Alternative Mathematics using MATLAB 7

Self-instructive text on undergraduate algebra, statistics, differential and integral calculus.

This e-book is based on the Student Edition of MATLAB 7, which includes a symbolic toolbox. The Professional Edition may of course also be used. The goal is to exploit a restricted subset of MATLAB commands and functions to explore most of the elements of undergraduate mathematics. All items from simple algebra to Fourier analysis are reduced to basic arithmetic operations. Sample chapters of the book may be downloaded from
http://www.phys.umu.se/gunnar
which includes ordering information.

Begin by including the unzipped M-files in the current MATLAB folder \work. To run one of these files, enter its name in the MATLAB Command Window.

TABLE OF CONTENTS
1 Introduction 1
2 MATLAB as a Calculator 6
3 Geometric Applications 13
4 Vectors in (x, y) and (x, y, z) 18
5 General Vectors 25
6 Systems of Linear Equations 31
7 Plotting Functions 38
8 Script Files 43
9 Functions and Function Files 50
10 Zeros and Extreme Points 62
11 Symbolic Algebra 70
12 Limits 77
13 Derivatives 82
14 Sums 89
15 Integrals 94
16 Symbolic Calculus 101
17 Random Events and Statistics 110
18 Curve Fitting (Optional) 122
19 First-Order Differential Equations 136
20 Second-Order ODEs 150
21 Symbolic Solutions to ODEs 161
22 Functions of Two Variables 169
23 Complex Numbers and Functions 177
24 Fourier Series 188
25 Fourier Transforms 199
Appendix: Fast Fourier Transforms 221
Appendix: Eigenvalues and Eigenvectors 226
Conclusion 237
Vocabulary of MATLAB 238