Lecture notes/ enrichment
Enrichment 1 (for hwk 1) notes: Examples of equations that are initially not separable but can be reduced to separable
Enrichment 2 (for hwk 2) notes:
Bernoulli equation as an example of nonlinear equation that can be
brought to linear one b y substitution
Enrichment 3 (for hwk 2)
notes: Nonexact equations that can be made exact using integrating
factor depending on single variables
Enrichment 4 (for hwk
4) notes: Abel's theorem for first order linear homogeneous
systems and higher order linear homogeneous equations
Enrichment 5 (for
hwk 6) notes: Euler's equation, which is another example of
second order homogeneous linear equation that can be explicitly solved
(actually reduced to the case of constant coefficient by sn appropriate
substitution)
Enrichment
6 (supplement to the first part of section 17 of the notes) :
factoring of differential operators and the method of reduction of
order.
Enrichment 7 (for bonus questions of homework #7) : the case of an eigenvalue of algebraic multiplicity 3
Enrichment 8 (for bonus questions of
homework #9) : inverse Laplace using partial fraction decomposition
over complex numbers
Enrichment 9 (for bonus question of himework #11): how to determine the shape of ellipss for the phase portrait of a center)
Review of complex numbers
Lecture notes on mechanical vibrations with solved examples
Lecture notes on forced vibrations
Some supporting material on generalized eigenvectors and fundamental set of solutions in the case of repeated eigenvalues: page 1-6, pages 7-12
Material on spiral points
Beamer presentation for the method of
partial fraction decomposition for calculating the inverse Laplace
transform and the beemer presentationof the main points of the material is
here, The handout version (for printing) of the same file is here
Inverse Laplace transform using complex roots