Publisher's Synopsis
Uniquely provides fully solved problems for linear partialdifferential equations and boundary value problems
Partial Differential Equations: Theory and Completely SolvedProblems utilizes real-world physical models alongsideessential theoretical concepts. With extensive examples, the bookguides readers through the use of Partial Differential Equations(PDEs) for successfully solving and modeling phenomena inengineering, 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
Each chapter concludes with summaries that outline key concepts.Readers are provided the opportunity to test their comprehension ofthe presented material through numerous problems, ranked by theirlevel of complexity, and a related website features supplementaldata and resources.
Extensively class-tested to ensure an accessible presentation,Partial Differential Equations is an excellent book forengineering, mathematics, and applied science courses on the topicat the upper-undergraduate and graduate levels.
