Mathematica as a Tool: An introduction with practical examples

ISBN-13: 9783764350314 / Angielski / Miękka / 1994 / 430 str.

Stephan Kaufmann

Opis

More than ten years ago, I wanted to carry out coordinate transformations for Hamiltonian systems, in order to discuss the stability of certain equilibrium posi tions. Basically, the calculations only involved rational expressions, but they turned out to be extremely complicated, because the third and fourth order terms had to be included. After several months of filling whole blocks of paper with for mulas, I was close to resignation. But, by a lucky incident, I met a colleague who showed me the computer algebra package Reduce. It still required a lot of patience and tricks, but Reduce finally did produce the desired results. After this experience, I wondered, why only a few engineers and scientists were aware of the strengths of such computer algebra programs. The mathematical treatment of scientific problems often leads to calculations which can only be solved "by hand" with a considerable investment of time, while a suitable com puter algebra program produces the solution within a couple of seconds or min utes. Even if a closed symbolic solution is not possible, such programs can often simplify a problem, before the cruder tool of numerical simulations is applied."

Recenzje

"Provides engineers, scientists, and applied mathematicians with a compact introduction to Mathematica, a software program combining computer algebra, graphics, animations, an elegant programming language, and numerical tools. Helps readers gain the skills necessary to use the program as a tool in their work."
-- Journal of Economic Literature

"This book is a valuable introductory textbook on Mathematica and is very useful to scientists and engineers who use Mathematica in their work."
-- Zentralblatt Math

"This book is very nicely written and recommended to everybody."
-- EMS Newsletter

Spis treści

1. Basics.- 1.1 Getting Started.- 1.1.1 Starting and Quitting.- 1.1.2 Interrupting and Quitting.- 1.2 Help!.- 1.3 Numerical Calculations.- 1.3.1 Simple Examples.- 1.3.2 External Packages: Units.- 1.3.3 Large Numbers: The RSA Public-Key Cryptosystem.- 1.4 Symbolic Calculations.- 1.4.1 Polynomials.- 1.4.2 Equations.- 1.4.3 Calculus.- 1.5 Plots: Different Pendulums.- 1.5.1 Two-Dimensional Plots.- 1.5.2 Example: The Triple Pendulum.- 1.5.3 Three-Dimensional Graphics and Animation: A Rotating Double Pendulum.- 1.5.4 Parametric Plots: A Rotating Double Pendulum.- 1.5.5 Plotting Data: The Random Generator.- 1.6 Lists.- 1.6.1 Creating and Formatting Lists.- 1.6.2 Calculations with Lists, Pure Functions.- 1.6.3 List Manipulation: The Cross Product.- 1.6.4 Vectors, Matrices, Tensors: The Jacobian.- 1.6.5 Eigenvectors and Eigenvalues: An Oscillator.- 1.7 Graphics Programming.- 1.7.1 The Structure of Graphics.- 1.7.2 Example: Animation of the Triple Pendulum.- 1.7.3 Example: The Oscillator.- 1.8 More Selected Tools.- 1.8.1 Graphics and Sound.- 1.8.2 Complex Numbers.- 1.8.3 Sums, Products, Series.- 1.8.4 Data Analysis,Interpolation.- 1.8.5 Transformations.- 1.8.6 Mathematical Functions.- 1.8.7 Polynomials.- 1.8.8 Linear Algebra, Linear Programming.- 1.8.9 File Manipulation.- 1.8.10 Custom Configuration.- 1.8.11 Resources.- 2. Structure.- 2.1 Expressions.- 2.1.1 The Structure of Expressions.- 2.1.2 Working with Parts of Expressions.- 2.2 Patterns.- 2.2.1 Simple Patterns.- 2.2.2 Restricted Patterns.- 2.2.3 More Complicated Patterns.- 2.2.4 Example: A Simple Integrator.- 2.3 Transformation Rules and Definitions.- 2.3.1 Transformation Rules.- 2.3.2 Definitions.- 2.3.3 Attributes.- 2.4 Evaluation and Tools for Programming.- 2.4.1 Standard Evaluation.- 2.4.2 Special Evaluation.- 2.4.3 Conditionals, Loops, and Control Structures.- 2.5 Modularity.- 2.5.1 Local Variables and Constants.- 2.5.2 Contexts and Packages.- 2.6 Strings, Text, Messages.- 2.6.1 Printing Text.- 2.6.2 Arranging Text.- 2.6.3 Built-in Formats.- 2.6.4 Formats for Numbers.- 2.6.5 Subscripts and Superscripts.- 2.6.6 Custom Formats.- 2.6.7 Strings.- 2.6.8 Messages.- 3. Programming.- 3.1 Programming Methodologies.- 3.1.1 Procedural Programming.- 3.1.2 Recursive Programming.- 3.1.3 Functional Programming.- 3.1.4 Rule-Based Programming.- 3.1.5 Programming with Constraint-Propagation.- 3.1.6 Data Types, Object-Oriented Programming.- 3.2 Developing Programs.- 3.2.1 Debugging.- 3.2.2 Example: NonNegativeQ?.- 3.2.3 Example: AbsArg?.- 3.2.4 Example: RSA?.- 3.2.5 Example: Perturbation?.- 3.3 Numerics.- 3.3.1 Compiling Expressions: Fractals.- 3.3.2 Precision and Accuracy.- 3.3.3 Controlling Numerical Built-in Functions.- 3.4 Long Calculations: RSA.- 3.4.1 Primes for RSA.- 3.4.2 Saving Results in a File.- 3.4.3 External Programs, Calculations in the Background.- References.

O autorze

Dr. Stephan Kaufmann ist Adjunkt und Dozent an der ETH Zürich.