Prerequisites: Math 2415 and either Math 3321 or Math 3331.
Course Description: Partial differential equations and boundary value problems, Fourier series, the heat equation, vibrations of continuous systems, the potential equation, spectral methods.
Text: Applied Partial Differential Equations with Fourier Series and Boundary Value Problems, 5th Edition, by Richard Haberman, Pearson Prentice Hall Pub. ISBN: 9780321797056
Introduction: The following syllabus consists of 13 blocks of material. Each block represents two 75 minute or three 50 minute lecture periods. This leaves two (75 minute) or three (50 minute) lecture periods for in-class testing.
1.1-1.4: Derivation of the Heat Equation; standard boundary conditions
2.3.4: -y″ = λy, subject to 4 basic sets of boundary conditions
2.3.1 - 2.3.3, 2.3.5-2.3.7: Heat equation in a rod with both ends at zero temperature.
2.4.1: Heat equation in a rod with both ends insulated; graphics
Examples + graphics: Homogeneous boundary data
Examples + graphics: Inhomogeneous boundary data
2.4.2. 3.1, 3.2: Circular ring (“5th” set of BC) and Fourier series
3.3.1, 3.3.2: Even & odd extensions; 2.3.6 & 2.4.1 revisited
4.2, 4.3: Derivation of wave equation; standard boundary conditions.
4.4: String with fixed ends, d'Alembert's solution.
Examples + graphics: Normal modes; specific initial data
7.3: Rectangular membrane with fixed boundary
Examples + graphics: Nodal curves; specific init data
7.7.5, 7.7.6: Euler's equation; Bessel's equation; graphics
7.7.7 expanded: Bessel functions: zeroes & orthogonality
7.7.1-7.7.4: Circular membrane: separation of variables & scaling
7.7.8: Circular membrane: Eigenfunctions & Initial value problems
7.7.9 + graphics: Circularly symmetric initial data.
2.5.1: Laplace's equation inside a rectangle
2.5.2: Laplace's equation on a circular disk.
2.5.4 expanded: Mean value property, Maximum principle, Poisson formula.
3.6, 10.3.1: Fourier convergence theorem in complex form.
10.3.2, 10.3.3: Fourier transform; Gaussians; graphics
10.6.3: Laplace's equation in a half plane.
10.4.3, 10.6.3: Convolution theorem. The half-plane revisited.
10.4.2, 10.4.3: Key properties of the transform; heat kernel.
Justin Dart Jr. Center Accommodations:
Academic Adjustments/Auxiliary Aids: The University of Houston System complies with Section 504 of the Rehabilitation Act of 1973 and the Americans with Disabilities Act of 1990, pertaining to the provision of reasonable academic adjustments/auxiliary aids for students who have a disability. In accordance with Section 504 and ADA guidelines, University of Houston strives to provide reasonable academic adjustments/auxiliary aids to students who request and require them. If you believe that you have a disability requiring an academic adjustments/auxiliary aid, please visit Justin Dart Jr. Student Accessibility Center website at https://www.uh.edu/accessibility/ for more information.
Accommodation Forms: Please visit: https://www.uh.edu/accessibility/faq/testing/. Details of this policy, and the corresponding responsibilities of the student are outlined in The Student Academic Adjustments/Auxiliary Aids Policy (01.D.09) . For more information please visit the Justin Dart Jr. Student Accessibility Center Policies page page.
Counseling and Psychological Services (CAPS) can help students who are having difficulties managing stress, adjusting to college, or feeling sad and hopeless. You can reach (CAPS) by calling 713-743-5454 during and after business hours for routine appointments or if you or someone you know is in crisis. No appointment is necessary for the "Let's Talk" program, a drop-in consultation service at convenient locations and hours around campus.