Introduction to partial differential equations

• 作者： Borthwick, David, author.
• 其他作者：
  • SpringerLink (Online service)
• 其他題名：
  • Universitext.
• 出版： Cham : Springer International Publishing :Imprint: Springer
• 叢書名： Universitext,
• 主題： Differential equations, Partial. , Mathematics. , Partial Differential Equations. , Mathematical Applications in the Physical Sciences.
• ISBN： 9783319489360 (electronic bk.) 、 9783319489346 (paper)
• FIND@SFXID: CGU
• 資料類型: 電子書
• 內容註: 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.
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• 摘要註: 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 equations, 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.
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