Basic partial differential equations

Author: (USA) Bruck, (USA) Kodas / Country:
Publisher:
Publish Date: 2006-06-01
Features: This book is a differential equations (mathematical physics equations) textbook designed for multiple professional curricula, written based on the authors' years of teaching experience. It is suitable for readers with a basic understanding of engineering calculus, linear algebra, and ordinary differential equations. The book is rich in content, covering the fundamental aspects of applied partial differential equations: characteristic line method, separation of variables, Fourier series, Sturm-Liouville theory, Duhamel's principle, conformal mapping methods, Fourier transforms, Green functions, special functions, and Laplace series, among others. Additionally, the book presents some basic theoretical issues of partial differential equations in a structured manner, such as uniqueness of solutions, maximum principle, the existence of solutions for certain special problems, and partial differential equations on manifolds. It also pays significant attention to the application of partial differential equation mathematical models in physics and mechanics. The book is well-argued, easy to understand, and clearly structured, allowing instructors to select appropriate materials based on the level of their students and curriculum requirements. It provides depth to the content while leaving space for self-study and further exploration for students of varying levels. This book is suitable for undergraduate and graduate students, as well as teachers and researchers in related fields... The book includes the basic content of applied partial differential equations: characteristic line method, separation of variables, Fourier series, Sturm-Liouville theory, Duhamel's principle, conformal mapping methods, etc.