Partial Differential Equations

P. R. Garabedian

• Publisher: American Mathematical Society
• Year: 2023
• Topic: Mathematics
• eBook ISBN:
  9781470475192
• Subtopic: Mathematics General
• Index: Mathematics

From a review of the original edition: This book is primarily a text for a graduate course in partial differential equations, although the later chapters are devoted to special topics not ordinarily covered in books in this field … [T]he author has made use of an interesting combination of classical and modern analysis in his proofs … Because of the author's emphasis on constructive methods for solving problems which are of physical interest, his book will likely be as welcome to the engineer and the physicist as to the mathematician … The author and publisher are to be complimented on the general appearance of the book. —Mathematical Reviews This book is a gem. It fills the gap between the standard introductory material on PDEs that an undergraduate is likely to encounter after a good ODE course (separation of variables, the basics of the second-order equations from mathematical physics) and the advanced methods (such as Sobolev spaces and fixed point theorems) that one finds in modern books. Although this is not designed as a textbook for applied mathematics, the approach is strongly informed by applications. For instance, there are many existence and uniqueness results, but they are usually approached via very concrete techniques. The text contains the standard topics that one expects in an intermediate PDE course: the Dirichlet and Neumann problems, Cauchy's problem, characteristics, the fundamental solution, PDEs in the complex domain, plus a chapter on finite differences, on nonlinear fluid mechanics, and another on integral equations. It is an excellent text for advanced undergraduates or beginning graduate students in mathematics or neighboring fields, such as engineering and physics, where PDEs play a central role.

Table of contents

• Front Cover
• Preface
• Contents
• 1 The Method of Power Series
• 2 Equations of the First Order
• 3 Classification of Partial Differential Equations
• 4 Cauchy's Problem for Equations with Two Independent Variables
• 5 The Fundamental Solution
• 6 Cauchy's Problem in Space of Higher Dimension
• 7 The Dirichlet and Neumann Problems
• 8 Dirichlet's Principle
• 9 Existence Theorems of Potential Theory
• 10 Integral Equations
• 11 Eigenvalue Problems
• 12 Tricomi's Problem; Formulation of Well Posed Problems
• 13 Finite Differences
• 14 Fluid Dynamics
• 15 Free Boundary Problems
• 16 Partial Differential Equations in the Complex Domain
• Bibliography
• Index
• Back Cover