REVIEW SHEET FOR TEST 2

The best way to prepare for a test is to review homework problems, examples from the textbook and class notes. Make sure that you can solve these problems in a reasonable amount of time without reference to the textbook or class notes. It is important that on the test you show all your work and explain your answers. Just answers (especially wrong ones!) without any explanation will earn you no credit.

List of major topics covered in class.

1. Solving linear differential equations by “integrating factors” method, pp. 126-134. Review problems: # 1, 3, 5, 6, 7, 9, 11, 12, 24, 25 on pp. 135-137.

2. Solving linear differential equations by finding a particular solution, Linearity Principle, pp. 112-120. Review problems: 3, 5, 9, 21, 23 on pp. 123-125.

3. Know at least one example of an initial value problem with more than one solution, and an example of an initial value problem with a solution that blows up (see class notes or examples in Sec. 1.5). Review problems: 1, 5, 14, 15, 18 on pp. 73-76.

4. Predator-Prey model: equilibrium solutions, initial conditions, solution curves, phase portrait (pp. 11-13 and 152-159), vector field, and direction field (pp. 170-171), modified predator-prey model (pp. 157-159), competing species (pp. 179-181). Review problems: 19, 20, 22 on pp. 19-20, and also 1, 2, 3, 4, 6, 8, 10, 16 after 2.1.

5. Simple harmonic oscillator model: equation of, reduction to a first order system, initial value problem, solution curves (pp.159-163), vector field, and direction field (pp. 171-173).  Review problems: 19, 20, 22 on pp. 167-168.

6. Geometry of systems: vector notation, vector field, direction field, solution curves, equilibrium points and how to find them, equilibrium solutions (pp. 169-178). Review problems: 2, 3, 6, 8, 9, 11, 13-18, 21, 23 on pp. 182-186.

7. Analytic methods: checking solutions (pp.187-189), solving completely and partially decoupled systems (pp. 189-192), plotting solutions and solution curves, examples in Sec. 2.3. Review problems: 1, 3, 4, 7, 8, 10, 19 on pp. 196-198.

There are also good review problems after Chapter 2 (pp.  220-222).

GOOD LUCK!