Bücher von Yisong Yang

There are two approaches in the study of differential equations of field theory. The first, finding closed-form solutions, works only for a narrow category of problems. Written by a well-known active researcher, this book focuses on the second, which is to investigate solutions using tools from modern nonlinear analysis.

This engaging textbook for advanced undergraduate students and beginning graduates covers the core subjects in linear algebra. The author motivates the concepts by drawing clear links to applications and other important areas, such as differential topology and quantum mechanics. The book places particular emphasis on integrating ideas from analysis wherever appropriate. For example, the notion of determinant is shown to appear from calculating the index of a vector field which leads to a self-contained proof of the Fundamental Theorem of Algebra, and the Cayley-Hamilton theorem is established by recognizing the fact that the set of complex matrices of distinct eigenvalues is dense. The material is supplemented by a rich collection of over 350 mostly proof-oriented exercises, suitable for students from a wide variety of backgrounds. Selected solutions are provided at the back of the book, making it suitable for self-study as well as for use as a course text.