Elements of Partial Differential EquationsGeared toward students of applied rather than pure mathematics, this volume introduces elements of partial differential equations. Its focus is primarily upon finding solutions to particular equations rather than general theory. Topics include ordinary differential equations in more than two variables, partial differential equations of the first and second orders, Laplace's equation, the wave equation, and the diffusion equation. A helpful Appendix offers information on systems of surfaces, and solutions to the odd-numbered problems appear at the end of the book. Readers pursuing independent study will particularly appreciate the worked examples that appear throughout the text. |
Other editions - View all
Common terms and phrases
applied arbitrary assume axis boundary bounded called characteristic charge complete integral conducting consider constant contains continuous coordinates corresponding curve cylinder Deduce defined denotes density derivatives determine diffusion direction displacement distance eliminating envelope equal equivalent Example exists expression Figure find first first-order follows Fourier function f given harmonic Hence independent infinite initial integral integral surface interior intersection known Laplace’s equation lies linear method motion normal obtain origin partial differential equation particular passes physical plane position potential prescribed problem Prove radius readily reduces region relation respect result satisfies satisfy Show shown side simple solution solve space sphere string Substituting Suppose temperature theorem theory transform uniform unit variables vector velocity wave equation write written zero