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Die Mathematica Applications Library

Mathematica hat sich in den vergangenen Jahren als unentbehrliches Werkzeug im Ingenieurwesen etabliert. Es bietet dem professionellen Anwender, durch seinen mächtigen und fortschrittlichen Funktionsumfang, eine unerreichte Flexibilität bei der Analyse, Modellierung und Visualisierung der während der täglichen Ingenieurarbeit anfallenden Daten. Im Sommer 1994 startete Wolfram Research die Veröffentlichung der Mathematica Anwendungs-Pakete, die dem Benutzer sofort einsetzbare Funktionen aus speziellen Anwendungsbereichen bieten. Dem Anwender wird durch diese Pakete der schrittweise Einstieg in die Thematik bis zum Expertenwissen leicht gemacht. Die Zahl der Zusatzpakete wurde seit dieser Zeit auf über 30 Zusatzpakete erweitert.

Ein Übersicht zu den Zusatzpaketen ist aktuell im INTERNET zu finden.

http://www.additive-net.de/software/mathematica/packages/mma.packages.shtml

About Wavelet Explorer

Wavelet Explorer is designed to provide users with convenient Mathematica tools that can be used in the study, exploration, and application of wavelets. In Wavelet Explorer we not only introduce the Mathematica functions and their usage but also explain the key aspects of the theoretical framework so it can be as self-contained as possible. Wavelet Explorer consists of a Mathematica package, this manual, and data files. 
Mathematica packages are collections of programs written in the Mathematica language, so Wavelet Explorer can only be used in conjunction with Mathematica. The package provided with Wavelet Explorer is Wavelets.m. It contains many of the functions and utilities necessary for both exploring wavelet theory and applying wavelet analysis to real data.
The purpose of this manual is twofold. Apart from introducing and illustrating the use of the functions contained in the package Wavelets.m, it also aims to provide some theoretical background on wavelets. The theoretical background provided in this manual is more extensive than in the usual manuals of this kind partly because existing materials on wavelet theory tend to be rather mathematical; this manual is designed for those whose primary goal is to understand the ideas behind wavelet theory and to use wavelet analysis as a tool in their field of application. 
This manual consists of three parts. Part 1, Fundamentals of Wavelets, provides the user with the basic ideas behind wavelet theory as well as with illustrative examples of using Mathematica to acquire intuitive understanding. It is meant to be an introduction to some of the mathematical aspects of wavelet theory. The emphasis is on basic ideas and logical structure, and the level of mathematical rigor can only be described as informal. For those who want to pursue detailed derivations, appropriate references are given at the end of the manual. The usage of the Mathematica functions introduced in Part 1 is further illustrated in Part 2 of the manual, Further Examples and Applications. Some data sets and images are analysed and additional utility functions are introduced. Part 3, Summary of Functions, summarizes all the Mathematica functions provided in the first two parts of the manual and gives simple examples illustrating the syntax and usage of the functions. Those formulas that help define terms and notations are again included in this part. This concise summary is meant to be a quick and handy reference to the functions in the package. 
Data sets used in the application examples are also provided with Wavelet Explorer so the results of the examples can be reproduced if desired. These data sets are contained in data files, which can be found in the subdirectory Data of the Wavelets directory.

Where to Find More Information about Mathematica

An elementary familiarity with the Mathematica language is required to use Wavelet Explorer. For general information on using Mathematica, see The Mathematica Book, Third Edition, by Stephen Wolfram. Many other publications on Mathematica are also available. For a complete listing see the Mathematica Products Catalog, available from Wolfram Research, Inc.

Installing and Loading Wavelet Explorer

Wavelet Explorer is easy to install. Make sure you have Mathematica installed on your computer and follow the steps described on the installation card. First you should decide on a directory where you would like to put Wavelet Explorer. Suppose you choose to install it in a directory called MathApps; the installation program will create a subdirectory Wavelets for Wavelet Explorer within the MathApps directory. All the data files will then be in the subdirectory Data of the Wavelets directory. After installing Wavelet Explorer, you must add the directory MathApps to the $Path variable. The installation card tells you how to do it. Once you have done so, you can load the Wavelets.m package as follows.

This loads the package Wavelets.m.

Needs["Wavelets`Wavelets`"]