*Mathematica*3 Notebooks

Computational Physics Project

Peter Sandev, 23/05/1998

This work is based on 14** **notebooks originally written on *Mathematica2*** **for NEXT** **computers by R.G. Palmer (a few words about him).

The goal of the project was to transfer the notebooks to* Mathematica3* for Unix and to utilize the new *Mathematica3 *features and functions. All notebooks are linked by hyperlinks to the other notebooks and to the* Mathematica3 Help *utility, which* *contrary to* Mathematica2, *is* *very big and thorough and among other things has the whole* Mathematica Book *in it. So use it without hesitation!

If you are unfamiliar with *Mathematica , *or do not have time to study it thoroughly , the best you can do is to start with the **Tour** and **NotebookIntroduction **notebooks.

**Tour** notebook gives you examples about the basic* Mathematica *features: algebraic and numerical computations, 2D , 3D and animated graphics, sound and programming. As in all notebooks, here the user is encouraged to execute some of the commands on-line and see how actually *Mathematica* works.

**Notebook Introduction **covers practically everything an average user has to know about *Mathematica*** **notebooks in order not to look up every function he uses in the *Help *utility. It saves you a great deal of time (not to speak about nerves). Notebook opening, saving, size and shape, all kinds of sections, cursors, cells, fonts, their look function and actual implementation in a notebook , all about expressions: *Mathematica* grammar rules, what, when and how to evaluate an expression, how to process the output, different kinds of graphics: plotting, layout conversion between different image formats... All this and more is in there and presented by means of examples which you can run and learn from the output or the error messages you receive.

The rest of the notebooks treat some mathematical and physical problems.

**Complex** and **Complex-soln **cover the complex functions and operators in the complex algebra and graphics. *Mathematica* packages for enhancing the computation power are treated. 6 problems on the subject as well as their solutions are included.

**De** and **De-soln **teach you to solve *analytically *ordinary differential equations by means of Laplace transforms and series expansions. 6 problems and their solutions help you make sure you got the subject. A few aspects of pure functions and extracting parts of expressions are treated.

**FFT** and **FFT-soln **provide you with the basic theory about the continuous and discrete Fourier transforms and teach you basic skills about loading ASCII data and processing it in order to extract its power, amplitude and frequency spectrum with the help of 3 problems and their solutions.

**Series** and **Series-soln** deal with Taylor and Lauren finite and infinite sums, their radius of convergence and graphical presentation of partial sums as well as operators and commands for their computation. One example is included.

**Chisq** and **Chisq-soln **use a C- function linked to *Mathematica *through* MathLink *and study its output with c ^{2} test.

**GammaBetta and GammaBetta-soln **give you in brief the definition, properties and usage of Gamma and Beta functions, their integration and derivation, Euler integrals and constant and more. 3 problems on the subject are included.