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OverviewThis 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 reaction–diffusion 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. Full Product DetailsAuthor: Peter J. CostaPublisher: Springer International Publishing AG Imprint: Springer International Publishing AG Edition: 2nd ed. 2024 ISBN: 9783031599743ISBN 10: 3031599748 Pages: 231 Publication Date: 19 November 2024 Audience: Professional and scholarly , Professional & Vocational Format: Hardback Publisher's Status: Forthcoming Availability: Not yet available This item is yet to be released. You can pre-order this item and we will dispatch it to you upon its release. Table of ContentsIntroduction.- The Equations of Maxwell.- Laplace's Equation.- Fourier Series, Bessel Functions, and Mathematical Physics .- The Fourier Transform, Heat Conduction, and the Wave Equation.- The Three–Dimensional Wave Equation.- An Introduction to Nonlinear Partial Differential Equations.- Raman Scattering and Numerical Methods.- Reaction–Diffusion Equations.- The Hartman–Grobman Theorem.ReviewsAuthor InformationPeter J. Costa, Ph.D., is a Principal Applied Mathematician at Hologic Incorporated in Marlborough, MA. Dr. Costa is the co–creator 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. Tab Content 6Author Website:Countries AvailableAll regions |