目录 Chapter 1 The Single First-Order Equation 1.Introduction 2.Examples 3.Analytic Solution and Approximation Methods in a Simple Example Problems 4.Quasi-linear Equations 5.The Cauchy Problem for the Quasi-linear Equation 6.Examples Problems 7.The General First-Order Equation for a Function of Two Variables 8.The Cauchy Problem 9.Solutions Generated as Envelopes Problems Chapter 2 Second-Order Equations: Hyperbolic Equations for Functions of Two Independent Variables 1.Characteristics for Linear and Quasi-linear Second-order Equations 2.Propagation of Singularities 3.The Linear Second-Order Equation Problems 4.The One-Dimensional Wave Equation Problems 5.Systems of First-Order Equations 6.A Quasi-linear System and Simple Waves Problem Chapter 3 Characteristic Manifolds and the Cauchy Problem 1.Notation of Laurent Schwartz Problems 2.The Cauchy Problem Problems 3.Real Analytic Functions and the Cauchy-Kowalevski Theorem (a) Multiple infinite series Problems (b) Real analytic functions Problems (c) Analytic and real analytic functions Problems (d) The proof of the Cauchy-Kowalevski theorem Problems 4.The Lagrange-Green Identity 5. The Uniqueness Theorem of Holmgren Problems 6.Distribution Solutions Problems Chapter 4 The Laplace Equation 1.Green's Identity, Fundamental Solutions, and Poisson's Equation Problems 2.The Maximum Principle Problems 3.The Dirichlet Problem, Green's Function, and Poisson's Formula Problems 4.Proof of Existence of Solutions for the Dirichlet Problem Using Subharmonic Functions ("Perron's Method")
占位居中
直播中，去观看