Partial Differential Equations II
本課程是由 國立陽明交通大學應用數學系 提供。
本課程屬研究所程度的微分方程課程，授課偏重於數學與物理間的連結，並且讓學生藉由此課程了解直觀地PDE概念。
Textbook：Fritz John, Partial Differential Equations (4th Edition), Applied Mathematical Sciences Vol.1 Springer-Verlag 1982.
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| Instructor(s) | Department of Applied Mathematics Prof. C. K. Lin |
|---|---|
| Course Credits | 3 Credits |
| Academic Year | 97 Academic Year |
| Level | Master's Students |
| Prior Knowledge | Calculus, Advanced Calculus, Linear Algebra, Ordinary differential equation, Complex Analysis and Real analysis |
| Related Resources | Course Video Course Syllabus Course Calendar |
| Week | Course Content | Course Video |
|---|---|---|
| 第五章 Hyperbolic Equations in Higher Dimensions 5-1 The Wave Equation in n-Dimensional Space | Watch Online | |
| 第五章 Hyperbolic Equations in Higher Dimensions 5-2 Higher-Order Hyperbolic Equations with Constant Coefficients | Watch Online | |
| 第五章 Hyperbolic Equations in Higher Dimensions 5-3 Symmetric Hyperbolic System | Watch Online | |
| 第六章 Higher-Order Elliptic Equations with Constant Coefficients 6-1 The Fundamental Solution for Odd n | Watch Online | |
| 第六章 Higher-Order Elliptic Equations with Constant Coefficients 6-2 The Dirichlet Problem | Watch Online | |
| 第六章 Higher-Order Elliptic Equations with Constant Coefficients 6-3 Sobolev Space | Watch Online | |
| 第七章 Parabolic Equations 7-1 The Heat Equation | Watch Online | |
| 第七章 Parabolic Equations 7-2 The Initial-Value Problem for General Second-Order Parabolic Equations | Watch Online | |
| 第八章 H. Lewys Example of a Linear Equation without Solutions 8-1 Brief introduction of Functional Analysis | Watch Online | |
| 第八章 H. Lewys Example of a Linear Equation without Solutions 8-2 Semigroups of linear operator | Watch Online | |
| 第八章 H. Lewys Example of a Linear Equation without Solutions 8-3 Perturbations and Approximations | Watch Online | |
| 第八章 H. Lewys Example of a Linear Equation without Solutions 8-4 The abstract Cauchy Problem | Watch Online | |
| 第八章 H. Lewys Example of a Linear Equation without Solutions 8-5 Application to linear partial differential equations | Watch Online | |
| 第八章 H. Lewys Example of a Linear Equation without Solutions 8-6 Applications to nonlinear partial differential equations | Watch Online | |
| 第八章 H. Lewys Example of a Linear Equation without Solutions 8-6 Applications to nonlinear partial differential equations | Watch Online |
課程目標
本課程屬研究所程度的微分方程課程，授課偏重於數學與物理間的連結，並且讓學生藉由此課程了解直觀地PDE概念。
課程章節
| 章節 | 主題內容 |
| 第五章 | Hyperbolic Equations in Higher Dimensions |
| 第六章 | Higher-Order Elliptic Equations with Constant Coefficients |
| 第七章 | Parabolic Equations |
| 第八章 | H. Lewys Example of a Linear Equation without Solutions |
課程書目
Fritz John, Partial Differential Equations (4th Edition), Applied Mathematical Sciences Vol.1 Springer-Verlag 1982.
A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, 1983.
評分標準
| 項目 | 百分比 |
| 平時作業 | 60% |
| 期中報告 | 20% |
| 期末報告 | 20% |
本課程行事曆提供課程進度與考試資訊參考。
| 章節 | 主題內容 |
| 第五章 Hyperbolic Equations in Higher Dimensions | 5-1 The Wave Equation in n-Dimensional Space 5-2 Higher-Order Hyperbolic Equations with Constant Coefficients 5-3 Symmetric Hyperbolic System |
| 第六章 Higher-Order Elliptic Equations with Constant Coefficients | 6-1 The Fundamental Solution for Odd n 6-2 The Dirichlet Problem 6-3 Sobolev Space |
| 第七章 Parabolic Equations | 7-1 The Heat Equation 7-2 The Initial-Value Problem for General Second-Order Parabolic Equations |
| 第八章 H. Lewys Example of a Linear Equation without Solutions | 8-1 Brief introduction of Functional Analysis 8-2 Semigroups of linear operator 8-3 Perturbations and Approximations 8-4 The abstract Cauchy Problem 8-5 Application to linear partial differential equations 8-6 Applications to nonlinear partial differential equations |
COURSE
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