應用數學方法

本課程介紹Maxwell 方程式,授課偏重於數學與物理間的連結與數學理論的介紹,讓學生了解Maxwell 方程式的理論與應用

Calculus, Linear algebra

無備註

版書

作業100%

• Introduction

  1.1 Maxwell’s Equations 1.2 The Constitutive Equations 1.3 Special Cases 1.3.1 Vacuum 1.3.2 Electro- and Magnetostatics 1.3.3 Time-Harmonic Fields

• Introduction

  1.4 Boundary and Radiation Conditions 1.5 The Reference Problems 1.5.1 Scattering by a Perfect Conductor 1.5.2 A Perfectly Conducting Cavity

• Expansion into Wave Functions

  2.1 Separation in Spherical Coordinates 2.2 Legendre Polynomials

• Expansion into Wave Functions

  2.3 Expansion into Spherical Harmonics 2.4 Laplace’s Equation in the Interior and Exterior of a Ball

• Expansion into Wave Functions

  2.5 Bessel Functions 2.6 The Helmholtz Equation in the Interior and Exterior of a Ball

• Expansion into Wave Functions

  2.7 Expansion of Electromagnetic Waves

• Scattering from a Perfect Conductor

  3.1 A Scattering Problem for the Helmholtz Equation 3.1.1 Representation Theorems 3.1.2 Volume and Surface Potentials

• Scattering from a Perfect Conductor

  3.1.3 Boundary Integral Operators 3.1.4 Uniqueness and Existence

• Scattering from a Perfect Conductor

  3.2.1 Representation Theorems

• Scattering from a Perfect Conductor

  3.2.2 Vector Potentials and Boundary Integral Operators 3.2.3 Uniqueness and Existence

• The Variational Approach to the Cavity Problem

  4.1 Sobolev Spaces 4.1.1 Basic Properties of Sobolev Spaces of Scalar Functions 4.1.2 Basic Properties of Sobolev Spaces of Vector Valued Functions

• The Variational Approach to the Cavity Problem

  4.2 The Cavity Problem 4.2.1 The Variational Formulation and Existence 4.2.2 Uniqueness and Unique Continuation

• The Variational Approach to the Cavity Problem

  4.3 The Time-Dependent Cavity Problem

• Boundary Integral Equation Methods for Lipschitz Domains

  5.1 Advanced Properties of Sobolev Spaces 5.1.1 Sobolev Spaces of Scalar Functions 5.1.2 Sobolev Spaces of Vector Valued Functions

• Boundary Integral Equation Methods for Lipschitz Domains

  5.1.2 Sobolev Spaces of Vector Valued Functions 5.1.3 The Case of a Ball Revisited

• Boundary Integral Equation Methods for Lipschitz Domains

  5.2 Surface Potentials

• Boundary Integral Equation Methods for Lipschitz Domains

  5.3 Boundary Integral Equation Methods

1. The Mathematical Theory of Time-Harmonic Maxwell's Equations, by Andreas Kirsch, Frank Hettlich, Springer, 2015 2. Boundary element methods with applications to nonlinear problems by Goong Chen, Jianxin Zhou, Paris: Atlantis Press, 2010

地點

SA348

時間

Thursday 4pm -5pm

聯絡方式

Email: liming@math.nctu.edu.tw Tel: 56439