第四章 The Laplace Equation, 4-1 Greens Identity, Fundamental Solutions, and Poissons Equation

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第四章 The Laplace Equation, 4-1 Greens Identity, Fundamental Solutions, and Poissons Equation

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

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