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Mathematica is a general computer Mathematica is a general computer software system and language intended for software system and language intended for mathematical and other applications.mathematical and other applications.

Mathematica is an exceptionaly flexible Mathematica is an exceptionaly flexible and powerful tool for producing and powerful tool for producing mathematical graphics . Mathematica mathematical graphics . Mathematica makes it easy to create graphs of makes it easy to create graphs of functions, plots of data pictures of functions, plots of data pictures of geometrical solids, and other mathematical geometrical solids, and other mathematical illustration either with built-in functions or illustration either with built-in functions or with simple programs of our own with simple programs of our own

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A A numericalnumerical and and symbolic calculatorsymbolic calculator where where You type in questions, and Mathematics prints You type in questions, and Mathematics prints

out answers.out answers.• A A visualization systemvisualization system for functions and data. for functions and data.• A A high level programming languagehigh level programming language in which in which

you can create programs ,large and small.you can create programs ,large and small.• A A modeling modeling and and data analysisdata analysis environment environment• A way to create A way to create interactive documentsinteractive documents that that

mix text ,animated graphics and sound with mix text ,animated graphics and sound with active formulas . active formulas .

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Mathematica is Mathematica is a very high level a very high level languagelanguage ,we call it Fourth Generation ,we call it Fourth Generation Language ..because it can do in one step Language ..because it can do in one step what the other languages (such as Basic, what the other languages (such as Basic, Fortran,Pascal,CFortran,Pascal,C++++ )can make it in many )can make it in many steps for example:steps for example:

4+7 (in Fortran) 4+7 (in Fortran) Read *,a,b Read *,a,b d=a+b d=a+b Print*,a,b,dPrint*,a,b,dStopStopEndEnd

In In MathematiMathematica ca 4+74+71111

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Stephen Wolfram designed Stephen Wolfram designed Mathematica program ,in 1988 Mathematica program ,in 1988 Wolfram Research company gave Wolfram Research company gave early versions of Mathematica early versions of Mathematica (1.03,1.04,1.1,1.2,…,2.0,2.1,2.2…..,6)(1.03,1.04,1.1,1.2,…,2.0,2.1,2.2…..,6)

It is very important to tell that we can It is very important to tell that we can use Mathematica under Dos or use Mathematica under Dos or Mackintosh or windows ..every Mackintosh or windows ..every system has special versionsystem has special version

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Mathematica DiagramMathematica Diagram

KernelKernel

Front EndFront End

UserUser

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The kernel is the computational engine of The kernel is the computational engine of

Mathematica you inter the constructions and the kernel responds with answers in the form of numbers, graphs ,matrices or other appropriate displays Mathematica you inter the constructions and the kernel responds with answers in the form of numbers, graphs ,matrices or other appropriate displays The interface between the user and the kernel is called the front end The interface between the user and the kernel is called the front end

The kernel is the computational engine of The kernel is the computational engine of

MathematicaMathematica

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?Name?Name?Log?Log?Plot?Plot??Plot??Plot

?A*?A*?Z*a?Z*a

Getting information from Getting information from

MathematicaMathematicaNext

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Numerical Calculations

There are four kinds of numbers:IntegersRationalsRealComplex

Mathematica & Expressions

Operatorors - Subtraction / division * Multiplication + addition ^ power

The numbers 0,1,2,…9

The symbols A,B,C,..,z

Paranthesis(),{},[]

Variables

When we choose the names of variables:

The names of the variables contain un limited numbers & symbols but we must not use(+,-,/,*).

The name of the variable must not start 2x ,2*x….but we can use x2

x y,xy,5x,x5,x^2y,?x

Relationals & Logical Operators

X=y X==y X>y X>=y X<y X<=y X!=y

!p P&&q P Pllq

Sqrt[x] Exp[x] Log[x] Log[x,b] Sin[x],Cos[x],Sinh[

x],Cosh[x]…..

To introduce some of thefunctions & Commands

Sqrt[x] Exp[x] Log[x] Log[x,b] Sin[x],Cos[x],Sinh[

x],Cosh[x]…..

Factor[Poly] Expand[expr] ExpandAll[expr] Together[expr] Simplify[expr] Collect[expr, x] Apart[expr] FindRoot

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Mathematica uses symbolic Mathematica uses symbolic expressions to provide a very general expressions to provide a very general representation of mathematical and representation of mathematical and other structures.other structures.

The generality of symbolic expressions The generality of symbolic expressions allows Mathematica to cover a wide allows Mathematica to cover a wide variety of applications with a fairly variety of applications with a fairly small number of methods from small number of methods from mathematics and computer science. mathematics and computer science.

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What is the difference between What is the difference between Mathematica and calculatorMathematica and calculator??

The simplest way to use Mathematica is like a The simplest way to use Mathematica is like a calculator. We type in a calculator calculations , calculator. We type in a calculator calculations , and Mathematica prints back the answer. The and Mathematica prints back the answer. The range of calculations that you can do with range of calculations that you can do with mathematica is however far greater than with a mathematica is however far greater than with a traditional electronic calculator, or, for that traditional electronic calculator, or, for that matter , with a traditional programming language matter , with a traditional programming language such as Fortran or BASIC. Thus , for such as Fortran or BASIC. Thus , for example ,while a traditional system might example ,while a traditional system might support perhaps 30 mathematical operations, support perhaps 30 mathematical operations, Mathematica has over 1000 built in functions. In Mathematica has over 1000 built in functions. In addition , while traditional systems handle only addition , while traditional systems handle only numerical computations, Mathimatica also numerical computations, Mathimatica also handles symbolic and graphical computations.handles symbolic and graphical computations.

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Very useful in many branches:

Calculus Differential Equations Linear algebra Vector analysis Complex Variables Fourier and Laplace

Transform Group theory Discrete

Mathaematica

Mathematical Programing

Advanced Computer Programing

Advanced Mathematics

Statistics Zoology & Botany

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To do the procedure of Plot we have to determine 3 main things

:Define the function we need to

draw .Define independent variable .Define the domain of independent

variables

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Two dimensional graphics:

A function with one variable is Y=f(x),where x is an independent variable Y is dependent variable ,and range is on Y axis .

Plot the fun. in a plane through (x,y) which satisfy Y=f(x).

The most important command is …..plot.

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Three dimensional graphics

A function in two variables is z=f(x,y),x,y are dependent variables ,z is independent variable

We can display the points (x,y) which show the fun. f(x,y) on z axis ,in 3D corresponding z=f(x,y)

The most important command is Plot3D

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Parametric Functions

F(x) is a parametric fun. with one magnitude ,then y=f(x) describe the curve

In the plane crossed by any vertical line . Y=f(x) for every single point,but we can deal

with the curves through parametric formulas By making x,y as functions of t, x=g(t),y=h(t)

then for every value of t there are new x,y. We called them parametric eqns.for the

curve and t is a parameter The suitable command is ParametricPlot

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Some examples

Here are some simple examples. Here are some simple examples. Each one consists of a short Each one consists of a short ““dialogdialog”” with Mathimatica. The text on the with Mathimatica. The text on the lines labeled in (n):=is what you type lines labeled in (n):=is what you type in; the lines labeled out (n)= are in; the lines labeled out (n)= are what Mathematica prints back.what Mathematica prints back.

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StatisticsAcademic level

No.of teacher(1)

No.of teacher (2)

Full Prof.47

Associ. Prof.1015

Assista. Prof.912

Lecturer710

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Prof Asso .pro Assis .Prof Lect .

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Prof Asso .pro Assis .Prof Lect .

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Prof Asso .pro Assis .Prof Lect .

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Asso .pro

Assis .Prof Lect .

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Prof

Asso .pro

Assis .ProfLect .

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The website is

www.wolfram.com

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References

Wolfram, Stephen ‘‘Mathematica’’Addison Wesley,1994.

Abell,Marthadl & Braselton,James P.’’Mathematica By Example’’ Academic Press,1992.

Smith,C. and Blachman,N.’’ The Mathematica Graphics Guidebook’’ Addison Wesley ,1995.

Meader,R.E.’’Computer Science With Mathematica’’Ronman E.Meader 2000.