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| 001 | 978-3-031-02434-4 | ||
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| 005 | 20240730163934.0 | ||
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| 008 | 220601s2021 sz | s |||| 0|eng d | ||
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_a10.1007/978-3-031-02434-4 _2doi |
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_aCosta, Peter J. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut _981283 |
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| 245 | 1 | 0 |
_aSelect Ideas in Partial Differential Equations _h[electronic resource] / _cby Peter J Costa. |
| 250 | _a1st ed. 2021. | ||
| 264 | 1 |
_aCham : _bSpringer International Publishing : _bImprint: Springer, _c2021. |
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| 300 |
_aXX, 214 p. _bonline resource. |
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| 336 |
_atext _btxt _2rdacontent |
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| 337 |
_acomputer _bc _2rdamedia |
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| 338 |
_aonline resource _bcr _2rdacarrier |
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_aSynthesis Lectures on Mathematics & Statistics, _x1938-1751 |
|
| 505 | 0 | _aPreface -- 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. | |
| 520 | _aThis 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. | ||
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_aMathematics. _911584 |
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_aSynthesis Lectures on Mathematics & Statistics, _x1938-1751 _981285 |
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