Mathematical and Physical Equations

Author: Wu Fangtong (Editor)
Publisher:
Publish Date: 2001-11-01
Features: This book carefully selects and arranges materials, fully considering the progressive nature of knowledge acquisition for readers. The introduction of new concepts is designed to avoid disconnecting from the explanation of classical theories. Therefore, after introducing the derivation of equations in Chapter 1, Chapter 2 demonstrates various classical solution methods by solving typical problems, providing readers with a practical understanding of the solutions and well-posedness of mathematical physics problems. This naturally leads to Chapter 3, which introduces the general theory of partial differential equations, including concepts such as classification and well-posedness. The next three chapters focus on the fundamental solutions of three typical types of equations, as well as Green's functions, a priori estimates, and energy methods for various boundary value problems. Finally, Chapter 7 introduces generalized solutions and variational methods. Additionally, new concepts such as generalized functions, Fourier transforms, and Sobolev spaces are introduced as needed based on the context of the problems discussed. The content is concise and to the point, without dedicating separate chapters for rigorous explanations. Of course, this may not meet the standards of strict mathematical rigor. However, the author's primary focus is on the applications of these concepts. It is more important to know how they are applied rather than their theoretical perfection. This is similar to how functions are perceived by physicists and engineers—what matters most is their practicality in solving problems, not the intricacies of their theory. The author's approach is intended to open a "window" for readers, showcasing the role and significance of these new concepts in solving mathematical physics problems, and providing clues for further exploration of related fields. Interested readers can delve deeper into specialized books on these topics.