第三章 Characteristic Manifolds and Cauchy Problem, 3-5 The Uniqueness Theorem of Holmgren
| Week | Course Content | Course Video |
|---|---|---|
| 第一章 The Single First-Order Equation 1-1 Introduction | Watch Online | |
| 第一章 The Single First-Order Equation 1-2 Examples | Watch Online | |
| 第一章 The Single First-Order Equation 1-3 Analytic Solution and Approximation methods in a simple example | Watch Online | |
| 第一章 The Single First-Order Equation 1-4 Quasilinear Equation | Watch Online | |
| 第一章 The Single First-Order Equation 1-5 The Cauchy Problem for the Quasilinear-linear Equations | Watch Online | |
| 第一章 The Single First-Order Equation 1-6 Examples | Watch Online | |
| 第一章 The Single First-Order Equation 1-7 The general first-order equation for a function of two variables | Watch Online | |
| 第一章 The Single First-Order Equation 1-8 The Cauchy Problem | Watch Online | |
| 第一章 The Single First-Order Equation 1-9 Solutions generated as envelopes | Watch Online | |
| 第二章 Second-Order Equations: Hyperbolic Equations for Functions of Two Independent Variables 2-1 Characteristics for Linear and Quasilinear Second-Order Equations | Watch Online | |
| 第二章 Second-Order Equations: Hyperbolic Equations for Functions of Two Independent Variables 2-2 Propagation of Singularity | Watch Online | |
| 第二章 Second-Order Equations: Hyperbolic Equations for Functions of Two Independent Variables 2-3 The Linear Second-Order Equation | Watch Online | |
| 第二章 Second-Order Equations: Hyperbolic Equations for Functions of Two Independent Variables 2-4 The One-Dimensional Wave Equation | Watch Online | |
| 第二章 Second-Order Equations: Hyperbolic Equations for Functions of Two Independent Variables 2-5 System of First-Order Equations | Watch Online | |
| 第二章Second-Order Equations: Hyperbolic Equations for Functions of Two Independent Variables 2-6 A Quasi-linear System and Simple Waves | Watch Online | |
| 第三章 Characteristic Manifolds and Cauchy Problem 3-1 Natation of Laurent Schwartz | Watch Online | |
| 第三章 Characteristic Manifolds and Cauchy Problem 3-2 The Cauchy Problem | Watch Online | |
| 第三章 Characteristic Manifolds and Cauchy Problem 3-3 Real Analytic Functions and the Cauchy-Kowalevski Theorem | Watch Online | |
| 第三章 Characteristic Manifolds and Cauchy Problem 3-4 The Lagrange-Green Identity | Watch Online | |
| 第三章 Characteristic Manifolds and Cauchy Problem 3-5 The Uniqueness Theorem of Holmgren | Watch Online | |
| 第三章 Characteristic Manifolds and Cauchy Problem 3-6 Distribution Solutions | Watch Online | |
| 第四章 The Laplace Equation 4-1 Greens Identity, Fundamental Solutions, and Poissons Equation | Watch Online | |
| 第四章 The Laplace Equation 4-2 The Maximal Principle | Watch Online | |
| 第四章 The Laplace Equation 4-3 The Dirichlet Problem, Greens Function, and Poisson Formula | Watch Online | |
| 第四章 The Laplace Equation 4-4 Perrons method | Watch Online | |
| 第四章 The Laplace Equation 4-5 Solution of the Dirichlet Problem by Hilbert-Space Methods | Watch Online |
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