

The videos below are part of my remotely delivered differential
equations course. Video presentations are seamlessly integrated with my differential
equations book, and the numbering of the modules is the same as
in the book. Nonetheless, these presentations can be used as
standalones without my book or for selfstudy. The idea was and is
to teach mathematics, no more and no less. Presentations are sorted by
topic. The names of the videos should be selfexplanatory. For the
"license", click here.
Note that the videos were shot almost without retakes in 48 hour
sessions. Thus some of them will have small "hiccups" and some may need to
be reshot. On the other hand, I do like the rather natural "classroom
feel" of the videos. No classroom presentation is ever flawless, and it
can be fun to catch the teacher misspeaking. (I kept an extra presentation
on Laplace transforms for integral equations for exactly that reason.)
The videos were produced with tegrity. For best performance, they
should be downloaded and then run with Internet Explorer as the default
browser. The slides were produced with the LaTeX beamer package.
Introduction.
This is an overview of the course and of my
philosophy for the course, the text and the videos. There is some popping
on the sound. I may need to reshoot this one.
Video. (26:13min,
81MB)
Slides.
Module 1. Modeling  some important examples.
 Derivation of the differential equation for a springmasssystem.
(Could be viewed right before Module 3.)
Video. (9:49min,
29MB)
Slides.
 Derivation of the differential equation for an LRC circuit. (Could
be viewed right before Module 3.)
Video. (7:11min,
21MB)
Slides.
 Derivation of the differential equations for a multiloop circuit,
Kirchhoff's laws. (Could be viewed right before Module 6.)
Video.
(7:27min,
23MB)
Slides.
 Derivation of the equation for an oscillating string. (Could be
viewed right before Module 7.)
Video. (16:23min,
49MB)
Slides.
 Derivation of the heat equation. (Could be viewed right before
Module 7.)
Video. (10:08min,
32MB)
Slides.
Module 2. First order
differential equations.
 General solution of separable differential equations.
Video. (8:47min,
27MB)
Slides. Solution
of an initial value problem for a separable differential equation.
(Reviews integration by substitution and integration by parts.) Video. (12:18min,
36MB)
Slides. Setting up
mixing problems and solving them with separable differential
equations. Video. (15:41min,
48MB)
Slides.
 Linear first order differential equations.
Video. (8:59min,
28MB)
Slides.
 Bernoulli equations.
Video. (15:36min,
47MB)
Slides.
 Homogeneous first order equations.
Video.
(9:01min,
27MB)
Slides.
 Exact differential equations.
Video. (8:27min,
26MB)
Slides.
 How to recognize types of first order equations and how to review
them. (I misspeak twice, possible candidate for reshoot.) (Section 2.7
in the book.)
Video. (15:58min,
47MB)
Slides.
Module 3. Second order
constant coefficient differential equations.
 Solution of linear homogeneous second order differential equations
with constant coefficients. (Sections 3.13.3 in the book.)
Video. (18:54min,
55MB)
Slides.
 The method of undetermined coefficients. (Section 3.4 in the
book.)
Video. (21:52min,
65MB)
Slides.
 The method of undetermined coefficients when the forcing function
solves the homogeneous equation. (Section 3.4 in the book.) There is
some popping on the sound. I may need to reshoot this one.
Video. (21:26min,
66MB)
Slides.
 The formula for Variation of Parameters. (Section 3.5 in the
book.)
Video. (19:49min,
62MB)
Slides.
 The formula for Variation of Parameters. (Solves some rather nasty
integrals. Typo on one slide, candidate to be reshot.)
Video. (19:24min,
61MB)
Slides.
 CauchyEuler equations. (Even though these equations do not have
constant coefficients, they fit in quite well at this spot.)
Video. (14:09min,
45MB)
Slides.
Module 4. Qualitative and
Numerical Approaches.
 Direction fields.
Video.
(6:59min,
23MB)
Slides. Autonomous
differential equations. Video. (11:19min,
36MB)
Slides.
 Euler's method.
Video. (21:06min,
75MB)
Slides.
 Improved Euler method and RungeKutta methods.
Video. (26:33min,
90MB)
Slides.
 Finite difference method.
Video. (25:42,
77MB)
Slides.
Module 5. Theory of linear differential
equations. (One long video only.)
 There is some popping on the sound. I may need to reshoot this
one.
Video.
(39:22min, 122MB)
Slides.
Module 6. Laplace transforms.
 Introduction to Laplace transforms.
Video. (23:38min,
71MB)
Slides.
 Solving initial value problems with Laplace transforms.
Video. (13:46min,
43MB)
Slides.
 Solving systems of differential equations with Laplace
transforms.
Video. (12:20min,
39MB)
Slides.
 An initial value problem that involves damped trigonometric
functions.
Video. (20:29min,
65MB)
Slides.
 Step functions and Laplace transforms.
Video. (19:55min,
61MB)
Slides. Delta
functions and Laplace transforms. Video. (20:05min,
63MB)
Slides.
Animation.
 Laplace transforms and convolutions.
Video. (14:44min,
47MB)
Slides. Laplace
transforms of periodic functions. Video. (23:46min,
72MB)
Slides. Laplace
transforms of integral equations. Video. (10:33min,
34MB)
Slides. The
first video (12:07min,
38MB) I made for this topic approaches the partial fractions in a clumsy
manner. It has a heartfelt comment about my own abilities slightly after
the 5:00 minute mark and another scary moment after the 8:45 mark.
(Unlike the other jokes, neither one was planned.)
Module 7. Separation of variables.
 Solving the equation for the oscillating string. (Sections 7.17.3
in the book.)
Video. (32:46min,
102MB)
Slides. Animation
1. Animation
2. Animation 3.
 Deriving the Legendre equation. (Section 7.4 in the book.) This
presentation plus the presentation on Legendre polynomials (see under
series solutions below) provide most of the mathematics for the quantum
mechanical description of the hydrogen atom.
Video. (22:00min,
71MB)
Slides.
 Deriving the Bessel equation. (Section 7.4 in the book.)
Video. (12:39min,
41MB)
Slides.
 Eigenvalues of the Laplace operator.
Video.
(9:32min,
31MB)
Slides.
Module 8. Series solutions.
Review
 Series solutions about ordinary points.
Video. (13:42min,
43MB)
Slides. Radius of
convergence of power series solutions. Video. (11:44min,
37MB)
Slides.
 Legendre polynomials. This presentation plus the presentation on
deriving the Legendre equation (see separation of variables above)
provide most of the mathematics for the quantum mechanical description
of the hydrogen atom.
Video. (31:47min,
101MB)
Slides.
 Method of Frobenius.
Video. (19:14,
60MB)
Slides. Method of
Frobenius: An example in which we only get one solution. (Also an
example of a specific Bessel equation.) There is some popping on the
sound. I may need to reshoot this one. Video. (26:05min,
75MB)
Slides.
 Bessel equations.
Video. (25:57min,
82MB)
Slides.
Animation
1.
Animation 2.
 Reduction of order. This topic fits here, because the fact that the
method of Frobenius sometimes gives only one solution motivates
reduction of order. There is some popping on the sound. I may need to
reshoot this one.
Video. (12:20min,
37MB)
Slides.
Module 9. Systems of linear differential
equations.
 Translation from higher order to first order systems.
Video. (10:19min,
34MB)
Slides.
 Matrix multiplication.
Video.
(9:00min,
28MB)
Slides.
 Diagonalizable systems of linear differential equations with
constant coefficients.
Video. (36:02min,
112MB)
Slides. Diagonalizable
systems of linear differential equations with constant coefficients,
complex eigenvalues. Video. (16:36min,
56MB) Slides.
 Nondiagonalizable systems of linear differential equations with
constant coefficients.
Video. (13:28min,
44MB) Slides.
"License".
Obviously, if I post something, I want people to use it. So do it. If
you like the videos, try the book.
If you are a teacher, feel free to use the videos and the slides in
classes. The goal is to get people to do better in mathematics.
One caveat: If you want to create an online course with the videos,
note that I have already done so. Please consider sending your students to
my course :)
Sample course outline (Winter term
20082009, 3 semester credit hours)
Slides for a presentation on
online delivery
