Getting Started Getting Started
with with
Mathematica Mathematica
by
Hakan Kutucu
What is
What is Mathematica Mathematica
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 Examples
Some 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 is
What is Mathematica Mathematica
How does
How does Mathematica Mathematica 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 does
How does Mathematica Mathematica 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 Mathematica Mathematica
Numerical ComputationNumerical Computation
Equation SolvingEquation Solving
Symbolic calculationSymbolic calculation
CalculusCalculus
GraphicsGraphics
Self-defined functionsSelf-defined functions
ListList
Pattern MatchingPattern Matching
AnimationAnimation
Mathematica Syntax Mathematica 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 Syntax Mathematica 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 CONSTANTS
SPECIAL CONSTANTS
Operation Operation
Symbol
Symbol 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 Operations
Arithmetic Operations
Arithmetic Operations Arithmetic Operations
Order of operation is important .
BEDMAS
N N (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 Functions Some Mathematical Functions
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 f.
Graphics
Graphics
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 Functions
Defining 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 Names
Function & 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 solving Equation solving
Use Solve to solve an equation with an Use Solve to solve an equation with an
exact solution, including a symbolic solution.
exact solution, including a symbolic 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 y. expr/ .x y.
Ma Ma trix Defining trix Defining
Entering a matrix:Entering a matrix:
a={{1,2,3},{4,5,6},{7,8,9}}
a={{1,2,3},{4,5,6},{7,8,9}}
Displays nicely only if told to:Displays nicely only if told to:
Menus exist but are harder to use than typing
Menus exist but are harder to use than typing
Ma Ma trix Operations trix 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.
Ma Ma trix trix Operations Operations (Multiplication)
(Multiplication)
Ma Ma trix trix Operations Operations (Transpose)
(Transpose)
Ma Ma trix trix Operations Operations (Inverse)
(Inverse)
16 5
4
12 2
3
2 2
6 2
Solve
q z
y x
q z
y x
q y
x
q z
y x
Ma Ma trix trix Operations Operations Exercises
Exercises
1.By using Solve Commabd
2.By using The equation Ax=b
