Art of Symbolic Computing - I using MATHEMATICA (A Fully Integrated Environment for Technical Computing) Software and Applications R.C. Verma Physics Department Punjabi University Patiala – 147 002 Refresher Course in Physics Panjab University Sept. 2010
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Refresher Course in Physics Panjab University Sept. 2010
Art of Symbolic Computing - I using MATHEMATICA (A Fully Integrated Environment for Technical Computing) Software and Applications R.C. Verma Physics Department Punjabi University Patiala – 147 002. Refresher Course in Physics Panjab University Sept. 2010. Education (Some Indian Statistics). - PowerPoint PPT Presentation
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Art of Symbolic Computing - Iusing MATHEMATICA
(A Fully Integrated Environment for Technical Computing)Software and Applications
Education (Some Indian Statistics)• Total population below 14 is around 250 million.
• Maximum number of ‘out of school’ children in world.• Nowhere Children:- Around 90 million children are neither enrolled in
school nor accounted for as labour.
• Only 60% of children reach grade V.• Many of those ‘completing’ primary school cannot read or write.• Every child is curious, creative, intelligent, innocent and beautiful. • Why and where he loose these qualities.
• Somewhere society (present normal setup of mind, current values and education modes) is responsible for this state of affairs.
• Hope:- Efforts under UGC, DST, NMEICT of MHRD etc.
Introduction:-Computer-based symbolic computation has a very significant role in
computer world. Still it is a very under-used, probably because of a reluctance to break from tradition. Today symbolic manipulation has become a powerful tool, which boosts productivity
It runs on most popular workstation OS, including Microsoft Windows, Apple Macintosh OS, Linux, and other Unix-based systems.
Mathematica today is used in all the branches of knowledge:
• Physical science,• Biological science, • Social science, • Commerce, • Education, • Enginering,• Computer science, etc.
Over 100 specialized commercial packages and
over 200 books for Mathematica and its applications
0. Phases of the computer algebra:-
First Generation:
Reduce has packages suited to the needs of the high energy physicist. Macsyma is slow and lacks a friendly interface.
Second Generation:
Maple has strong algebraic and graphics capability.
Third Generation:
Mathematica is a very user-friendly interface and superb graphic abilities. A standard tool for research, development and production of software.MatLab & MathCad are also available with similar facilities.
1. Who Created Mathematica?
Stephen Wolfram is the creator of Mathematica.
His early work: mainly in high-energy physics, quantum field theory, and cosmology.
In 1979, he began the construction the computer algebra system.
He began the development of Mathematica in 1986.
1st version released on June 23, 1988, hailed as a major advance in computing world.
In 1991, its Window version 2 was developed by him and his team.
Before 2004, versions 3, 4 and 5, now 6 introduced with new capabilities.
Parallel Processing and Grid-Mathematica have also been launched.
http://www.wolfram.com/
2. What can Mathematica do for you?
STANDARD ARITHMETICOperations with Integer, Rational, Real, and Complex nos with LARGE precisionRICH in Built-in Constants & functions; Special functions, Creating New functions
FRONT-END: serves as the channel on which a user communicates with the kernel.
STANDARD PACKAGES: special topics, like vector analysis, statistics, algebra, to graphics, etc.
MATHSOURCE: collection of packages and notebooks created by Mathematica users.Feyndia, Math-Tensor, Graphics, and other Addons
WebMathematica
4. Ten Commandments
1. Mathematica distinguishes between uppercase and lowercase letters.
2. Mathematica commands, built-in functions, & constants start with a capital letter. 3. Use lowercase letters for defining variables or functions.
4. Arguments of all commands & functions are enclosed in square brackets [ ]. 5. Use curly brackets { } for lists of items, and range of parameters of the function. 6. Parenthesis ( ) is reserved for indicating the grouping of terms.
7. Double brackets [ [ ] ] are used for indexing the components of an object.
8. All functions, for numerical calculations, start with a capital N.
9. Giving Remarks. Statements starting with (* and ends with *) are not executed.
10. When Mathematica detects a syntax error, it prints a message.
5. How to Start Mathematica and Execute its Commands?
Double click the Mathematica icon, or Math.Exe file
When Mathematica starts, it shows you a blank notebook.
Enter Mathematica commands into the notebook, and then press Shift-Enter keys to process the input given.
Pressing the Enter key generates a new line.
For getting Help on Mathematica Commands, use Help ortype double question marks ?? before the command name.
For instance ??Integrate
Math 6.0 - Help
• Documentation Center
• Index of Functions
• 5 minutes with Mathematica
• Demonstration Projects
Special Features (given in Help)• Core Language
The uniquely powerful symbolic language that is the foundation for Mathematica
Mathematics and AlgorithmsThe world's largest integrated web of mathematical capabilities and algorithms
Data Handling & Data SourcesPowerful primitives and sources for large volumes of data in hundreds of formats
Visualization and GraphicsSymbolic graphics and unparalleled function and data visualization
Systems Interfaces & DeploymentUnique customizability and connectivity powered by symbolic
Capabilities that define a new kind of dynamic interactive computingNotebooks and Documents
Program-constructible symbolic documents with uniquely flexible formatting.
6. Input and Output Labels
In[1] : =
An input label appears at the beginning of every Input cell.
These are numbered according to the order of evaluation.
The result of the command is displayed in an Output cell,
Out[n]=
which is labeled according to the input label.
Mathematica formats the material in Output cells in mathematical notation. e.g.
type 5.3+2.9 and press Shift-Enter keys
Mathematica shows:
In[1]:= 5.3 + 2.9 Out[1] = 8.2
7. Number Representation & Arithmetic Computations
Mathematica can distinguish between
integer, rational, real, complex numbers.
Following symbols are used to denote them:
Addition +
Subtraction -
Multiplication *
Division /
Exponentiation ^
Parenthesis ( ) can be used to change order of operations.
Note: - Multiplication can be represented by a space.
Caution: x y means x * y but xy is treated as a new variable xy.
8. MIXED MODE OPERATIONS:
When two constants or variables of the same type are combined through any of these fundamental operations, the result would be of the same type as that of the operands.
Mathematica gives out of integer operation as integer,
15. Trigonometric Functions Sin[x] sine of x x must be in radians.
Cos[x] cosine of x -do-
Tan[x] tangent of x -do-
Cot[x] cotangent of x -do –
Sec[x] secant of x -do –
Csc[x] cosecant of x -do –
In[33]:= Cos[Pi/4]Out[33]=
1-------Sqrt[2]
In[34]:= Tan[3Pi/4]Out[34]= -1
15.1 Inverse Trigonometric Functions
ArcSin[x] inverse of sine ArcCos[x] inverse of cosine
ArcTan[x] inverse of tangent
ArcCot[x] inverse of cotangent ArcSec[x] inverse of secant ArcCsc[x] inverse of cosecant
In[35]:= ArcTan[-1]Out[35]=
-Pi---
4
15.25 Hyperbolic Functions
Sinh[x] hyperbolic-sine of x
Cosh[x] hyperbolic-cosine of x Tanh[x] hyperbolic- tangent of x Coth[x] hyperbolic-cotangent of x Sech[x] hyperbolic-secant of x Csch[x] hyperbolic-cosectant of x
In[36]:= Sinh[2.0]Out[36]= 3.62686
15.3 Inverse Hyperbolic Functions
ArcSinh[x] inverse-hyperbolic-sine of x
ArcCosh[x] inverse-hyperbolic-cosine of x ArcTanh[x] inverse-hyperbolic- tangent of x ArcCoth[x] inverse-hyperbolic-cotangent of x ArcSech[x] inverse-hyperbolic-secant of x ArcCsch[x] inverse-hyperbolic-cosectant of x
In[37]:= ArcCosh[2.0]Out[37]= 1.31696
16. Functions involving two or more arguments
MOD[m, n] command yields the remainder on division of m by n.