| 週次 |
授課內容 |
| 第1週 |
Part 1: Ordinary Differential Equations
Chapter 1 Introduction to Differential Equations (Definition and Terminology, Initial-Value Problems) |
| 第2週 |
Part 1: Ordinary Differential Equations
Chapter 1 Introduction to Differential Equations (Differential Equations ad Mathematical Models)
Chapter 2 First-Order Differential Equations (Separable Equations, Linear Equations) |
| 第3週 |
Chapter 2 First-Order Differential Equations (Linear Equations, Exact Equation, Solutions by Substitutions) |
| 第4週 |
Chapter 2 First-Order Differential Equations (Solutions by Substitutions, Linear Models)
|
| 第5週 |
Chapter 3 Higher-Order Differential Equations (Theory of Linear Equations, Reduction of Order) |
| 第6週 |
Chapter 3 Higher-Order Differential Equations (Linear Equations with Constant Coefficients, Undetermined Coefficients) |
| 第7週 |
Chapter 3 Higher-Order Differential Equations (Undetermined Coefficients, Variation of Parameters, ) |
| 第8週 |
Chapter 3 Higher-Order Differential Equations (Cauchy-Euler Equations, Nonlinear Equations, Linear Models: Initial-Value Problems) |
| 第9週 |
Chapter 3 Higher-Order Differential Equations (Linear Models: Initial-Value Problems, Liner Models: Boundary-value Problems, Solving Systems of Linear DEs) |
| 第10週 |
Chapter 4 The Laplace Transform (Definition of the Laplace Transform, Inverse Transforms and Transforms of Derivatives) |
| 第11週 |
Chapter 4 The Laplace Transform (Translation Theorems, Additional Operation Properties, Derivatives of Transforms) |
| 第12週 |
Chapter 4 The Laplace Transform (Transforms of Integrals, Transform of a Periodic Function, Dirac Delta Function) |
| 第13週 |
Chapter 4 The Laplace Transform (Dirac Delta Function, Systems of Linear Equations)
Chapter 5 Series Solutions of Linear Equations (Solutions by Ordinary Points) |
| 第14週 |
Chapter 5 Series Solutions of Linear Equations (Solutions by Ordinary Points, Solutions about Singular Points) |
| 第15週 |
Chapter 5 Series Solutuions of Linear Equations (Solutions about Singular Points, Bessel Functions )
|
| 第16週 |
Chapter 5 Series Solutuions of Linear Equations (Legendre Functions)
Part 4: Fourier Series and Partial Differential Equations
Chapter 12 Orthogonal Functions and Fourier Series (Orthogonal Functions, Fourier Series)
Chapter 12 Orthogonal Functions and Fourier Series (Fourier Cosine and Sine Series, Complex Fourier Series)
Final exam |
自主學習
內容 |
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