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Our intention in this book is to cover the core material in numerical analysis normally taught to students on degree courses in computer science. The main emphasis is placed on the use of analysis and programming techniques to produce well-designed, reliable mathematical software. The treatment should be of interest also to students of mathematics, science and engineering who wish to learn how to write good programs for mathematical computations. The reader is assumed to have some acquaintance with Pascal programming. Aspects of Pascal particularly relevant to numerical computation are revised and developed in the first chapter. Although Pascal has some drawbacks for serious numerical work (for example, only one precision for real numbers), the language has major compensating advantages: it is a widely used teaching language that will be familiar to many students and it encourages the writing of clear, well structured programs. By careful use of structure and documentation, we have produced codes that we believe to be readable; particular care has been taken to ensure that students should be able to understand the codes in conjunction with the descriptive material given in the book.

Introduction to Numerical Computation in Pascal

1 Fundamental Techniques.- 1 Programming in Pascal.- 2 Principles of Mathematical Software.- 3 Basic Mathematics and Applications.- 4 Real Numbers, Machine Numbers and Errors.- 2 Development of Mathematical Software.- 5 Solution of Non-linear Equations in One Variable: Newton's Method.- 6 Solution of Non-linear Equations in One Variable: Interval Methods.- 7 Systems of Linear Equations.- 8 Numerical Integration: Fixed-point Rules.- 9 Numerical Integration: Adaptive Methods.- Appendix A: Predeclared Mathematical Functions in Pascal.- Appendix B: Summary of the mathlib Library.- Appendix C: The Utility Functions powerr, poweri and roundt.- Appendix D: Notes on Portability.- Solutions to Exercises.- References.