Partial Differential Equations, Spring 2018

• Course Information
• Lectures and Homework

Mon 5/14: Office hours and final exam.

• Office hours this week will be Monday 3:00-4:30 and Tuesday 2:00-4:00.
• The final exam is Wednesday 3:30-6:30 in Heiser E168.

Mon 5/7: Solution to Wave equation in 2d and 3d; Huygens’s principle.

• Reading: Sections 9.2
• Homework: (due Friday 5/11) (9.2) #8, 9*, 10.

Thu 5/3: Causality for wave equation in 3D.

• Reading: Sections 9.1
• Homework: (due Friday 5/11) (9.1) #5, 6*.

Tue 5/1: No office hours on 5/1.

• There will be no office hour today, Tuesday 5/1. Please feel free to email me with questions or to set up another time to meet.

Mon 4/30: Solid vibrations in a ball; spherical harmonics.

• Reading: Sections 10.3.
• Homework: (due Friday 5/4) (10.3) #2, 5*, 6.

Thu 4/26: Wave and Heat equations on domains; vibrations of a drum.

• Reading: Sections 10.1, 10.2.
• Homework: (due Friday 5/4) (10.1) #1, (10.2) #2*, 5.

Mon 4/23: Bacc week: no class.

• Despite my earlier intentions, I have decided not to hold class on Monday 4/23 during bacc week.
• I will hold my usual office hours (M,T,Th 3:30-4:30), and class will resume on Thursday 4/26.

Mon 4/16: General eigenvalue problems for the Laplacian.

• Guest Lectures this week by Prof. McDonald, who will lecture on:
• Reading Sections 11.1, 11.2.
• Homework (for both lectures) (due Friday 4/20) (11.1) #1*, 4. (11.2) #1*, 2.

Thu 4/12: Green’s Functions.

• In light of Monday’s cancellation of class, Thursday’s lecture will be what Monday’s was meant to be.
• Reading: Section 7.3, 7.4.
• Homework: (due Friday 4/20) (7.4) #5, 6, 11*.

Mon 4/9: Green’s Functions.

• Reading: Section 7.3, 7.4.
• Homework: (due Friday 4/13) (7.4) #5, 6, 11*.
• Note: there is an outside chance that I will have to cancel class due to jury duty, but unless announced otherwise, class is planned.

Thu 4/5: Greens Identities.

• Reading: Section 7.1, 7.2.
• Homework: (due Friday 4/13) (7.1) #2, 7*, (7.2), #1.

Mon 4/2: Poisson Kernel.

• Reading: Section 6.3
• Homework: (due Friday 4/6) (6.3) #1, 2*, 4.

Thu 3/29: Solving Laplace’s Equation by separation.

• Reading: Section 6.2
• Homework: (due Friday 4/6) (6.2) #1, 2, 5, 7*.

Mon 3/26: Harmonic functions and the Laplacian.

• Reading: Section 6.1
• Homework: (due Friday 3/30) (6.1) #4, 7*, 10*, 11.

Thu 3/15: Convergence of Fourier Series.

• Reading: Section 5.4, 5.5.

Thu 3/8: Review for Midterm.

• Midterm Exam will be in class on Monday 3/12, covering material from 1.1-1.4, 2.1-2.5, 3.1-3.4, 4.1-4.2, and 5.1-5.3.

Mon 3/5: Fourier series continued: even/odd/periodic extensions, general orthogonality.

• Reading: Sections 5.2, 5.3
• Homework: (due Friday 3/9) (5.2) #5, 10, 11*, (5.3) #6*, 9.

Thu 3/1: Fourier Series.

• Reading: Sections 5.1
• Homework: (due Friday 3/9) (5.1) #2, 5, 8*, 11.

Mon 2/26: Separation of variables for Dirichlet and Neumann problems in 1+1D.

• Reading: Sections 4.1, 4.2
• Homework: (due Friday 3/2) (4.1) #2, 6*. (4.2) #1, 2.

Thu 2/22: Diffusions and waves with a source.

• Reading: Sections 3.3, 3.4
• Homework: (due Friday 3/2) (3.2) #1, 5*, (3.3) #2*, (3.4) #1, 3.

Mon 2/19: Diffusion on the half line.

• Reading: Sections 2.5, 3.1, (3.2?)
• Homework: (due Friday 2/23) (2.5) #2, (3.1) #2.

Thu 2/15: Diffusion on the whole line.

• Reading: Sections 2.4.
• Homework: (due Thursday 2/22) (2.4) #1, 3, 5*, 11*, 15.

Mon 2/12: Uniqueness, stability for the diffusion equation.

• Reading: Sections 2.3.
• Homework: (due Thursday 2/15) (2.3) #1, 4*.

Thu 2/8: Wave equation in 1+1D.

• Reading: Sections 2.1, 2.2.
• Homework: (due Thursday 2/15) (2.1) #3, 5*, 7, 8, (2.2) #1, 6*.

Mon 2/5: Physical derivation of diffusion equation; initial and boundary value problems.

• Reading: Sections 1.3, 1.4.
• Homework: (due Thursday 2/8) (1.3) #2, 5*, 6*, 7, 9 (assigned last Thursday). (1.4) #2, 3.

Thu 2/1: First order linear PDE, continued; Physical derivations.

• Reading: Sections 1.2, 1.3.
• Homework: (due Thursday 2/8, along with a few more problems to be assigned later) (1.3) #2, 5*, 6*, 7, 9.

Mon 1/29: What is a PDE; First order linear PDE.

• Reading: Sections 1.1, 1.2.
• Homework: (due Thursday 2/1) (1.1) #3*, 4; (1.2) #1, 2, 5*, 9, 11*.
• Starred problems are to be written up seperately from unstarred problems.