Solving Polynomial Systems Using Continuation for Engineering and Scientific Problems

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.

Solving Polynomial Systems Using Continuation for Engineering and Scientific Problems 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