Mathematical Physics Equations: Fourier Analysis and Its Applications (English Version)

Author: Gerald B. Folland (USA)
Publisher:
Publishing Date: Not available
Features: The main feature of this book is to present the method of Fourier analysis as a tool for solving physical and engineering problems. The author aims to make the book suitable for both engineering professionals and pure mathematicians. The author begins by introducing the background of basic mathematical physics problems, then discusses the fundamental theory of Fourier series. In handling convergence issues, only piecewise smooth functions are involved, and then the L2 theory is introduced, with the prerequisite of acknowledging the Lebesgue integral theory. The book takes Fourier analysis as the main thread and aims to develop relevant mathematical theories to solve typical mathematical physics equations, making it a textbook for mathematical physics courses. It is suitable for senior undergraduate and graduate students in mathematics, physics, and engineering programs at comprehensive universities and engineering universities in China. The requirements for studying this book are a foundation in calculus, ordinary differential equations, and basic complex analysis. From the content of the book, the author's mathematical expertise is quite deep, as the mathematical theory is clearly and clearly explained when combined with practical equations. The course of mathematical physics itself is highly comprehensive and applied, with relatively low theoretical difficulty but a wide range of knowledge and broad basic requirements. There are not many good textbooks on mathematical physics equations in China. This book can meet the needs of domestic teaching, and its structure centered on Fourier analysis and relatively clear and rigorous logical arrangement are highly commendable. Of course, from a purely mathematical perspective, the theoretical depth of the book's content is not very high, so it is highly readable and has a wide readership.