MATH 3363 - Introduction to Partial Differential Equations - University of Houston

# MATH 3363 - Introduction to Partial Differential Equations

Prerequisites: Math 2433 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

Course Outline:

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.

Block 1.

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

Block 2.

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

Block 3.

Examples + graphics:   Homogeneous boundary data
Examples + graphics:   Inhomogeneous boundary data

Block 4.

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

Graphics:  Convergence theorem & Gibbs phenomenon

Block 5.

4.2, 4.3:  Derivation of wave equation; standard boundary conditions.
4.4:  String with fixed ends, d'Alembert's solution.

Block 6.

Examples + graphics:  Normal modes; specific initial data
7.3:  Rectangular membrane with fixed boundary

Block 7.

Examples + graphics:  Nodal curves; specific init data
7.7.5, 7.7.6:  Euler's equation; Bessel's equation; graphics

Block 8.

7.7.7 expanded:  Bessel functions: zeroes & orthogonality
7.7.1-7.7.4:  Circular membrane: separation of variables & scaling

Block 9.

7.7.8:  Circular membrane: Eigenfunctions & Initial value problems
7.7.9 + graphics:  Circularly symmetric initial data.

Block 10.

2.5.1:  Laplace's equation inside a rectangle
2.5.2:  Laplace's equation on a circular disk.

Block 11.

2.5.4 expanded:  Mean value property, Maximum principle, Poisson formula.
3.6, 10.3.1:  Fourier convergence theorem in complex form.

Block 12.

10.3.2, 10.3.3:  Fourier transform; Gaussians; graphics
10.6.3:   Laplace's equation in a half plane.

Block 13.

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.

CSD Accommodations:

Accommodation Forms: Students seeking academic adjustments/auxiliary aids must, in a timely manner (usually at the beginning of the semester), provide their instructor with a current Student Accommodation Form (SAF) (paper copy or online version, as appropriate) from the CSD office before an approved accommodation can be implemented.

Details of this policy, and the corresponding responsibilities of the student are outlined in The Student Academic Adjustments/Auxiliary Aids Policy (01.D.09) document under [STEP 4: Student Submission (5.4.1 & 5.4.2), Page 6]. For more information please visit the Center for Students with Disabilities Student Resources page.

Additionally, if a student is requesting a (CSD approved) testing accommodation, then the student will also complete a Request for Individualized Testing Accommodations (RITA) paper form to arrange for tests to be administered at the CSD office. CSD suggests that the student meet with their instructor during office hours and/or make an appointment to complete the RITA form to ensure confidentiality.

*Note: RITA forms must be completed at least 48 hours in advance of the original test date. Please consult your counselor ahead of time to ensure that your tests are scheduled in a timely manner. Please keep in mind that if you run over the agreed upon time limit for your exam, you will be penalized in proportion to the amount of extra time taken.

UH CAPS

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