Math 4581 News and Announcements

  • Week 1, 8/21-8/25: Idea of the method of the separation of variables. Vector space, normed space, inner product space, orthogonality, orthogonal projections. You can read Chapter 3 of "Linear Algebra" by Tom M. Apostol or Section 8 of "The Elements of Real Analysis" by Robert G. Bartle on these topics. Please read Sections 0.1 and 0.2 of the textbook to refresh your basic knowledge of ODE.
  • All students should have access to the recordings of lectures. Please go to HELIX web site and follow the instructions there on how to access the videos of the lectures.
  • Week 2, 8/28-9/1: Notion of a Hilbert space, orthonormal approximating basis, Sturm-Liouville problems and Fourier series. Please read sections 2.7 and 1.1 of the textbook.
  • Week 3, 9/4-9/8: Fourier series. Please read sections 1.2-1.5 of the textbook (you can also read section 1.6 which has a different introduction to the L^2 convergence).
  • Week 4, 9/11-9/15: Please read sections 2.1, 2.2, 4.1, 4.2 of the textbook.
  • Test 1 is on Wednesday, 9/20. You can have a one page (one side only) formula sheet during the test. The test covers the introductory material about vector spaces, normed spaces, inner product spaces, Hilbert spaces, span, orthogonality, approximating basis, Sturm-Liouville theory (section 2.7), and Fourier series (sections 1.1-1.5).
  • Week 5, 9/18-9/22: Please read sections 4.3 and 4.5 of the textbook.
  • Week 6, 9/15-9/29: Please read sections 4.3, 4.5 and 4.4 of the textbook. There is a misprint in the definition of the function f in problem 1(a) of the suggested homework 2. There should be `pi/2 less than y less than pi'. Also in the definition of the orthogonal approximating basis there should be n=0, 1, 2, ... instead of n=1, 2, ... The solutions have been updated.
  • Week 7, 10/2-10/6: Please read sections 1.9, 1.10 and 2.3-2.5 of the textbook.
  • Week 8, 10/9-10/13: Please read section 2.6 of the textbook.
  • Test 2 is on Monday, 10/23. You can have a one page (one side only) formula sheet during the test. The test covers the material of weeks 4-8 on the Laplace and heat equations (starting with section 2.1). The material on the wave equation will not be covered by this test.
  • Week 9, 10/16-10/20: Please read sections 3.1-3.3.
  • My office hours on Tuesday, 10/17 are canceled. I'll have additional office hours on Wednesday, 10/18, 11-12.
  • Week 10, 10/23-10/27: Parallelogram rule, wave equation in higher dimensions. Please read sections 3.6, 5.1-5.3. Sections 5.1 and 5.2 are supplemental reading as the material there was not covered in class.
  • Week 11, 10/30-11/3: Wave equation in higher dimensions, nonhomogeneous wave equation. Please read sections 5.4-5.7 of the textbook.
  • Test 3 is on Friday, 11/17. You can have a one page (one side only) formula sheet during the test. The test covers the wave equation, separation of variables, vave equation in a rectangle, vave equation in polar coordinates, Bessel functions, D'Alembert's formula and its versions in bounded domains and the half-line, parallelogram rule, non-homogeneous wave equation, boundary value problems, domain of dependence, dispersion and damping (the material covered in weeks 9-12). Laplace transform will not be covered by this test.
  • Week 12, 11/6-11/10: Wave equation with lower order terms, dispersion and damping. Laplace transform. Please read sections 6.1, 6.2 of the textbook.
  • My office hours on Tuesday, 11/14 are moved to 10-11 am.
  • Week 13, 11/13-11/17: Properties of the Laplace transform. Solving ODE and PDE using Laplace transform. Please read sections 6.1, 6.2 and 6.3 of the textbook.
  • Week 14, 11/20-11/24: Solving PDE using Laplace transform. Wave equation. Please read sections 6.3 and 6.4 of the textbook.
  • The final exam is on Wednesday, 12/13, 11:30 am - 2:20 pm. You can have a one two-sided page of notes during the final. In addition I will provide for everybody a copy of the two tables from pages 382 and 383 of the textbook containing elementary Laplace transforms and elementary properties of Laplace transforms.
  • Week 15, 11/27-12/1: Solving ODE and PDE using Laplace transform. Wave and Heat Equations. Please read sections 6.3, 6.4 of the textbook.
  • My office hours on Tuesday, 12/5 and Monday 12/11 are canceled. I'll have additional office hours on Wednesday, 12/6, 11-12 and Thursday, 12/7, 10-11 am.

    Last modified on December 4, 2017.