Ramanasri Institute Ramanasri Institute Ramanasri Institute Ramanasri Institute Ramanasri Institute Ramanasri Institute Ramanasri Institute Ramanasri Institute Ramanasri Institute Ramanasri Institute Ramanasri Institute Ramanasri Institute Ramanasri Institute Ramanasri Institute Ramanasri Institute Ramanasri Institute Ramanasri Institute Ramanasri Institute Ramanasri Institute Ramanasri Institute Ramanasri Institute Ramanasri Institute Ramanasri Institute Ramanasri Institute Ramanasri Institute Ramanasri Institute Ramanasri Institute Ramanasri Institute Ramanasri Institute Ramanasri Institute Ramanasri Institute Ramanasri Institute Ramanasri Institute Ramanasri Institute Ramanasri Institute Ramanasri Institute Ramanasri Institute Ramanasri Institute Ramanasri Institute Ramanasri Institute Ramanasri Institute Ramanasri Institute Ramanasri Institute Ramanasri Institute Ramanasri Institute Ramanasri Institute Ramanasri Institute Ramanasri Institute Ramanasri Institute Ramanasri Institute Ramanasri Institute Ramanasri Institute Ramanasri Institute Ramanasri Institute Ramanasri Institute Ramanasri Institute Ramanasri Institute Ramanasri Institute Ramanasri Institute Ramanasri Institute Ramanasri Institute Ramanasri Institute Ramanasri Institute Ramanasri Institute Ramanasri Institute Ramanasri Institute Ramanasri Institute Ramanasri Institute Ramanasri Institute Ramanasri Institute Ramanasri Institute Ramanasri Institute Ramanasri Institute Ramanasri Institute Ramanasri Institute Ramanasri Institute Ramanasri Institute Ramanasri Institute Ramanasri Institute Ramanasri Institute xcvbnmqwertyuiopasdfghjklzxcvbnmq Ramanasri IAS/IFoS Institute Mathematics Optional Brochure 2018-19
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Reputed Institute for IAS/IFoS Exams Page 1
Ramanasri Institute Ramanasri Institute Ramanasri Institute Ramanasri Institute
Ramanasri Institute Ramanasri Institute Ramanasri Institute Ramanasri Institute
Ramanasri Institute Ramanasri Institute Ramanasri Institute Ramanasri Institute
Ramanasri Institute Ramanasri Institute Ramanasri Institute Ramanasri Institute
Ramanasri Institute Ramanasri Institute Ramanasri Institute Ramanasri Institute
Ramanasri Institute Ramanasri Institute Ramanasri Institute Ramanasri Institute
Ramanasri Institute Ramanasri Institute Ramanasri Institute Ramanasri Institute
Ramanasri Institute Ramanasri Institute Ramanasri Institute Ramanasri Institute
Ramanasri Institute Ramanasri Institute Ramanasri Institute Ramanasri Institute
Ramanasri Institute Ramanasri Institute Ramanasri Institute Ramanasri Institute
Ramanasri Institute Ramanasri Institute Ramanasri Institute Ramanasri Institute
Ramanasri Institute Ramanasri Institute Ramanasri Institute Ramanasri Institute
Ramanasri Institute Ramanasri Institute Ramanasri Institute Ramanasri Institute
Ramanasri Institute Ramanasri Institute Ramanasri Institute Ramanasri Institute
Ramanasri Institute Ramanasri Institute Ramanasri Institute Ramanasri Institute
Ramanasri Institute Ramanasri Institute Ramanasri Institute Ramanasri Institute
Ramanasri Institute Ramanasri Institute Ramanasri Institute Ramanasri Institute
Ramanasri Institute Ramanasri Institute Ramanasri Institute Ramanasri Institute
Ramanasri Institute Ramanasri Institute Ramanasri Institute Ramanasri Institute
Ramanasri Institute Ramanasri Institute Ramanasri Institute Ramanasri Institute
xcvbnmqwertyuiopasdfghjklzxcvbnmq
Ramanasri
IAS/IFoS
Institute
Mathematics
Optional
Brochure
2018-19
Ramanasri IAS/IFoS Institute
Reputed Institute for IAS/IFoS Exams Page 2
Syllabus for IAS
Mathematics Optional
PAPER – I
(1) Linear Algebra:
Vector spaces over R and C, linear
dependence and independence, subspaces,
bases, dimension; Linear transformations,
rank and nullity, matrix of a linear
transformation. Algebra of Matrices; Row
and column reduction, Echelon form,
congruence’s and similarity; Rank of a
matrix; Inverse of a matrix; Solution of
system of linear equations; Eigen values and
eigenvectors, characteristic polynomial,
Cayley-Hamilton theorem, Symmetric,
skew-symmetric, Hermitian, Skew-
Hermitian, orthogonal and unitary matrices
and their eigen values.
(2) Calculus:
Real numbers, functions of a real variable,
limits, continuity, differentiability, mean
value theorem, Taylor’s theorem with
remainders, indeterminate forms, maxima
Ramanasri IAS/IFoS Institute
Reputed Institute for IAS/IFoS Exams Page 3
and minima, asymptotes; Curve tracing;
Functions of two or three variables: limits,
continuity, partial derivatives, maxima and
minima, Lagrange’s method of multipliers,
Jacobian. Riemann’s definition of definite
integrals; Indefinite integrals; Infinite and
improper integrals; Double and triple
integrals (evaluation techniques only);
Areas, surface and volumes.
(3) Analytic Geometry:
Cartesian and polar coordinates in three
dimensions, second degree equations in
three variables, reduction to canonical
forms, straight lines, shortest distance
between two skew lines; Plane, sphere,
cone, cylinder, paraboloid, ellipsoid,
hyperboloid of one and two sheets and their
properties.
(4) Ordinary Differential Equations:
Formulation of differential equations;
Equations of first order and first degree,
integrating factor; Orthogonal trajectory;
Equations of first order but not of first
degree, Clairaut’s equation, singular
solution. Second and higher order linear
equations with constant coefficients,
complementary function, particular integral
and general solution. Second order linear
equations with variable coefficients, Euler-
Cauchy equation (Homogeneous linear
equations); Determination of complete
solution when one solution is known using
method of variation of parameters. Laplace
and Inverse Laplace transforms and their
properties; Laplace transforms of
elementary functions. Application to initial
value problems for 2nd order linear
equations with constant coefficients.
(5) Dynamics & Statics:
Rectilinear motion, simple harmonic
motion, motion in a plane, projectiles;
constrained motion; Work and energy,
conservation of energy; Kepler’s laws, orbits
under central forces. Equilibrium of a
system of particles; Work and potential
energy, friction; common catenary;
Principle of virtual work; Stability of
equilibrium, equilibrium of forces in three
dimensions.
(6) Vector Analysis:
Scalar and vector fields, differentiation of
vector field of a scalar variable; Gradient,
divergence and curl in Cartesian and
cylindrical coordinates; Higher order
derivatives; Vector identities and vector
equations. Application to geometry: Curves
in space, Curvature and torsion; Serret-
Frenet’s formulae. Gauss and Stokes’
theorems, Green’s identities.
Ramanasri IAS/IFoS Institute
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PAPER – II
(1) Modern Algebra:
Groups, subgroups, cyclic groups, cosets,
Lagrange’s Theorem, normal subgroups,
quotient groups, homomorphism of groups,
basic isomorphism theorems, permutation
groups, Cayley’s theorem. Rings, sub rings
and ideals, homeomorphisms of rings;
Integral domains, principal Ideal domains,
Euclidean domains and unique factorization
domains; Fields, quotient fields.
(2) Real Analysis:
Real number system as an ordered field
with least upper bound property;
Sequences, limit of a sequence, Cauchy
sequence, completeness of real line; Series
and its convergence, absolute and
conditional convergence of series of real and
complex terms, rearrangement of series.
Continuity and uniform continuity of
functions, properties of continuous
functions on compact sets. Riemann
integral, improper integrals; Fundamental
theorems of integral calculus. Uniform
convergence, continuity, differentiability
and integrability for sequences and series of
functions; Partial derivatives of functions of
several (two or three) variables, maxima
and minima.
(3) Complex Analysis:
Analytic functions, Cauchy-Riemann
equations, Cauchy’s theorem, Cauchy’s
integral formula, power series
representation of an analytic function,
Taylor’s series; Singularities; Laurent’s
series; Cauchy’s residue theorem; Contour
integration.
(4) Linear Programming:
Linear programming problems, basic
solution, basic feasible solution and optimal
solution; Graphical method and simplex
method of solutions; Duality.
Transportation and assignment problems.
(5) Partial differential equations:
Family of surfaces in three dimensions and
formulation of partial differential equations;
Solution of quasi linear partial differential
equations of the first order, Cauchy’s
method of characteristics; Linear partial
differential equations of the second order
with constant coefficients, canonical form;
Equation of a vibrating string, heat
equation, Laplace equation and their
solutions.
(6) Numerical Analysis & Computer
Programming:
Numerical methods: Solution of
algebraic and transcendental equations of
one variable by bisection, Regula-Falsi and
Ramanasri IAS/IFoS Institute
Reputed Institute for IAS/IFoS Exams Page 5
Newton-Raphson methods; solution of
system of linear equations by Gaussian
elimination and Gauss-Jordan (direct),
Gauss-Seidel (iterative) methods. Newton’s
(forward and backward) interpolation,
Lagrange’s interpolation.
Numerical integration: Trapezoidal rule,
Simpson’s rules, Gaussian quadrature
formula. Numerical solution of ordinary
differential equations: Euler and Runga
Kutta-methods.
Computer Programming: Binary
system; Arithmetic and logical operations
on numbers; Octal and Hexadecimal
systems;
Conversion to and from decimal systems;
Algebra of binary numbers. Elements of
computer systems and concept of memory;
Basic logic gates and truth tables, Boolean
algebra, normal forms. Representation of
unsigned integers, signed integers and reals,
double precision reals and long integers.
Algorithms and flow charts for solving
numerical analysis problems.
(7) Mechanics and Fluid Dynamics:
Generalized coordinates; D’ Alembert’s
principle and Lagrange’s equations;
Hamilton equations; Moment of inertia;
Motion of rigid bodies in two dimensions.
Equation of continuity; Euler’s equation of
motion for in viscid flow; Stream-lines, path
of a particle; Potential flow; Two-
dimensional and axisymmetric motion;
Sources and sinks, vortex motion; Navier-
Stokes Equation for a viscous fluid.
IAS MATHS OPTIIONAL
ANALYSIS Note:
LA Linear Algebra
CAL Calculus
AG Analytical Geometry
ODE Ordinary Differential Equations
VA Vector Analysis
D&S Dynamics & Statics
MA Modern Algebra
RA Real Analysis
CA Complex Analysis
LP Linear Programming
PDE Partial Differential Equations
NA&CP Numerical Analysis & Computer Programming
M&FD Mechanics & Fluid Dynamics
IAS-2013 Maths question
& Topic wise Analysis
Paper-I
Section A
Q. No Sub Q. No Topic Marks
1 1.a LA 10
1.b LA 10
1.c CAL 10
1.d AG 10
Ramanasri IAS/IFoS Institute
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1.e AG 10
2 2.a (i) LA 10
2.a (ii) LA 8
2.b (i) LA 8
2.b (ii) LA 8
2.c (i) LA 8
2.c (ii) LA 8
3 3.a CAL 20
3.b CAL 15
3.c CAL 15
4 4.a AG 15
4.b AG 15
4.c AG 20
Section B
5 5.a ODE 10
5.b ODE 10
5.c D&S 10
5.d D&S 10
5.e VA 10
6 6.a ODE 10
6.b ODE 10
6.c ODE 15
6.d ODE 15
7 7.a D&S 20
7.b D&S 15
7.c D&S 15
8 8.a VA 10
8.b VA 10
8.c VA 15
8.d VA 15
Paper-II
Section A
Q. No Sub Q. No Topic Marks
1 1.a MA 10
1.b MA 10
1.c RA 10
1.d CA 10
1.e LP 10
2 2.a MA 10
2.b MA 13
2.c RA 13
2.d RA 14
3 3.a MA 15
3.b MA 15
3.c RA 10
3.d RA 10
4 4.a LP 15
4.b CA 15
4.c LP 20
Ramanasri IAS/IFoS Institute
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Section B
5 5.a PDE 10
5.b PDE 10
5.c NA&CP 10
5.d M&FD 10
5.e M&FD 10
6 6.a PDE 15
6.b PDE 15
6.c PDE 20
7 7.a NA&CP 20
7.b NA&CP 15
7.c NA&CP 15
8 8.a M&FD 15
8.b M&FD 15
8.c M&FD 20
IAS-2014 Maths question
& Topic wise Analysis
Paper-I
Section A
Q. No Sub Q. No Topic Marks
1 1.a LA 10
1.b LA 10
1.c CAL 10
1.d CAL 10
1.e AG 10
2 2.a LA 15
2.b LA 10
2.c LA 10
2.d CAL 15
3 3.a CAL 15
3.b CAL 20
3.c(i) LA 8
3.c (ii) LA 7
4 4.a(i) AG 10
4.a(ii) AG 10
4.b AG 15
4.c AG 15
Section B
5 5.a ODE 10
5.b VA 10
5.c D&S 10
5.d D&S 10
5.e VA 10
6 6.a ODE 10
6.b ODE 20
6.c VA 20
7 7.a ODE 15
7.b D&S 15
7.c D&S 20
Ramanasri IAS/IFoS Institute
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8 8.a ODE 15
8.b D&S 15
8.c ODE 20
Paper-II
Section A
Q. No Sub Q. No Topic Marks
1 1.a MA 10
1.b RA 10
1.c CA 10
1.d CA 10
1.e LP 10
2 2.a MA 15
2.b RA 15
2.c LP 20
3 3.a MA 15
3.b RA 15
3.c RA 20
4 4.a MA 15
4.b RA 15
4.c LP 20
Section B
5 5.a PDE 10
5.b NA&CP 10
5.c NA&CP 10
5.d NA&CP 10
5.e M&FD 10
6 6.a PDE 15
6.b NA&CP 15
6.c NA&CP 20
7 7.a M&FD 15
7.b NA&CP 15
7.c M&FD 20
8 8.a PDE 15
8.b NA&CP 15
8.c M&FD 20
IAS-2015 Maths question
& Topic wise Analysis
Paper-I
Section A
Q. No Sub Q. No Topic Marks
1
1.a LA 10
1.b LA 10
1.c CAL 10
1.d CAL 10
1.e AG 10
2
2.a LA 12
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2.b CAL 13
2.c LA 12
2.d AG 13
3
3.a LA 12
3.b CAL 13
3.c AG 13
3.d CAL 12
4
4.a CAL 13
4.b LA 12
4.c AG 13
4.d CAL 12
Section B
5
5.a ODE 10
5.b ODE 10
5.c D&S 10
5.d D&S 10
5.e VA 10
6
6.a ODE 12
6.b D&S 13
6.c ODE 12
6.d D&S 13
7
7.a ODE 12
7.b D&S 13
7.c VA 12
7.d ODE 13
8
8.a D&S 12
8.b D&S 13
8.c VA 12
8.d ODE 13
Paper-II
Section A
Q. No Sub Q. No Topic Marks
1
1.a MA 10
1.b MA 10
1.c RA 10
1.d CA 10
1.e LP 10
2
2.a MA 15
2.b RA 15
2.c CA 20
3
3.a CA 15
3.b RA 15
3.c LP 20
4
4.a MA 15
Ramanasri IAS/IFoS Institute
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4.b RA 15
4.c LP 20
Section B
5
5.a PDE 10
5.b PDE 10
5.c NA&CP 10
5.d M&FD 10
5.e M&FD 10
6
6.a PDE 15
6.b M&FD 15
6.c NA&CP 20
7
7.a PDE 15
7.b NA&CP 15
7.c M&FD 20
8
8.a PDE 15
8.b NA&CP 15
8.c M&FD 20
IAS-2016 Maths question
& Topic wise Analysis
Paper-I
Section A
Q. No Sub Q. No Topic Marks
1
1.a LA 10 (4+6)
1.b LA 10 (7+3)
1.c CAL 10
1.d AG 10
1.e AG 10
2
2.a LA 16 (10+6)
2.b LA 16 (8+8)
2.c LA 18
3
3.a CAL 20
3.b CAL 15
3.c CAL 15
4
4.a AG 10
4.b AG 10
4.c CAL 15
4.d AG 15
Section B
5
5.a ODE 10
5.b VA 10
5.c ODE 10
5.d ODE 10
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5.e D&S 10
6
6.a ODE 10
6.b ODE 15
6.c ODE 15
6.d ODE 10
7
7.a D&S 15
7.b D&S 15
7.c D&S 20
8
8.a VA 10
8.b VA 10
8.c D&S 15
8.d VA 15
Paper-II
Section A
Q. No Sub Q. No Topic Marks
1
1.a MA 10
1.b RA 10
1.c RA 10
1.d CA 10
1.e LP 10
2
2.a RA 15
2.b MA 15
2.c LPP 20
3
3.a MA 20
3.b RA 15
3.c CA 25
4
4.a MA 15
4.b RA 15
4.c CA 20
Section B
5
5.a PDE 10
5.b M&FD 10
5.c M&FD 10
5.d NA&CP 10
5.e PDE 10
6
6.a PDE 15
6.b M&FD 15
6.c NA&CP 20
7
7.a PDE 15
7.b M&FD 20
7.c NA&CP 15
8
Ramanasri IAS/IFoS Institute
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8.a PDE 20
8.b M&FD 15
8.c NA&CP 15
IAS-2017 Maths question
& Topic wise Analysis
Paper-I
Section A
Q. No Sub Topic Marks
1 1.a LA 10
1.b LA 10
1.c CAL 10
1.d AG 10
1.e AG 10
2
2.a CAL 15
2.b AG 15
2.c AG 10
2.d LA 10
3
3.a LA 15
3.b LA 10
3.c CAL 15
3.d AG 10
4
4.a AG 15
4.b LA 15
4.c CAL 10
4.d CAL 10
Section B
5
5.a ODE 10
5.b D&S 10
5.c D&S 10
5.d VA 10
5.e VA 10
6
6.a(i) ODE 8
6.a(ii) ODE 8
6.b (i) ODE 10
6.b (ii) ODE 7
6.c D&S 17
7
7.a VA 16
7.b (i) ODE 9
7.b (ii) ODE 8
7.c D&S 17
8
Ramanasri IAS/IFoS Institute
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8.a D&S 16
8.b ODE 17
8.c (i) VA 9
8.c(ii) VA 8
IAS-2017 Maths question
& Topic wise Analysis
Paper-II
Section A
Q. No Sub Q. No Topic Marks
1
1.a RA 10
1.b MA 10
1.c RA 10
1.d CA 10
1.e LP 10
2
2.a RA 15
2.b CA 15
2.c MA 20
3
3.a MA 15
3.b CA 15
3.c LP 20
4
4.a CA 15
4.b LP 15
4.c RA 20
Section B
5
5.a PDE 10
5.b NA&CP 10
5.c NA&CP 10
5.d PDE 10
5.e M&FD 10
6
6.a PDE 15
6.b NA&CP 15
6.c M&FD 20
7
7.a PDE 15
7.b NA&CP 20
7.c M&FD 15
8
8.a PDE 20
8.b NA&CP 15
8.c M&FD 15
[Type text]
Reputed Institute for IAS/IFoS Exams Page 14
Ramanasri IAS/IFoS Institute
Reputed Institute for IAS/IFoS Exams Page 15
IAS Mathematics Optional Books List
PAPER – I Books
1. Linear Algebra
1. Linear Algebra – A.R. Vasistha (Krishna Series)