. Characteristic of a good point estimator , methods of point estimation Concept of interval estimation. Methods of interval estimation. Interval estimation of mean and variance of normal distribution. Test of significance in small and large samples. Comparison of means , proportions and variance. Test of homogeneity of variances, Test for R X C contingency tables.

Books Recommended:1. Hoel P.G.: Introduction to Mathematical Statistics2. Hogg and Craig: Introduction to Mathematical Statistics3. Mood, Graybill and Boes: Introduction to the Theory of Statistics4. Mostafa M.G.: Methods of Statistics, Bangladesh

PHY-101 MECHANICS PROPERTIES OF MATTER AND WAVESTheory: 4 Hours/Week, 4 Credits

Mechanics: Different co-ordinate systems; projectile motion; Newton’s laws of motion; friction; conservation theorems (momentum and energy) collision; rotational motion; angular momentum and torque: moment of inertia; parallel and perpendicular axes theorems; central forces and gravitation; gravitational potential; escape velocity, Kepler’s laws. Properties of Matter: Hooke’s law; elastic modulli and their inter-relations; bending of beams cantilever; surface tension; capillarity; concepts of fluid flow; Bernoulli’s equation and its applications; viscosity; Poiseuille’s equation. Waves: Simple harmonic motion; simple and compound pendulum; travelling waves; interference; stationary waves; vibrations in strings; sound; beats; Doppler effect

Books Recommended:1. Halliday, D. and Resnick, R.: Physics (Part I)2. Mathur, D.S.: Elements of Properties of Matter3. Puri, S. P.: Fundamentals of Vibrations and Wave

PHY-201M HEAT, THERMODYNAMICS AND OPTICSTheory: 3 Hours/Week, 3 Credits

Heat: Heat and temperature, principles of thermometry, gas thermometers, resistance thermometers, thermocouples and temperature scale; Newton’s law of cooling; Kinetic Theory of ideal gas; microscopic model of an ideal gas and different gas laws; equipartition of energy. Thermodynamics: First law of Thermodynamics; isothermal and adiabatic changes; Second law of Thermodynamics; reversible and irreversible processes; Carnot’s cycle; absolute scale of temperature; entropy and change of entropy in reversible and irreversible processes; entropy of a perfect gas, thermodynamic potentials; Maxwell’s thermodynamic relations; black body radiation; Planck’s law and deduction of Wein’s law and Rayleigh-Jean’s law from it. Optics: Nature and propagation of light, electromagnetic spectrum, interference, Young’s experiment; Michelson interferometer; Newton’s rings

Books Recommended:1. Halliday, D. and Resnick, R.: Physics (Vol. I & II)2. Jenkins and White: Fundamentals of Optics3. Hossain T. : A Text Book of Heat4. Brijlal.: Heat and Thermodynamics5. Zemansky: Heat and Thermodynamics

PHY-203M ELECTROMAGNETISM AND MODERN PHYSICSTheory:3 Hours/Week, 3 Credits

Electromagnetism: Different electric units; Coulomb’s law; electric field; electric potential and potential function. Gauss’s law and its applications; electric dipole; Ohm’s law; Kirchhoff’s laws with applications. Faraday’s and Lenz’s law of electromagnetic induction; self and mutual induction; Biot-Savart law; magnetic force on charge and current. Ampere’s law; alternating voltage and current and their graphical representation; rms values; AC Voltage and AC current applied to circuits


containing resistors, capacitors, and inductors, Modern Physics: Photoelectric effect; Compton effect; de Broglie waves; uncertainty principle; atomic models; atomic spectra; nucleons; nuclear size; binding energy; radioactive decays.

Books Recommended:1. Resnick and Halliday: Physics( Vol II)2. Kip A.: Fundamentals of Electricity and Magnetism3. Beiser, A.: Perspectives of Modern physics

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