getting started with mathematica
DESCRIPTION
Getting Started with Mathematica. by Hakan Kutucu. What is Mathematica. Mathematica is a computer program created by Wolfram Research In c.(1988) Mathematica is a powerful desktop computer program capable of doing algebraic calculations, numerical approximations, and computer graphics. - PowerPoint PPT PresentationTRANSCRIPT
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