Getting Started Getting Started

with with

MathematicaMathematica

byHakan Kutucu

What isWhat is MathematicaMathematica

Mathematica is a computer program

created by Wolfram Research Inc.(1988) Mathematica is a powerful desktop

computer program capable of doing

algebraic calculations, numerical

approximations, and computer graphics. It is suitable for both numeric and

symbolic work, and it has remarkable word-

processing capabilities as well.

Some Graphical ExamplesSome Graphical Examples

Mathematica has two parts: the Kernel and the Front End. The Kernel is the main part of the system, which accepts Mathematica commands, processes them and sends back results. This is called evaluating the command. The Front End is the part of the system that handles such things as screen display, printing and the creation of Mathematica documents.

What isWhat is MathematicaMathematica

How doesHow does MathematicaMathematica work?work?

Mathematica documents are called Notebooks. A Notebook is a bit like a word-processor document; you can type and edit commands, send them to the Kernel for evaluation, display the results and save your work.

How doesHow does MathematicaMathematica work?work?

You send commands to be evaluated by

holding down the “shift” key and pressing

the “enter” key Another easy way to evaluate by pressing

the “enter” key at the right hand side of

keyboard.

Functionalities of Functionalities of MathematicaMathematica

Numerical ComputationNumerical Computation Equation SolvingEquation Solving Symbolic calculationSymbolic calculation CalculusCalculus GraphicsGraphics Self-defined functionsSelf-defined functions ListList Pattern MatchingPattern Matching AnimationAnimation

Mathematica SyntaxMathematica Syntax

Mathematica commands start with a

CAPITAL letter, e.g. Sin[x]. If the command

is really severalwords in English joined

together then each one starts with a capital

but WithNoSpacesInBetween. Case Sensitive: the word Fun is different

from the word fun which is different from

the word fuN.

Mathematica SyntaxMathematica Syntax

Mathematica uses a lot of brackets and all

the different sorts of them, ( [ { } ] ). Arguments of functions are given in

square brackets [ ]. Curly brackets, called “braces”, {…} are

used to make a list, usually to allow several

objects to be treated as one. Expression are cascaded by () pairs.

Mathematica protects these names; they

cannot be used as names for other

quantities.

SPECIAL CONSTANTSSPECIAL CONSTANTS

Operation Operation SymbolSymbol

Operation Operation NameName

SampleSample

++ AddAdd 3+53+5

-- SubstructSubstruct 8-38-3

// DivideDivide 4/64/6

* or Space* or Space MultiplyMultiply 2*4 or 2 42*4 or 2 4

^̂ PowerPower 3^43^4

Arithmetic OperationsArithmetic Operations

Arithmetic OperationsArithmetic Operations

Order of operation is important .

BEDMAS

NN (Numerical) (Numerical)

(a) N[expr] displays 6 digits by default

(b) N[expr, n] displays 6 digits when n<16

(c) N[expr, n] does not display more digits

than n originally has.

Some Mathematical Some Mathematical FunctionsFunctions

Sqrt[x]Sqrt[x] square root ( )square root ( )

Exp[x]Exp[x] exponential (eexponential (exx))

Log[x]Log[x] natural logarithm lnxnatural logarithm lnx

Log[b, x]Log[b, x] logarithm to base b (loglogarithm to base b (logbbx)x)

Sin[x], Sin[x],

Cos[x], Tan[x]Cos[x], Tan[x]trigonometric functions (with trigonometric functions (with

arguments in radians)arguments in radians)

nn!! factorial of nfactorial of n

Mod[Mod[nn, , mm]] n modulo mn modulo m

FactorInteger[FactorInteger[nn]] prime factors of nprime factors of n

Mathematica incorporates a wide range of two-and three-dimensional graphics functions. The simplest is Plot, which generates two-dimensional Cartesian graphs Plot[f, {x, xmin, xmax}] generates a plot of f as a function of x from xmin to xmax. Plot[{f1, f2, … }, {x, xmin, xmax}] plots several functions fi.

GraphicsGraphics

Graphics (Example)Graphics (Example)

Graphics(Options)Graphics(Options)

Graphics(Options)Graphics(Options)

For Other Options the command is Options[Plot]

3 Dimensional Plotting

Plot3D[ f, {x,xmin,xmax}, {y,ymin,ymax}] will draw the graph of z = f(x,y) over the rectangle [xmin,xmax]×[ymin,ymax] in the xy-plane.

3 Dimensional Plotting(Options)

Three Dimensional Plotting(Options)

A function may return a symbol, a real

number, a complex matrix, another function.... Any mathematical object is an acceptable

value for a function. A function may be written using mathematical

notation, it may be created using programming

constructs (like for, if/then, etc.), or it could even

be written in another language entirely (Fortran,

C, etc.).

Defining FunctionsDefining Functions

Mathematica variable names can be long, but they must not begin with a number, Because Mathematica interprets, say, 2dimension as 2 * dimension. Names can end with a number, though: x1 is a useful way of writing in Mathematica a subscripted variable like x1. Note also that combinations of letters without spaces are interpreted as new variables: ax does not mean a*x.

Function & Variable NamesFunction & Variable Names

A function can be defined by using the

following form:

f[x_] := an expression involving x (no

underbar)

Example: f[x_]:=x^2+3x

f[4]

f[a+1]

?f (This shows the definition you made for

f. )

Defining Functions

Equation solvingEquation solving

Use Solve to solve an equation with an Use Solve to solve an equation with an

exact solution, including a symbolic exact solution, including a symbolic

solution.solution.

Use NSolve or FindRoot to obtain a Use NSolve or FindRoot to obtain a

numerical approximation to the solution.numerical approximation to the solution.

To use solutions need to use To use solutions need to use expr/ .x expr/ .x

y. y.

MaMatrix Definingtrix Defining Entering a matrix:Entering a matrix:

a={{1,2,3},{4,5,6},a={{1,2,3},{4,5,6},

{7,8,9}}{7,8,9}}

Displays nicely only if told to:Displays nicely only if told to:

Menus exist but are harder to use than Menus exist but are harder to use than typingtyping

MaMatrix Operationstrix Operations

Matrix multiplication

(also called dot or

inner product) is

carried out in

Mathematica with the

function Dot, typically

entered with a dot

short-hand syntax.

MaMatrix trix Operations Operations (Multiplication)(Multiplication)

MaMatrix trix Operations Operations (Transpose)(Transpose)

MaMatrix trix Operations Operations (Inverse)(Inverse)

1654

1223

22

62

Solve

qzyx

qzyx

qyx

qzyx

MaMatrix trix Operations Operations ExercisesExercises

1.By using Solve Commabd

2.By using The equation Ax=b