Select Ideas in Partial Differential Equations

This book provides a concise but thorough introduction to partial differential equations which model phenomena that vary in both space and time. The author begins with a full explanation of the fundamental linear partial differential equations of physics. The text continues with methods to understand and solve these equations leading ultimately to the solutions of Maxwell's equations. The author then addresses nonlinearity and provides examples of separation of variables, linearizing change of variables, inverse scattering transform, and numerical methods for select nonlinear equations. Next, the book presents rich sources of advanced techniques and strategies for the study of nonlinear partial differential equations. This second edition includes updates, additional examples, and a new chapter on reactiondiffusion equations. Ultimately, this book is an essential resource for readers in applied mathematics, physics, chemistry, biology, and engineering who are interested in learning about the myriad techniques that have been developed to model and solve linear and nonlinear partial differential equations.

Includes MATLAB code to help the reader visualize, provide analytic solutions, and help better understand the theory Provides exercises, figures, tables, and worked examples to enhance reader understanding Presents previously unpublished material using functional analysis, including the HartmanGrobman Flow Theorem

Autorentext

Peter J. Costa, Ph.D., is a Principal Applied Mathematician at Hologic Incorporated in Marlborough, MA. Dr. Costa is the cocreator of MATLAB's Symbolic Math Toolbox. He has developed mathematical methods for the diagnosis of cervical cancer, tracking of airborne vehicles, the diffusion of nonlinear optical systems, and the transmission of infectious diseases through a population. His research interests include mathematical physics and mathematical biology. He received the Ph.D. in Applied Mathematics, specializing in nonlinear partial differential equations, from the University of Massachusetts at Amherst.

Inhalt

Introduction.- The Equations of Maxwell.- Laplace's Equation.- Fourier Series, Bessel Functions, and Mathematical Physics .- The Fourier Transform, Heat Conduction, and the Wave Equation.- The ThreeDimensional Wave Equation.- An Introduction to Nonlinear Partial Differential Equations.- Raman Scattering and Numerical Methods.- ReactionDiffusion Equations.- The HartmanGrobman Theorem.