Introduction to Partial Differential Equations
Springer International Publishing (Verlag)
978-3-319-84051-2 (ISBN)
Within each section the author creates a narrative that answers the five questions:
- What is the scientific problem we are trying to understand?
- How do we model that with PDE?
- What techniques can we use to analyze the PDE?
- How do those techniques apply to this equation?
- What information or insight did we obtain by developing and analyzing the PDE?
David Borthwick, Department of Mathematics and Computer Science, Emory University, Atlanta, GA 30322
1. Introduction.- 2. Preliminaries.- 3. Conservation Equations and Characteristics.- 4. The Wave Equation.- 5. Separation of Variables.- 6. The Heat Equation.- 7. Function Spaces.- 8. Fourier Series.- 9. Maximum Principles.- 10. Weak Solutions.- 11. Variational Methods.- 12. Distributions.- 13. The Fourier Transform.- A. Appendix: Analysis Foundations.- References.- Notation Guide.- Index.
"The book under review is intended for an introductory course for students. The author gives a balanced presentation that includes modern methods, without requiring prerequisites beyond vector calculus and linear algebra. Concepts and definitions from analysis are introduced only as they are needed in the text." (Dian K. Palagachev, zbMATH 1364.35001, 2017)
| Erscheinungsdatum | 28.02.2019 |
|---|---|
| Reihe/Serie | Universitext |
| Zusatzinfo | XVI, 283 p. 68 illus., 61 illus. in color. |
| Verlagsort | Cham |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Gewicht | 468 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| Mathematik / Informatik ► Mathematik ► Angewandte Mathematik | |
| Naturwissenschaften ► Physik / Astronomie | |
| Schlagworte | heat equation • Laplace equation • Linear equations • Mathematical Analysis • Partial differential equations • wave equation |
| ISBN-10 | 3-319-84051-7 / 3319840517 |
| ISBN-13 | 978-3-319-84051-2 / 9783319840512 |
| Zustand | Neuware |
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