Mathematica as a Tool

An introduction with practical examples
1994
ISBN: 978-3-7643-5031-4
Verlag: Springer

Buch, Englisch, 430 Seiten, Paperback, Format (B × H): 178 mm x 254 mm, Gewicht: 837 g

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.

Zielgruppe

Research

Autoren/Hrsg.

Kaufmann, Stephan

Fachgebiete

• Naturwissenschaften Chemie Chemie Allgemein Chemometrik, Chemoinformatik
• Technische Wissenschaften Technik Allgemein Computeranwendungen in der Technik
• Technische Wissenschaften Technik Allgemein Mathematik für Ingenieure
• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Mathematik | Informatik EDV | Informatik Professionelle Anwendung Computer-Aided Design (CAD)
• Mathematik | Informatik EDV | Informatik Business Application Mathematische & Statistische Software
• Mathematik | Informatik EDV | Informatik Angewandte Informatik Computeranwendungen in Wissenschaft & Technologie
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Computeranwendungen in der Mathematik

Inhaltsverzeichnis

1. Basics.- 1.1 Getting Started.- 1.2 Help!.- 1.3 Numerical Calculations.- 1.4 Symbolic Calculations.- 1.5 Plots: Different Pendulums.- 1.6 Lists.- 1.7 Graphics Programming.- 1.8 More Selected Tools.- 2. Structure.- 2.1 Expressions.- 2.2 Patterns.- 2.3 Transformation Rules and Definitions.- 2.4 Evaluation and Tools for Programming.- 2.5 Modularity.- 2.6 Strings, Text, Messages.- 3. Programming.- 3.1 Programming Methodologies.- 3.2 Developing Programs.- 3.3 Numerics.- 3.4 Long Calculations: RSA.- References.