工程數學 Chapter 12 PDE 楊學成 老師
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
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
Basic concepts one dimension two dimension two - dimension wave equation x,y,z are contesion coodinate.
Basic concepts Non homogeneous Eq. Laplace equation Boundary condition Initial condition Theorem Superposition.
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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
Basic concepts T2 u B Q T1 P X X+0X X
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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
Basic concepts Boundary Condition initial condition X=0 X=L initial deflection initial velocity method of separating variable.
Basic concepts 1. Let u(x , t) = F(x) G(t) K :is any constant
Basic concepts 2. Satisfying the B、C.
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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
Basic concepts where u=(x,y,z,t) distribution of temperature. thermal conductivity. specific heel . density . One dimensional heat equation.
Basic concepts Boundary Condition u(0,t)=0 , u(L,t)=0 Initial temperature u(x,0)=f(x) 1.
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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
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