偏微分方程(一)

Partial Differential Equations (I)

學期

109-1

學分

3 學分

當期課號

5410

永久課號

IAM5525

開課單位

應用數學系

授課教師

葉立明

校區

光復

類別

選修

上課時間表

* 根據陽明交大上課時間表所列

概述

本課程屬大學部與研究所程度的微分方程課程,授課偏重於數學與物理間的連結,並且讓學生藉由此課程了解直觀地PDE概念。

先修科目

Calculus, Linear algebra, Ordinary differential equation

評分方式

平時作業 60% 期中考 40%

週次計畫

週次	主題
第 1 週	Wave and diffusion: the wave equation, causality and energy, comparison of waves and diffusions
第 2 週	Wave and diffusion: the diffusion equation, diffusion on the whole line
第 3 週	Boundary problems: separation of variables, the Dirichlet condition
第 4 週	Boundary problems: the Neumann condition, the Robin condition
第 5 週	Fourier series: the coefficients, even, odd, periodic and complex functions
第 6 週	Fourier series: orthogonality and general Fourier series completeness
第 7 週	Fourier series: completeness and the Gibbs phenomenon inhomogeneous boundary conditions
第 8 週	Harmonic functions: Laplace's equation rectangle and cubes
第 9 週	Harmonic functions: Poisson's formula circle, wedge, and annuli
第 10 週	Green's identity: Green's first identity Green's second identity
第 11 週	Green's identity: Green's functions half space and sphere
第 12 週	Waves in space: energy and causality the wave equation in space-time
第 13 週	waves in space: Ray, singularity, and sources the diffusion and the Schrodinger equations
第 14 週	Boundaries in the plane and in space: Fourier's method. revisited vibration of a drumhead
第 15 週	Boundaries in the plane and in space: solid vibrations in a ball nodes Bessel functions
第 16 週	Boundaries in the plane and in space: Legendre functions angular momentum in quantum mechanics

教科書

Walter A. Strauss Partial differential equations, An Introduction John Wiley & Sons, Inc. 2008

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