Math 211 Slides --- Fall 2003
There are two choices for each lecture. The first one is in color and
is meant for viewing online. The second is meant for printing. It is
in black & white, and it is formatted with 3 slides per page along the
left-hand margin, with half of the page available for taking notes.
The slides are .pdf files and can be viewed in Adobe Acrobat Reader.
However, it is recommended that you use version 5 or later of the
reader to maximize compatibility. See the Math 211 FAQ
for details about obtaining the latest version of the reader.
Some people are having trouble printing pdf files. If this happens
to you, try to download the document by right-clicking on the link and
choosing "Save link as ...". Remember where on your computer you save
the document (the desktop is a good place for this). Then
double-click on the icon to open the document in Adobe Acrobat
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Review lectures.
Revised version of Chapter 9.
In Section 2 we will be following a path that is somewhat different
from what is in the textbook. This path is described in the following
pdf document. The principal change is that the exponential of a matrix
is used from the very beginning, instead of bringing it in only at the
end.
Slides intended for Section 2.
- Lecture #1, Introduction, August 25, 2003
(For viewing)
(For printing.)
- Lecture #2, The Use of MATLAB, August 28, 2003. No slides
- Lecture #3, Solutions of Differential Equations, August 30, 2003
(For viewing)
(For printing.)
- Lecture #4, Solutions to Separable Equations, September 3, 2003
(For viewing)
(For printing.)
- Lecture #5, Models of Motion, September 5, 2003
(For viewing)
(For printing.)
- Lecture #6, Linear Equations, September 8, 2003
(For viewing)
(For printing.)
- Lecture #7, Mixing Problems, September 10, 2003
(For viewing)
(For printing.)
- Lecture #8, Existence & Uniqueness, September 12, 2003
(For viewing)
(For printing.)
- Lecture #9, Qualitative Analysis, September 15, 2003
(For viewing)
(For printing.)
- Lecture #10, Population Models, September 17, 2003
(For viewing)
(For printing.)
- Lecture #11, Financial Models, September 19, 2003
(For viewing)
(For printing.)
- Lecture #12, Euler's Method, September 22, 2003
(For viewing)
(For printing.)
- Lecture #13, Runge-Kutta Methods, September 24, 2003
(For viewing)
(For printing.)
Download
odesolvedemo.m for a comparison of the errors made by
Euler's method and the Runge-Kutta methods. This is a MATLAB
program. Execute
odesolvedemo. odesolvedemo.m is also a simple
example of MATLAB programming.
- Lecture #14, MATLAB's Solvers, September 26, 2003
(For viewing)
(For printing.)
- Lecture #15, Linear Systems of Equations, September 29, 2003
(For viewing)
(For printing.)
- Lecture #16, Geometry of Solution Sets, October 1, 2003
(For viewing)
(For printing.)
- Lecture #17, Solving Systems of Equations, October 3, 2003
(For viewing)
(For printing.)
- Lecture #18, Properties of Solution Sets, October 6, 2003
(For viewing)
(For printing.)
- Lecture #19, Solution Sets, October 8, 2003
(For viewing)
(For printing.)
- Lecture #20, Basis of a Subspace, October 10, 2003
(For viewing)
(For printing.)
- Lecture #21, Determinants, October 15, 2003
(For viewing)
(For printing.)
- Lecture #22, Systems of ODEs, October 17, 2003
(For viewing)
(For printing.)
- Lecture #23, Qualitative Analysis, October 20, 2003
(For viewing)
(For printing.)
- Lecture #24, Linear Systems of ODEs, October 23, 2003
(For viewing)
(For printing.)
- Lecture #25, The Exponential of a Matrix, October 25, 2003
(For viewing)
(For printing.)
- Lecture #26, Solutions of a Planar System, October 27, 2003
(For viewing)
(For printing.)
- Lecture #27, Planar System, October 29, 2003
(For viewing)
(For printing.)
- Lecture #28, Phase Plane Portraits, October 31, 2003
(For viewing)
(For printing.)
- Lecture #29, Higher Dimensional Systems,
November 3, 2003
(For viewing)
(For printing.)
- Lecture #30, Solutions of Systems and Stability, November 5, 2003
(For viewing)
(For printing.)
- Lecture #31, Higher Order Equations, Harmonic Motion, November 7, 2003
(For viewing)
(For printing.)
- Lecture #32,Harmonic Motion, November 10, 2003
(For viewing)
(For printing.)
- Lecture #33, Inhomogeneous Equations, Forced Harmonic Motion,
November 12, 2003
(For viewing)
(For printing.)
- Lecture #34, Forced Harmonic Motion, November 14, 2003
(For viewing)
(For printing.)
- Lecture #35, Nonlinear Systems,
November 17, 2003
(For viewing)
(For printing.)
- Lecture #36, The Use of the Linearization,
November 19, 2003
(For viewing)
(For printing.)
- Lecture #37, The Linearization in Higher Dimensions,
November 21, 2003
(For viewing)
(For printing.)
The M-file for analyzing the
Lorenz system.
- Lecture #38, Invariant Sets and Nullclines,
November 24, 2003
(For viewing)
(For printing.)
- Lecture #39, Long Term Behavior of Solutions to Planar Systems,
November 26, 2003
(For viewing)
(For printing.)
- Lecture #40, Limit Sets of Solution Curves,
December 1, 2003
(For viewing)
(For printing.)
- Lecture #41, The Pendulum and Predator-Prey,
December 3, 2003
(For viewing)
(For printing)
- Lecture #42, Immunity to Infectious Deseases
December 5, 2003
(For viewing)
(For printing)
The M-file for analyzing the
Anderson-May model of the immune system.