# 工程數學 Chapter 12 PDE 楊學成 老師.

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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)

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

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

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12.3 One – dimensional wave equation

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.

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

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