偏微分方程 [ODE]
- Introduction
to PDE 1.1 Boundary and Initial Value Problems 1.2
Classification 1.3
Examples
- Transport Equations
2.1 Derivation of General Solution 2.2 Particular Solution
2.3 Examples
- First order semilinear equations
3.1 The Method of Characteristics Second
Order PDE 3.2 Examples [First
Order Equation]
- Wave Equations
4.1 Derivation of the General Solution (1)Factoring the Operator
(2)Change of Variables 4.2 Derivation of Particular Solution 4.3
Examples
- Properties of the Wave Equation on R 5.1 Causality 5.2 Wave
eq with One Boundary Condition 5.3 Examples 5.4 General Boundary
Condition
- Heat Equation(Diffusion Equation) 6.1
Fundametal Solution 6.2 Particular Solution to the Homogeneous(Inhomogeneous)
IVP 6.3 Examples
- Properties of the Heat Equation 7.1 Well-Posed 7.2
Symmetry 7.3 Examples 7.4 Maximum Principle
- Eigenvalue Problems 8.1 Common Eigenvalue Problems 8.2 Orthogonality
of Eigenfunctions 8.3 Examples
- Fourier Series
- Separation of Variables Separation of Variables
- Laplace's Equation on Circular Domains
- Properties of Laplace's Equation in R^2
- Fourier Transform Plancherel's theorem
- [偏微分方程的方法---丘成桐]
[微分方程與物理學]
- 有朋自遠方來---(1) 陳恕行
(2) Neil
Trudinger---汪徐家(Xu-Jia
Wang) Peter
Lax (2)]
- Nonlinear
PDE國際會議---紀念Neil Trudinger (1942--) [A Glimpses
of PDE]
- What is the geometric
PDE ?
- Lectures on PDE Vladimir
I. Arnold
- Justin Ko [Justin
Ko]
- Methods of Mathematical Physics(II) R.Courant
and D.Hilbert
- Partial Differential Equations Christopher C. Tisdell (有YouTube講解)
- Partial Differential Equations in Action Gianmaria Verzini
有Exercises and Solved
Problems
- Methods for PDE Marcelo R.Ebert Michael Reissig
[ResearchGate]
- Geometry of PDE Paul
Bracken [ResearchGate]
- Partial Differential Equations with Mathematica and Maple Ioannis
P. Stavroulakis Stepan
A Tersian