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Table of Contents for R. H. Rand
Computer Algebra in Applied Mathematics
Research Notes in Mathematics 94
An Introduction to Macsyma
Pitman Advanced Publishing Program Boston London Melbourne

Chapter 1. Introduction to MACSYMA .......................................   1
Example 1. Complex Variables .............................................   1
Example 2. Euler-Lagrange equation .......................................   3
Example 3. First Order O.D.E.'s ..........................................   5
Example 4. Period of a nonlinear oscillator ..............................   9
Example 5. Laplace transforms ............................................  15
Example 6. Eigensolution of a system of O. D. E.'s .......................  18
Exercise. Boundary Value Problem .........................................  25

Chapter 2. Housekeeping in MACSYMA .......................................  31
Disk files ...............................................................  31
Special keys .............................................................  36
The editor ...............................................................  38

Chapter 3. Programming in MACSYMA ........................................  41
Example 1. Taylor series solution of O. D. E's ...........................  42
Example 2. Lagrange'S equations ..........................................  52
Example 3. Hamilton's equations ..........................................  57
Exercise. Laplace Transforms .............................................  64

Chapter 4. Perturbation Methods ..........................................  71
Example 1. Van der Pol's equation ........................................  71
Example 2. Mathieu's equation ............................................  87
Example 3. Duffing's equation ............................................ 124
Questions of convergence ................................................. 135
Exercise. The Two Variable Expansion Method .............................. 145

Epilogue. On Bugs ........................................................ 162

Appendix. Sample Batch program ........................................... 164

Glossary of MACSYMA Functions ............................................ 169

References ............................................................... 175

Index .................................................................... 177