Select Ideas in Partial Differential Equations
Seiten
2021
Morgan & Claypool Publishers (Verlag)
978-1-63639-097-0 (ISBN)
Morgan & Claypool Publishers (Verlag)
978-1-63639-097-0 (ISBN)
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Provides an introduction to the applications and implementations of partial differential equations. The text familiarizes 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.
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techniques and strategies for the study of nonlinear partial differential equations, including unique and previously unpublished results.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.
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.
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: MATLAB® Commands and Functions
References
Index
| Erscheinungsdatum | 02.08.2021 |
|---|---|
| Reihe/Serie | Synthesis Lectures on Mathematics and Statistics |
| Verlagsort | San Rafael |
| Sprache | englisch |
| Maße | 216 x 279 mm |
| Gewicht | 333 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| Mathematik / Informatik ► Mathematik ► Computerprogramme / Computeralgebra | |
| Naturwissenschaften ► Physik / Astronomie | |
| ISBN-10 | 1-63639-097-8 / 1636390978 |
| ISBN-13 | 978-1-63639-097-0 / 9781636390970 |
| Zustand | Neuware |
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