傅立葉分析

本課程介紹如何利用Fourier series 找出偏微分方程的解,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

Calculus, Linear algebra

無備註

版書

三次期中考100%

• Fourier series

  Fourier sine series, Fourier cosine series,uniform convergence of Fourier series

• Fourier method

  Linear operator, principle of superposition, temperature problem, slab with internally heat

• Fourier method

  Vibration string problem, verification of solution

• Boundary value problem

  A string with initial velocity, an elastic bar, resonance, periodic boundary condition

• Separation of variable

  Heat equation

• Separation of variable

  Wave equation

• Separation of variable

  Laplace equation

• Calculus of Fourier series

  Differentiation of Fourier series, integration of Fourier series, Gibbs phenomenon

• Sturm-Liouville eigenvalue problems

  Introduction of Sturm-Liouville eigenvalue problems, Rayleigh quotient

• Sturm-Liouville eigenvalue problems

  Some PDE examples, homogeneous boundary conditions of the third kind

• Classical PDE problems

  Laplace equation in differnent coordinate systems

• Classical PDE problems

  Transverse vibrations of a thin beam

• Classical PDE problems

  Schrodinger equation

• Fourier integral

  Fourier sine integral, Fourier cosine integral

• Fourier integral

  Laplace transform and application

• Fourier integral

  Fourier transform solution method of PDEs

• Fourier series

  Inner product, orthonormal set, generlized Fourier series

Fourier Series and Boundary Value Problems, by James Ward Brown, Ruel V Churchill, 8th Edition, 2012 A Very Applied First Course in Partial Differential Equations, by Michael K. Keane, Prentice Hall, 2002

地點

SA348

時間

Thursday 4pm -5pm

聯絡方式

Email: liming@math.nctu.edu.tw Tel: 56439