工程數學 III

Part (I) Fourier Analysis

1 Periodic Function

2 Fourier Series

3 Coefficient of Fourier Series

4 Even and Odd Function

5 Half Range Expansion

6.1 Complex Fourier Series

6.2 Sturm Liouville Problem

7 Orthogonality of Eigenfuncion ynx Special Case

8 Orthogonality of Eigenfuncion ynx General Case

9 2 nd Order ODEs with Homogeneous B.C.

10 2 nd Order ODEs with Non Homogeneous B.C.

11 Fourier Integrals

Part (II) Ordinary Differential Equations

Ch1. 1 st Order ODEs with Constant Coefficients

Ch2. 2 nd Order ODEs with Constant Coefficients

Part (III) Partial Differential Equations

Chapter 1 Introduction and Derivations

1.1 Heat Equation

1.2 Wave Equation

1.3 Laplace Equation

Chapter 2 Non-Homogeneous Heat Equation

2.1 Non-Homogeneous Heat Equation with Homogeneous B.C.

2.2 Non-Homogeneous Heat Equation with Non-Homogeneous B.C.

Chapter 3 Non-Homogeneous Wave Equation

3.1 Non-Homogeneous Wave Equation with Homogeneous B.C.

3.2 Non-Homogeneous Wave Equation with Non-Homogeneous B.C.

Chapter 4 Non-Homogeneous Laplace Equation

4.1 Non-Homogeneous Laplace Equation with Homogeneous B.C.

4.2 Non-Homogeneous Laplace Equation with Non-Homogeneous B.C.

Chapter 5 Nonlinear 1 st Order PDEs