
Select Ideas in Partial Differential Equations
Peter J. Costa(Author)
Springer (Publisher)
Published on 15. June 2021
Book
Paperback/Softback
XX, 214 pages
978-3-031-01306-5 (ISBN)
Description
This text provides an introduction to the applications and implementations of partial differential equations. The content is structured in three progressive levels which are suited for upper-level undergraduates with background in multivariable calculus and elementary linear algebra (chapters 1-5), first- and second-year graduate students who have taken advanced calculus and real analysis (chapters 6-7), as well as doctoral-level students with an understanding of linear and nonlinear functional analysis (chapters 7-8) respectively. Level one gives readers a full exposure to the fundamental linear partial differential equations of physics. It details methods to understand and solve these equations leading ultimately to solutions of Maxwell's equations. Level two addresses nonlinearity and provides examples of separation of variables, linearizing change of variables, and the inverse scattering transform for select nonlinear partial differential equations. Level three presents rich sources of advanced techniques and strategies for the study of nonlinear partial differential equations, including unique and previously unpublished results. Ultimately the text aims to familiarize readers in applied mathematics, physics, and engineering with some of the myriad techniques that have been developed to model and solve linear and nonlinear partial differential equations.
More details
Series
Language
English
Place of publication
Cham
Switzerland
Publishing group
Springer International Publishing
Target group
Professional and scholarly
Illustrations
XX, 214 p.
Dimensions
Height: 280 mm
Width: 216 mm
Thickness: 13 mm
Weight
605 gr
ISBN-13
978-3-031-01306-5 (9783031013065)
DOI
10.1007/978-3-031-02434-4
Schweitzer Classification
Other editions
Additional editions

Peter J. Costa
Select Ideas in Partial Differential Equations
E-Book
06/2022
Springer
€64.19
Available for download
Person
Peter J. Costa, is Principal Applied Mathematician at Hologic Incorporated in Marlborough, MA. Dr. Costa is the co-creator of MATLABs 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 throughout a population. His research interests include mathematical physics and mathematical biology. He received the PhD in Applied Mathematics, specializing in nonlinear partial differential equations, from the University of Massachusetts at Amherst.
Content
Preface.- Acknowledgments.- Introduction.- The Equations of Maxwell.- Laplace's Equation.- Fourier Series, Bessel Functions, and Mathematical Physics.- 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.- The Hartman-Grobman Theorem.- Appendix: MATLABĀ® Commands and Functions.- References.- Index.