Mathematical Methods of Mechanics

Author: Zhang Jiyuan (Compiler)
Publisher:
Publishing Date: 2003-01-01
Features: This book includes common direct and iterative methods for solving systems of linear algebraic equations; general iterative methods for nonlinear algebraic equations; Newton-Raphson method and Zhan Zhongxi method; globally convergent solution methods: interval analysis, homotopy method, and elimination method; function approximation methods (including interpolation approximation, uniform approximation, square approximation, and function fitting); common algorithms for numerical differentiation and numerical integration; effective solution methods for nonlinear differential equations; practical algorithms for constrained optimization problems; augmented Lagrangian method, direct solution methods, and genetic algorithms, as well as the promising new solution method—decomposition method. The book also presents multiple new algorithms proposed or improved by the author. The entire content forms a systematic approach to solving common mathematical models in mechanical engineering. This book has three key features: first, the content is relatively novel and the methods are innovative; second, the methods are practical and highly targeted; third, the language is easy to understand. It is a comprehensive work on nonlinear problem-solving methods that covers a wide range, has a certain depth, offers novelty, and to some extent meets engineering needs. It holds significant value for engineering technicians, researchers, university teachers, and graduate students who did not major in mathematics. As long as readers have a college undergraduate level, a grasp of basic advanced mathematics theory, and some knowledge of computer programming languages, they can understand and use this book with effort.