偏微分方程   [Outline]

1. Introduction  to PDE  1.1 Boundary and Initial Value Problems   1.2 Classification

2. Transport Equations   2.1 Derivation of General Solution    2.2 Particular Solution

3. First order semilinear equations    3.1 The Method of Characteristics  3.2 [First Order Equation]    Second Order PDE  

4. Wave Equations   4.1 Derivation of the General Solution    (1)Factoring the Operator (2) Change of Variables    4.2 Derivation of Particular Solution

5. Properties of the Wave Equation on R     5.1 Causality    5.2 Wave eq with One Boundary Condition     5.3 General Boundary Condition

6. Heat Equation(Diffusion Equation)  6.1 Fundametal Solution     6.2 Particular Solution to the Homogeneous(Inhomogeneous) IVP

6.3 Properties of the Heat Equation    6.4 Well-Posed  and Symmetry   6.5 Maximum Principle

7. Eigenvalue Problems  7.1 Common Eigenvalue Problems  872 Orthogonality of Eigenfunctions
8. Fourier Series
9. Separation of Variables      Separation of Variables
10. Laplace's Equation on Circular Domains
11. Properties of Laplace's Equation in R^2
12. Fourier Transform   Plancherel's theorem

1. Introduction to Partial Differential Equations       Peter J. Olver
2. An Introduction to PDE                                      Walter A. Strauss
3. A Basic Course in PDE    Qing Han(韓青Notre Dame大學)  [ResearchGate]
4. Partial Differential Equations                              Christopher C. Tisdell (有YouTube講解)
5. Partial Differential Equations in Action              Gianmaria Verzini       有Exercises and Solved Problems
6. Methods for PDE                                                Marcelo R.Ebert     Michael Reissig    [ResearchGate]
7. Justin Ko  [Justin Ko]
8. Lectures on PDE                                                 Vladimir I. Arnold
9. Methods of Mathematical Physics(II)                 R.Courant and D.Hilbert
10. Geometry of PDE                                               Paul Bracken   [ResearchGate]
11. Partial Differential Equations with Mathematica and Maple      Ioannis P. Stavroulakis   Stepan A Tersian
12. Advanced Calculus for Applications                  Peter D. Lax   Maria Shea Terrell  Ch 9
13. 教科書/參考書書評  (2)PDE   Lawrence C. Evans   (3)PDE   Fritz John   (4)Elliptic PDE of second order   David Gilbarg,Neil S. Trudinger

1. [偏微分方程的方法---丘成桐]
2. 有朋自遠方來---(1) 陳恕行  (2) Neil Trudinger---汪徐家(Xu-Jia Wang)   Peter Lax (2)]
3. Nonlinear PDE國際會議---紀念Neil Trudinger (1942--)   [A Glimpses of PDE]
4. What is the geometric PDE ?