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Mathematica is a general computer
software system and language intended
for mathematical and other applications.
 Mathematica is an exceptionaly flexible
and powerful tool for producing
mathematical graphics . Mathematica
makes it easy to create graphs of
functions, plots of data pictures of
geometrical solids, and other mathematical
illustration either with built-in functions or
with simple programs of our own
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A numerical and symbolic calculator where
You type in questions, and Mathematics prints out
answers.
A visualization system for functions and data.
A high level programming language in which you
can create programs ,large and small.
A modeling and data analysis environment
A way to create interactive documents that mix text
,animated graphics and sound with active formulas .
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Mathematica is a very high level language
,we call it Fourth Generation Language
..because it can do in one step what the other
languages (such as Basic, Fortran,Pascal,C++
)can make it in many steps for example:
 4+7 (in Fortran)
 Read *,a,b
In
 d=a+b
Mathematica
 Print*,a,b,d
4+7
 Stop
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 End
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Stephen Wolfram designed Mathematica
program ,in 1988 Wolfram Research
company gave early versions of
Mathematica
(1.03,1.04,1.1,1.2,…,2.0,2.1,2.2…..,6)
 It is very important to tell that we can use
Mathematica under Dos or Mackintosh or
windows ..every system has special version
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Mathematica Diagram
User
Front End
Kernel
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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
 The interface between the user and the
kernel is called the front end
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 ?Name
 ?Log
 ?Plot
 ??Plot
 ?A*
 ?Z*a
Getting information from
Mathematica
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Numerical Calculations
There are four kinds of numbers:
 Integers
 Rationals
 Real
 Complex
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Mathematica & Expressions
Operatorors
 Subtraction
 /
division
 * Multiplication
 +
addition
 ^
power
The numbers
0,1,2,…9
 The symbols
A,B,C,..,z
 Paranthesis(),{},[]
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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
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Relationals & Logical Operators
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X=y
X==y
X>y
X>=y
X<y
X<=y
X!=y
!p
 P&&q
 P
 Pllq
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To introduce some of the
functions & Commands
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Sqrt[x]
Exp[x]
Log[x]
Log[x,b]
Sin[x],Cos[x],Sinh[x],
Cosh[x]…..
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Factor[Poly]
Expand[expr]
ExpandAll[expr]
Together[expr]
Simplify[expr]
Collect[expr, x]
Apart[expr]
FindRoot
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Mathematica uses symbolic expressions to
provide a very general representation of
mathematical and other structures.
 The generality of symbolic expressions
allows Mathematica to cover a wide
variety of applications with a fairly small
number of methods from mathematics and
computer science.
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What is the difference between
Mathematica and calculator?
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The simplest way to use Mathematica is like a calculator.
We type in a calculator calculations , and Mathematica
prints back the answer. The range of calculations that
you can do with mathematica is however far greater
than with a traditional electronic calculator, or, for that
matter , with a traditional programming language such
as Fortran or BASIC. Thus , for example ,while a
traditional system might support perhaps 30
mathematical operations, Mathematica has over 1000
built in functions. In addition , while traditional systems
handle only numerical computations, Mathimatica also
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
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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
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Here are some simple examples. Each one
consists of a short “dialog” with
Mathimatica. The text on the lines labeled
in (n):=is what you type in; the lines
labeled out (n)= are what Mathematica
prints back.
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Statistics
Academic level
Full Prof.
No.of
teacher(1)
4
No.of teacher
(2)
7
Associ. Prof.
10
15
Assista. Prof.
9
12
Lecturer
7
10
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10
8
6
4
2
Prof
Asso .pro
Assis .Prof
Lect .
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14
12
10
8
6
4
2
Prof
Asso .pro
Assis .Prof
Lect .
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25
20
15
10
5
Prof
Asso .pro
Assis .Prof
Lect .
Next
Asso .pro
Prof
Assis .Prof
Lect .
Next
Asso .pro
Prof
Lect .
Assis .Prof
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The website is
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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.
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