Homework I due January 26

Section 1.4, 1bde, 2,6,7ab,10

January 26

Homework 1 due today

Videos to watch before class:

2.2 Linear Operators (6:06)

2.2 Linear Equations (2:14)

You might also want to review the following videos from last week:

1.2 Heat Equation (5:03)

1.3 Boundary Values(2:41)

1.4 Steady State Solutions (9:08)

1.4 Steady State Solutions for Insulated Boundaries(9:00)

Homework II due February 2

Section 1.4, 1bde, 2,6,7ab,10

Section 2.2, 2

January 28

Videos to watch before class:

2.2 Superposition (5:19)

2.3 Separation of variables (8:52)

These videos from my ODE class might be useful if you don't remember separable equations and eigenvalue problems:

1.4 Separable equations (3:39)

1.4 Separable equations example (2:55)

3.8 Introduction to endpoint problems (1:32)

3.8 Eigenvalues (6:36)

3.8 Eigenvalue example I (8:29)

3.8 Eigenvalue example II (5:15)

Homework II due February 2

Section 2.2, 4

Section 2.3, 1bcd, 2bc

February 2

Homework 1 due today

I have decided to teach a class on boundary value problems, since it seems like very few students have learned it in ODEs

Videos to watch before class:

3.8 Introduction to endpoint problems (1:32)

3.8 Eigenvalues (6:36)

3.8 Eigenvalue example I (8:29)

3.8 Eigenvalue example II (5:15)

Homework III due February 9

Section 2.3 2bc

February 4

Videos to watch before class:

2.3 Heat equation example with trigonometric initial condition (4:53)

2.3 Introduction to Fourier Series (5:13)

2.3 Heat equation example using Fourier series (9:10)

2.4 Heat equation with insulated ends using Fourier series (7:45)

2.4 Heat equation for a circular rod (6:40)

Homework III due February 9

Section 2.3 3b,5,6

Section 2.4 1ab,3,4,7a

February 9

Homework 3 due today

Videos to watch before class:

2.5 Introduction to the Laplace equation (3:28)

2.5 Steady state temperatures of a rectangle (9:56)

2.5 Steady state temperatures of a disk (9:48)

2.5 Mean value theorem (2:23)

2.5 Maximum Principle (2:56)

2.5 Well-posedness (5:49)

Homework IV due February 18

Section 2.5 1ac,2,3a,13,14

February 11

Please re-watch the following videos before class:

2.5 Steady state temperatures of a disk (9:48)

2.5 Mean value theorem (2:23)

2.5 Maximum Principle (2:56)

2.5 Well-posedness (5:49)

2.5 Uniqueness (2:45)

No additional homework

February 16

Test I today. Please note the practice test at the top of this page. Test will cover Chapters 1 and 2.

I will hold additional office hours on Monday, Feb 15 5-6pm. I should also be in my office for most of the day on Monday starting from 9.30am (other than a lunch break noon-1 or so, and a seminar talk I'm giving from 3.30-4.30), so feel free to drop by if you need to ask anything.

February 18

Homework 4 due today

Videos to watch before class:

3.2 Fourier's Theorem (3:40)

3.2 Fourier's Theorem example (5:31)

3.3 Fourier sine and cosine series (4:25)

Homework V due February 23

Section 3.2 1cg,2g,

Section 3.3 1ac,16,18

February 23

Homework 5 due today

Videos to watch before class:

3.6 Complex Fourier Series (9:13)

4.2 Vibrating String Equation (10:31)

Homework VI due March 1

Section 3.6 1,2

Section 4.2 1,2. (equilbrium means a solution that doesn't change with respect to time)

February 25

Videos to watch before class:

4.2 Vibrating String Equation (10:31)

4.4 Vibrating String Equation with fixed ends (10:35)

4.4 Normal Modes of Vibration (1:16)

4.4 Vibrating String- Normal Modes (0:50)

Homework VI due March 1

Section 4.4 1ab,7,8

March 1

Homework 6 due today

Videos to watch before class:

5.2 Intro to Sturm-Liouville problems (4:18)

5.3 Sturm-Liouville theorems (5:21)

Homework VII due March 8

Section 5.3 2,5,6ab

March 3

Videos to watch before class:

5.5 Lagrange's identity and Green's formula (5:48)

5.5 Self-adjointness of the S-L operator (6:49)

5.5 Proof of orthogonal eigenfunctions (4:26)

5.5 Real eigenvalues proof (7:41)

5.5 Unique eigenfunctions proof (6:51)

Homework VII due March 8

Section 5.5 1, 8bcde (8b involves a lot of integration by parts)

March 8

Homework 7 due today

Videos to watch before class:

5.5 Unique eigenfunctions proof (6:51)

March 10

Test II today, covering chapters 3-5 (including the material on March 8)

Extra office hours, 4-6PM in PHSC 1007

There will be no practice test

March 22

Rayleigh Quotient Derivation (5:05)

Minimization Principle (3:08)

Eigenvalue Estimates (9:55)

Homework VIII due March 29

Section 5.6 1ab,2,4a

March 24

7.2 Higher Dimensional PDEs (3:38)

7.2 Higher Dimensional Product Solutions (3:42)

7.3 Higher Dimensional Eigenvalue Problems (6:54)

7.3 Double Fourier Series (5:46)

7.3 Solving the Vibrating Membrane equation(9:47)

Homework VIII due March 29

Section 7.2 1,2,3ac

March 29

Homework 8 due today

7.3 Double Fourier Series (5:46)

7.3 Solving the Vibrating Membrane equation(9:47)

Homework IX due April 5

Section 7.3 1ab, 2a,5

March 31

7.4 Properties of the Helmholtz equation (5:07)

7.5 Multi-dimensional Lagrange identity and Green's formula (5:02)

7.5 Self-adjointenss of the Laplacian (2:48)

7.5 Orthogonal Helmholtz eigenfunctions

Homework IX due April 5

Section 7.4 1

April 5

Homework IX due today

7.5 Multi-dimensional Lagrange identity and Green's formula (5:02)

7.5 Self-adjointenss of the Laplacian (2:48)

7.5 Orthogonal Helmholtz eigenfunctions

7.7 Introduction to the Circular Vibrating Membrane problem (8:40)

7.7 Introduction to Bessel functions (8:05)

7.7 The Bessel eigenvalue problem (7:37)

Homework X due April 12

Section 7.7 1,7

April 7

8.2 Time-independent nonhomogeneous parts (9:37)

8.2 Reference distributions (6:58)

Also, these videos from Chapter 1 might be helpful:

1.4 Steady State Solutions (9:08)

1.4 Steady State Solutions for Insulated Boundaries(9:00)

Homework X due April 12

Section 8.2 1ad

April 12

Homework X due today

8.2 Reference distributions (6:58)

8.3 Eigenfunction expansions for non-homogeneous boundary conditions(9:00)

Homework XI due April 19

Q4 in the worksheet (but NOT Q5, despite what I said in class). Watch these two videos if you can't remember how to do integrating factors: Video 1 Video 2.

Homework XI due April 19

Section 8.3 1bf

April 14

8.4 Eigenfunction expansion for nonhomogeneous boundary conditions (10:42)

Homework XI due April 19

Section 8.4 1b,2

April 19

Homework XI due today

6.2 Difference approximations for derivatives (6:06)

6.2 Difference approximations for second derivatives (8:17)

Homework XII due April 26

Section 6.2 1,3,4, Q7 in worksheet

April 21

6.3 Finite difference methods for the heat equation (7:15)

6.3 Finite difference method example (9:59)

Homework XII due April 26

(1) Redo the calculation in Q4 (don't do the bonus question), except look for u₃⁽²⁾ with initial conditions f(x_0)=f(x_6)=0, f(x_1)=f(x_2)=f(x_3)=1, f(x_4)=-3, f(x_5)=2.

(2) Redo the calculation in Q4 (don't do the bonus question), except with initial condition given by a discretized version of u(x,0)=sin(PI*x/L)^2.

April 26

Homework XII due today

6.3 Fourier-von Neumann stability analysis (5:53)

6.3 Product solutions for partial difference equations (9:46)

6.3 Stability analysis using product solutions (4:46)

Homework XIII due Friday, April 22 at PHSC 423 (before office closes at 5)

Section 6.3 3,6de

April 28

Test III today, covering chapters 5.6,6.2-6.3,7.2-7.5,7.7,8.2-8.3

Extra Office hours 5-6pm Wednesday, April 27 at PHSC 1025

May 3

(optional) Review for final. Please bring a laptop or other computing device

May 5

(optional) Review for final.