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Introduction to Partial Differential Equations
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| 概要 | This modern take on partial differential equations does not require knowledge beyond vector calculus and linear algebra. The author focuses on the most important classical partial differential equatio...ns, including conservation equations and their characteristics, the wave equation, the heat equation, function spaces, and Fourier series, drawing on tools from analysis only as they arise.Within each section the author creates a narrative that answers the five questions: (1) What is the scientific problem we are trying to understand? (2) How do we model that with PDE? (3) What techniques can we use to analyze the PDE? (4) How do those techniques apply to this equation? (5) What information or insight did we obtain by developing and analyzing the PDE? The text stresses the interplay between modeling and mathematical analysis, providing a thorough source of problems and an inspiration for the development of methods.続きを見る |
| 目次 | 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.続きを見る |
| 冊子版へのリンク | https://hdl.handle.net/2324/1001620805 |
| 本文を見る | Springer Nature Mathematics and Statistics (R0) eBooks 2016 English/International: 2016 |
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| 登録日 | 2023.09.29 |
| 更新日 | 2024.01.30 |