Introduction to Mathematica

1
Introduction to Mathematica
PhD Program UOS

• Mathematica
• A System for Doing
• Mathematics on a Computer

Roland.Franzius_at_Physik. UOS.de
2
Todays Topics in Mathematica

• System Description
• Numerics Algebra Graphics
• Programming in Mathematica

Further Information...
In case of problems with Installation,
Environment, Special Programming
Techniques, Mathematics behind MMA or
solutions Contact Roland.Franzius_at_Physik.
UOS.de or 969-2683 or E91/physics building
3
Where to Run Mathematica

• CIP Pool Physik (Physics students)
• Suse Linux, Windows 2k and XWindows systems, MMA
  Vs 4.01
• CIP Pool Computing Center (AVZ)
• Windows 2k, MMA Vs 4.01
• Many workstations of research groups

CIPComputer Investment Program of German
Federal Gov.
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Where to Buy Mathematica

• Regular, Student, Teacher and Campus, Editions.
  Student Editon contains all systems (Win, Linux,
  Mac). Updates from earlier versions available
• Germany
• http//www.ordinate.de/info.htm
• http//www.ordinate.de/wolfram/mma_serv.htm
• International
• http//store.wolfram.com/catalog/
• Prices from 137 (student update) to 2500 (Unix
  prof.)

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Where To Find Net Ressources

• Wolfram Research
• http//www.wolfram.com/
• Support libraries
• http//library.wolfram.com/
• http//library.wolfram.com/tutorials/
• http//www.mathsource.com/
• Newsgroups
• Comp.soft-sys.math.mathematica (moderated)
• zB auf Server News//news.rrzn.uni-hannover.de

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What Mathematica Is
Roland.Franzius_at_Physik. UOS.de

• A system for doing mathematics and other
  technical calculations.
• Type in a question and Mathematica gives back one
  (or more or no) answers.
• Mathematica contains a powerful programming
  language that allows us to create simple or
  sophisticated functions and programs,
• The interface does word processing, outlining,
  and mathematical typesetting with export to all
  kind of programs.

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Mathematica Is Too
Roland.Franzius_at_Physik. UOS.de

• Difficult to learn, understand, maintain.
• An extremely slow and RAM consuming interpreting
  AI language.
• A system with no feeling for good mathematics.
• Using complex arithmetic bare of any knowledge
  about Riemann surfaces and their topology
• A system with more formula content as all known
  books together

8
Mathematica Can Do for You
Roland.Franzius_at_Physik. UOS.de

• Check equations and solutions.
• Quick check numerical approximations to any
  (sensible) degree of accuracy.
• Generate nice data visualisations and export them
  into your LaTeX system or XML editor.
• Develop, check, trace and encode complex
  programming paradigms for later fast
  implementation in C or FORTRAN
• Develop numeric approximations as
  InterpolatingFunction by Fit or Interpolate

9
Mathematica Subsystems
Roland.Franzius_at_Physik. UOS.de

• The Mathematica system constist of
• Front end
• Mathematicas interface, providing a
  word-processing and outlining environment called
  a notebook for entering commands and accompanying
  text
• Kernel
• performs the mathematical computations. One ore
  more kernels can run locally or on a remote
  server simultaneously.
• Help Database
• Application Extensions

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The ComputerAlgebraSystem MMA
Roland.Franzius_at_Physik. UOS.de

• does three classes of computations.
• Numerical arithmetic expressions, calculates and
  approximates numerical values of functions,
  performs Fast Fourier Transform of data lists
• Algebraical Evaluates and manipulates symbolic
  algebra, linear algebra, trigonometric
  expressions, symbolic calculus including
  differentiation, integration, series, solving
  equations and (some) differential equations
• Graphical calculates and displays two- and
  three-dimensional graphs of curves, functions or
  data lists.

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Where To Find Help
Roland.Franzius_at_Physik. UOS.de

• Definitive reference
• Wolframs The Mathematica Book
  for all of Mathematicas built-in functions
  and commands.
• Standard Add-On Packages reference
• Getting Started with Mathematica

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Online Help Locally
Roland.Franzius_at_Physik. UOS.de

• Mathematica Book
• Book is part of the software package (not
  Students Edition)
• complete text with 1300 pages available on-line
  by Help Browser .

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Help System Categories
Roland.Franzius_at_Physik. UOS.de

• Help Browser in the Help menu has
• 6 radio buttons to choose a help categorie to
  browse.
• Built In Functions Addons Book
• Getting Started Other Master

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Help Built In Functions
Roland.Franzius_at_Physik. UOS.de

• Click the Built-in Functions button.
• Mathematica presents a list of topics the
  built-in functions fall into.
• Selecting a topic with the mouse pointer
• opens a list of subtopics, and selecting a
  subtopic brings up a list of Mathematica commands
  that fall under that subtopic.
• Type or select a command name
• provides the usage message for the command, any
  special considerations to be aware of when using
  the command, hyperlinks to related functions, and
  examples for the command that can be evaluated,
  edited, or pasted into another notebook.
• Check a function name using the mouse and press
  help key F1

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Help Master Index
Roland.Franzius_at_Physik. UOS.de

• The Master Index builds up an alphabetical index
  of all information contained in all categories of
  the Help Browser.

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Help Introduction to MMA
Roland.Franzius_at_Physik. UOS.de

• Clicking Getting Started/Demos allows us to
  browse the contents of
• Getting Started with Mathematica,
• along with many examples of Mathematica
  computations, graphics, and typesetting related
  to various fields.

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Help Other Information
Roland.Franzius_at_Physik. UOS.de

• Other Information category contains information
  about the front ends menu items and keyboard
  shortcuts, a reference guide for entering
  two-dimensional typeset formulas, information on
  how to contact Wolfram Research, and other
  Mathematica-related information.

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Starting the Front End
Roland.Franzius_at_Physik. UOS.de

• At Starting the front end opens an empty
  notebook. The kernel starts at execution of the
  first calculation
• Open a notebook with extension .nb in
  Menu/File/Notebook.
• You may open an input palette for special
  characters Menu/File/Palettes

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Starting and Stopping the Kernel
Roland.Franzius_at_Physik. UOS.de

• The kernel is launched as an independent program
  with a special communication line special
  connected to the front end. The kernel starts at
  any execution of a calculation in an input cell.
• To stop the kernel goto
  Menu/Kernel/Quit Kernel.
• Stop and relaunch the kernel if you restart a
  series of definitions, programs calculations
• MMA is unforgiving and remembers everything

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Stop the Kernel to Forget
Roland.Franzius_at_Physik. UOS.de

• Stop and relaunch the kernel if you restart a
  series of definitions, programs calculations
  after experimental definitions
• MMA is unforgiving and remembers everything.
• Never use a, x and y as names of numbers (eg x5)
  or f,g as names of functions (eg fx_x2)

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Explore The Calculator
Roland.Franzius_at_Physik. UOS.de

• Integer 18
• Real 1.020-10-17
• Complex Exp 2.2 7 I
• Long Real NPi,155
• Rational RationalizePi, 10-29

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Explore MMA Graphics I
Roland.Franzius_at_Physik. UOS.de

• Plot of a Real Function
• Plot fx, x,0,1
• Plot of Curve
• ParametricPlot ut, vt , t,0,1
• Plot of a surface given by a function triple
• Plot3D fx,y,x,0,1,y,0,1

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Explore MMA Graphics II
Roland.Franzius_at_Physik. UOS.de

• Plot of Complex Functions.
• ContourPlotRe(xI y)2 ,x,0,1,y,0,1
• Plot of Numerical Data
• ListPlotdata, PlotJoined-gtTrue

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Moderate Task Equation Solver

• Give your solution the name eg solution1
• solution1 Solveaxy,bx-y, x,y
• solution1 is a replacement rule for the names x,y
• x-gt (ab)/2, y-gt (a-b)/2
• Use solution1 to name values by any name eg xy
• Explicit form of replacement
• xyReplacex,y, solution1
• Xyx,y/.solution1

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Programming Define a Function

• Solve an Equation
• sol Solve 4 x 3 1/x 0 , x
• x-gt .., x-gt ..
• Define one solution of sol as a function.
• Dont use SetDelayed since you need
  value of sol now, not later
• Choose for f one element of sol e.g.
  sol 1
• myFx_ x /. sol 1

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Difficult Task Trigonometry

• ASumSinn Pi/12,n,1,13
• Expand A as a rational product of rxponentials
• Help Mathematica to find a way by a replacement
  technique