I set up the following notes to complement the textbook with more conceptually focused material. I make them available with the hope that others may find them useful.

**I reserve the copyright in all course material created by me and made
available here. You are welcome to use it for teaching, learning, or
research as long as you are not using it commercially.**

I have no pretense that they are a substitute for the textbook.

notesCh1.ps,
notesCh1.pdf

3 1/2 pages on concepts and basic facts

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notesCh2.ps,
notesCh2.pdf

5 pages on different types of 1st order equations. You won't find exact
differential equations here, because I consider them as a footnote to vector
calculus. But
I do include the energy integral from Newton's equations as a
different illustration for the *idea* of an integrating factor.

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notesCh3.ps,
notesCh3.pdf

In the modelling section, the textbook(s) have/has so many brine problems that
one could think the Great Salt Lake came into existence when an experimental
ODE class ran out of control. Here is a challenge problem that is pure
modelling (no solution technique); I did a lot of individual tutoring with
this one. I have a solution, but won't make it available lest this problem
contract the brinomania, too.

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notesCh4.ps,
notesCh4.pdf

This is on 2nd (and higher) order linear equations, and here I deviate
significantly from the usual textbook approach. I first
lay out a roadmap (aka table of contents) for solution techniques;
then I stress that the methods work for n-th order as well as for 2nd and have
much more to do with linearity than ODEs proper. Otherwise, the contrary claim
would be absorbed by the students tacitly. -- I am adamant about including
the case n=1, such as to relate the new material with the old on 1st order.
And I stress the role of complex numbers. The rule
``You try e^{rx} and if you find r=2+3i or 2-3i, then you abandon
our attempt and declare e^{2x}(a cos 3x + b sin 3x) a solution''
is an offense to the brain. So I make Euler's formula into core material,
not auxiliary material.

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notesCh4a.ps,
notesCh4a.pdf

The free and forced oscillator:

We can't do everything: I omit the critical and overdamped case in favor
of a really thorough discussion of the case of small damping, including
a careful discussion of resonance *and phase shifts*, and their
qualitative interpretation, and the convenience of complex numbers in
practical calculations here. I expect my students to recognize the resonance
phenomenon when they encounter it in the real world. That's tough on them,
but it would be even tougher to require their attention while pretending
it's not meant to be used outside the classroom.

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notesCh7.ps,
notesCh7.pdf

On Laplace transforms

These notes are regretfully incomplete, because, near the end of the semester,
I couldn't include convolution nor delta impulses. I still hope they may be
useful to get the gist of the method even from the introductory secions on.

No, I did not include a section on partial fraction decomposition in the notes, fine-tuned to the new context. Calculus notes on the subject are available, and students must adapt to the somewhat different notation and context. (Yes, we did repeat it in class.)

Link to those of my calculus notes concerning (integration by) partial
fractions:

pdf file or
dvi file or
ps file. Textbook references
therein refer to Thomas Calculus ed 10, used in the course for which I
prepared these notes originally.