Mathematical Routes to the Physical World

Mathematical physics is a fundamental course for undergraduate students in physics and is crucial for subsequent physics courses such as Electrodynamics and Quantum Mechanics. Currently, there are numerous textbooks, but most of them tend to be concise, focusing more on problem-solving methods and lacking in-depth explanations of the underlying mathematical and physical thoughts.In this book we have added and deepened topics such as analytic function theory, elliptic functions, conformal mapping, and conformal self-mapping, as well as systematic explanations of Hilbert space, eigenvalue theory, and Green’s function theory. Regarding the structure of the book, we have introduced ENDNOTEs at the ends of most sections to extend the main text. These endnotes attempt to explore the origin and evolution of mathematical concepts, revealing the intrinsic connections between various phenomena in mathematics and physics. We do not emphasize strict logic but focus on broadening thinking and providing intuitive explanations, making it easier for readers to understand and grasp the essence of the ideas. Readers can skim and contemplate them independently, extending their horizons and effectively addressing the contradiction between teaching content and limited class hours.