Practical Mathematics Using Matlab - Softcover

Backstrom, Gunnar

Softcover

ISBN 10: 9144015526 ISBN 13: 9789144015521

Publisher: Professional Pub Service, 2000

Synopsis

Mathematics for science and engineering undergraduates. Demonstrates basic numerical algorithms by comparison with analytic results. Explains applied mathematics in terms of elementary arithmetic. Teaches elementary programming by means of MATLAB. The MATLAB student editions are sufficient.

About this title

About the Author

Gunnar Backstrom has served as a senior lecturer at Uppsala University, Sweden, and later as professor of physics at Umea University. He has also produced several books on the fields of physics, illustrated by the solution of partial differential equations.

From the Back Cover

This volume is intended to be a guide for individual study or supervised courses in applied mathematics for scientists at undergraduate level. It may serve as an entry to college mathematics by introducing concepts in a striking manner or it may be used to illustrate the conventional, rather abstract, courses offered at universities.

This book is based on the student versions of MATLAB 5, which provide unique means for exploring algebra and calculus by a minimum of commands and syntactic rules.

In the first few chapters, MATLAB is used as an ordinary calculator. The concept of vectors is then introduced, and these serve as tools for drawing curves. The graphics is used in a direct way to find zeros, extreme points and limits, so that the relation to elementary arithmetic becomes obvious.

By very simple and concrete methods the reader is guided through algebra, calculus, probability theory and curve fitting, ordinary differential equations, and Fourier analysis. The student is supposed to type the short scripts employed, thus gradually becoming acquainted with basic programming.

Each group of subjects is completed by an introduction to the symbolic facilities of MATLAB. In this part of the software, the recipes of traditional mathematics are available, and analytic results may be obtained with little effort.

Excerpt. © Reprinted by permission. All rights reserved.

How to use this Book

This volume aspires to confer understanding of mathematics by visual and intuitive means. It also aims to instill confidence in mathematics, but by numerical verifications rather than by proofs. Detailed proofs are strictly an affair between the Mathematician and his Creator.

The research material exploited in this work dates from before 1900. The main theorems are products of giant minds, and academics have since verified them in a variety of ways. No one seriously doubts the validity of this mature part of mathematics. It could thus be taken as our cultural heritage, not to be questioned or revised.

The problem is how to incorporate mathematics into one's stock of knowledge and skill. The author believes the answer is learning by doing. The doing need not extend to first principles, however. To save time, one should compile blocks of knowledge, which later can serve as tools for more advanced tasks. It is important to inspect the structure of a tool, in order to gain confidence, but each tool can soon be regarded as a black box. The next step is to understand what the tool can do for you, and here simple, practical demonstrations are preeminent.

In this book, we learn to master mathematics by means of the MATLAB program package, which contains a large number of tools, in the form of black boxes. The essential purpose is to verify that these tools produce results in agreement with known results of mathematics.

Here are a few principles to keep in mind while working with this book.

Do not be afraid of making errors. The computer does not go up in smoke, and by correcting errors you learn the syntax of MATLAB.

It is not enough to read the book. It shows a large number of results, but running the files yields additional figures that are essential to understanding.

Typing command lines and files is a way of learning. These lists express the principles and practice of mathematical verification, and the command words constitute the language of MATLAB.

As you work with script files, take the opportunity of displaying more than is normally shown. A statement closed by a semicolon does not display numerical values, but you can gain more insight by peeking at intermediary results. When you have learnt what is hidden, close the statement again.

Be inquisitive! Do not accept MATLAB statements until you understand what they do. Make a small test of your own, on one line if possible, otherwise by a short script file. Occasionally modify examples in the book to watch the effect.

Allot time for the exercises. Some of them are simple variations of examples in the same chapter. Others expect you to be more independent. The important thing is to be active.

Learn by doing!

Edition details

• Publisher: Professional Pub Service
• Publication date: 2000
• Language: English
• ISBN 10: 9144015526
• ISBN 13: 9789144015521
• Binding: Paperback
• Number of pages: 252