工程數學 Chapter 12 PDE 楊學成 老師.

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1 工程數學 Chapter 12 PDE 楊學成 老師

2 單元架構 12-1 PDE (Partial Differential Equation) 12-2 Modeling
12-3 One – dimensional wave equation 12-4 Heat equation Solation by Fourier Series 12-5 D’Alembert’s Solution of the wave Equ

3 12.1 PDE (Partial Differential Equation)
學習目標 學習完本小節後，您將能： 1. 能說出什麼是PDE 2. 能寫出PDE的方程式 3. 能計算基本的PDE方程式 4. 能說出PDE可應用的地方

4 Basic concepts one dimension two dimension
two - dimension wave equation x,y,z are contesion coodinate.

5 Basic concepts Non homogeneous Eq. Laplace equation Boundary condition
Initial condition Theorem Superposition.

6 Basic concepts

7 12.2 Modeling 學習完本小節後，您將能： 1. 能說出何謂Modeling 2. 能具體描述Modeling意義
學習目標 學習完本小節後，您將能： 1. 能說出何謂Modeling 2. 能具體描述Modeling意義 3. 能寫出何謂Modeling 4. 能進行Modeling的繪製

8 Basic concepts T2 u B Q T1 P X X+0X X

9 Basic concepts

10 Basic concepts

11 12.3 One – dimensional wave equation
學習目標 學習完本小節後，您將能： 1. 能說出何謂wave equation 2. 能具體描述wave equation意義 3. 能寫出何謂One–dimensional wave equation 4. 能進行One–dimensional wave equation的運算

12 Basic concepts Boundary Condition initial condition X=0 X=L
initial deflection initial velocity method of separating variable.

13 Basic concepts 1. Let u(x , t) = F(x) G(t) K ：is any constant

14 Basic concepts 2. Satisfying the B、C.

15 Basic concepts

16 12.4 Heat equation Solution by Fourier Series.
學習目標 學習完本小節後，您將能： 1. 能說出何謂Heat equation 2. 能具體描述Heat equation意義 3. 能寫出Heat equation Solution by Fourier Series 4. 能進行Heat equation Solution by Fourier Series 的運算

17 Basic concepts where u=(x,y,z,t) distribution of temperature.
thermal conductivity. specific heel . density . One dimensional heat equation.

18 Basic concepts Boundary Condition u(0,t)=0 , u(L,t)=0
Initial temperature u(x,0)=f(x) 1.

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31 12.5 D’Alembert’s Solution of the wave Equ
學習目標 學習完本小節後，您將能： 1. 能說出什麼是D’Alembert’s Solution of the wave Equ 2. 能寫出D’Alembert’s Solution of the wave Equ 的方程式 3. 能計算D’Alembert’s Solution of the wave Equ方程式

32 Basic concepts

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