Preface to Partial Differential Equations: Theory and Completely Solved Problems
This textbook on linear partial differential equations (POEs) consists of two parts. In Part I we present the theory, with an emphasis on completely solved examples and intuition. In Part II we present a collection of exercises containing over 150 explicitly solved problems for linear POEs and boundary value problems. These problems are based on more than 30 years of collective experience in teaching introductory POE courses at several North American universities.
Partial Differential Equations: Theory and Completely Solved Problems utilizes real-world physical models along side essential theoretical concepts. With extensive examples, the book guides readers through the use of Partial Differential Equations(PDEs) for successfully solving and modeling phenomena in engineering, biology, and the applied sciences.
The book focuses exclusively on linear PDEs and how they can besolved using the separation of variables technique. The authorsbegin by describing functions and their partial derivatives whilealso defining the concepts of elliptic, parabolic, and hyperbolicPDEs. Following an introduction to basic theory, subsequentchapters explore key topics including:
• Classification of second-order linear PDEs
• Derivation of heat, wave, and Laplace’sequations
• Fourier series
• Separation of variables
• Sturm-Liouville theory
• Fourier transforms
“The book gives a vivid description of the theory for solving linear PDEs. The excellent method, the expensive use of examples, and the overview of the existing solutions make the book very useful for students and for researchers. It is highly recommended.”
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