M331     Lecture Notes

 
I. First Order Equations
1. General aspects of 1st order differential equations; differential equations as mathematical models in science; example from
population dynamics: constant  per-capita growth (exponential growth law) and linear per-capita growth (the logistic equation).
Qualitative/geometric methods of solution; the phase line; stability and instability of equilibria.

1a. Numerical and graphical discussion of population dynamics models.

2. Analytic methods of solution: separable equations and the solution of initial value problems; partial fractions expansions; implicit
and explicit form of the solution; blowup  and the interval of existence.

3. Applictions of 1st order sepeparable equations (mixing, etc.); existence and uniqueness
of solutions; slop fields