Select Ideas in Partial Differential Equations

2. Auflage 2025
ISBN: 978-3-031-59974-3
Verlag: Springer Nature Switzerland

Buch, Englisch, 241 Seiten, Format (B × H): 173 mm x 246 mm, Gewicht: 642 g

Reihe: Synthesis Lectures on Mathematics & Statistics

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 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. 

Zielgruppe

Graduate

Autoren/Hrsg.

Costa, Peter J.

Fachgebiete

• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Mathematik | Informatik Mathematik Mathematik Allgemein
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Numerische Mathematik
• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis

Inhaltsverzeichnis

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 Three–Dimensional Wave Equation.- An Introduction to Nonlinear Partial Differential Equations.- Raman Scattering and Numerical Methods.- Reaction–Diffusion Equations.- The Hartman–Grobman Theorem.

Über Autor(innen)

Peter 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.