Supplementary Material
1. Review of some useful facts and
formulas from
algebra and calculus
several formulas with illustrative examples that will be useful
throughout the term:
exponentials and natural logs, trig formulas, integration
(elementary functions, substitutions,
integration by parts, partial fractions.
2. Examples:
classifying linear
homogeneous/nonhomogeneous, and nonlinear differential equations.
3. More examles of solving 1st
order linear
nnonhomogeneous DE
4. An
example
illustrating
use of partial
fractions and calculation of intervals of existence for a
separable equation
5. Application: example using Newton's
law of
cooling (continuation of example discussed during lecture on 2/23).
6. Application: mixing
problem in solution
with a time-varying volume.
7. Lecture notes for material first order DE:
linear DE
separable
DE
Applications: 1 2
(second link includes material on pop dynamics and exact DE,
which will not be on Exam I)
8. Example on population
dynamics (as presented
in class-along with calculation of interval of existence).
9.Writeup of damped spring mass problem
from Lecture on Wednesday, April 15
10.Formula sheet for Exam II
11. Extra lectures notes material on Laplace Transforms (more examples,
etc)
LT1
LT2