Video Lectures, Powerpoint
presentations, pdfs, etc
March 23, 2020
1.
Reading
Assignment: Pages 115 - 118
2.
Introduction
to Sturm-Liouville Theory
5.
Homework1 – problems 2 and 4 pages
126-127. You need to use Theorem 4.3
page 120 for problem 2.
6.
March 25, 2020
1.
Reading Assignment: Pages 118 - 124
2.
Continuation
with Sturm-Liouville Theory
March 27, 2020
1.
Reading
Assignment: Pages 125-129
2.
There will be no more collected homework this semester,
not even Homework1.
3.
Periodic
Sturm-Liouville Theory (mp4 movie)
4.
Singular
Sturm-Liouville Theory – the definition on page 129 and the example 4.2.1 at
bottom of page
5.
Exercise 8, 9,
and 12 in section 4.1
March 28, 2020
1.
Reading Assignment:
Pages 129 – 131: Section 4.2: ``Singular Sturm-Liouville Theory’’
2.
Singular
Sturm-Liouville Theory
3.
Boundary
Conditions in Singular SL Theory
4.
Exercises 1,
2, 3, 5, and 7 in section 4.2
March 30, 2020
1.
Reading
Assignment: Pages 131- 134: “Examples of (famous) Sturm-Liouville Problems”
2.
The Singular
Sturm-Liouville Theorem
3.
Legendre
Polynomials
4.
Exercises 1, 2,
3, 5, 7 in section 4.2
5.
April 1, 2020
1.
Reading
Assignment: Pages 135-141 (Legendre’s equation and Bessel’s equation)
2.
Bessel Functions
(video)(https://youtu.be/z8HejV_oDSY)
3.
Exercise 3 in
Section 4.2 Solution(video)( https://www.youtube.com/watch?v=LF94UmuUhRw )
4.
Exercise 7
in Section 4.2 (pdf) (solution)
April 3, 2020
1.
Reading
Assignment: Pages 135-141 (General orthogonal expansions)
2.
A singular SL
problem with Bessel’s equation of order n (video)(
https://www.youtube.com/watch?v=yaX9-jcLjdk
)
3.
General Orthogonal
Expansions (video)
4.
Study
Guide for Test #2 (April 10-11) (pdf)
April 4, 2020
1.
Reading Assignment: Section 5.5: Pages 181-182: ``Laplace’s
Equation in 2-D’’
2.
Reading Assignment: Section 5.6: Pages 186-188: ``The 2-D Wave
and Heat Equations”
3.
Section 5.5: Exercises 1,2,3 – parts (a) only
4.
Exercise
#1 Section 5.6 Solution (.pdf)
5.
Animation
of solution of problem 1, section 5.6 (video)
April 6, 2020
1.
Reading
Assignment: Pages 189-192: ``Laplace’s
Equation in Polar Coordinates”
2.
Derivation
of Laplacian Operator in Polar Coordinates (.pdf)
3.
Comments on Laplace’s
equation in a disk (video)
4.
Exercises: Be able to do problems 1, 2, 3, 4, 9, 10
April 8, 2020
1.
Review Day: Available all day (9 am – 4 pm) to answer
question by email. I’ll check my email
hourly.
2.
Solutions
to Exercises 8, 9, and 12 in section 4.1 and Exercises 1, 2 and 5 in section 4.2.
3.
April 10, 2020
1.
Test Day #1:
April 11, 2020 Test Day #2: Test #2 is due at 11:59 pm at Moodle.
1.
Reading
Assignment: Pages 189 – 198: More on
Section 6.1: “Laplace’s Equation in Polar Coordinates”
2.
Problem #2,
page 196: Boundary
value problem on the exterior of a disk
(video)
3.
April 13, 2020
1.
Reading
Assignment: Pages 204 – 209: Section 6.3:
``The Wave and Heat Equations in Polar Coordinates”
2.
Survey of the
solution of the wave equation in polar coordinates (video)
3.
Exercise
1 on page 209 (pdf)
4.
Exercise 1 on page 209 (video)
5.
Exercise 3 page 197, section
6.1 (video)
April 15, 2020
1.
Reading
Assignment: Pages 210 – 216: Section
6.4: “Laplace’s equation in cylindrical coordinates”
2.
Laplace’s equation in a cylinder,
pages 210-212 (video)
3.
Problem 3,
Section 6.4 (.pdf), “Laplace’s equation in a half-cylinder”
April 17, 2020
1.
Finish section 6.4 on Laplace’s equation in
cylindrical coordinates
2.
Reading
Assignment: Pages 217-219: “Laplace’s
equation in spherical coordinates: The
rotational symmetric case”
3.
Problem 5
in Section 6.4: {.pdf}
April 20, 2020
1.
Reading
Assignment: Pages 217-219: 6.5: “Laplace’s equation in spherical
coordinates: The rotational symmetric
case”
2.
Exercise:
Solve Laplace’s equation in the interior of a sphere ( .pdf) (pages
218-219 in textbook)
3.
Exercise:
Solve Laplace’s equation in the exterior of a sphere ( .pdf) (Exercise 7,
page 229)
4.
April 22, 2020
1.
Reading
Assignment: Section 6.5, pages 220 –
222.
2.
Laplace’s equation in a sphere: the general case: (.pdf) In this pdf I
expand the discussion on pages 220-222 to 7 pages in order to clarify and
expand the discussion provided by the author.
3.
