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Full Description
This book introduces the numerical technique of polynomial continuation, which is used to compute solutions to systems of polynomial equations. Originally published in 1987, it remains a useful starting point for the reader interested in learning how to solve practical problems without advanced mathematics.
It is easy to understand, requiring only a knowledge of undergraduate-level calculus and simple computer programming. The book is also practical; it includes descriptions of various industrial-strength engineering applications and offers Fortran code for polynomial solvers on an associated Web page. It provides a resource for high-school and undergraduate mathematics projects.
Contents
Preface to the Classics Edition
Preface
Introduction
Part I: The Method: Chapter 1: One Equation in One Unknown
Chapter 2: Two Equations in Two Unknowns
Chapter 3: General Systems
Chapter 4: Implementation
Chapter 5: Scaling
Chapter 6: Other Continuation Methods
Part II: Applying the Method: Chapter 7: Reduction
Chapter 8: Geometric Intersection Problems
Chapter 9: Chemical Equilibrium Systems
Chapter 10: Kinematics of Mechanisms
Appendices: Appendix 1: Newton's Method
Appendix 2: Emulating Complex Operations in Real Arithmetic
Appendix 3: Some Real-Complex Calculus Formulas
Appendix 4: Proofs of Results from Chapter 3
Appendix 5: Gaussian Elimination for System Reduction
Appendix 6: Computer Programs
Bibliographies and References
Brief Bibliography
Addition Bibliography
References
Index
