Math 212
Study Guide for Hour Quiz #1
C.S.Davis
You are responsible for the subject matter in sections 1.1 - 1.2 and 2.1 - 2.6. The following topics are notable in their importance. Typical exercises from Differential Equations with Boundary Value Problems, 6th edition, by Zill and Cullen are assigned at the end of each objective. Work additional exercises if you need more practice. The answers to the odd numbered problems are in the back of the text.
1.1 Be able to apply the following terms in an exercise:
differential equation (DE), solution, ordinary DE, partial DE, order,
linear, nonlinear, explicit solution,
implicit solution,
n-parameter family of solutions,
particular solution, singular solution, general solution.
P10#1-27odd
1.2
a. Given a one or two parameter family of solutions to a DE,
find the solution to the initial value problem (IVP). P16#1,7,13
b. Apply the existence and uniqueness theorem for first
order IVP. P17#17,19,21,25,27
In Chapter 2, we solve ist order
DE's and IVP's using the rule of three,
i.e., we solve them graphically (2.1), algebraically (2.2-2.5)
and numerically (2.6).
2.1 a.
Given a direction field for
a DE or IVP, sketch the graphs of some samples of the
general solution
and the graph of the solution to the IVP. P46#1,2,3,4
b. Sketch
sample lineal elements (arrows) for the direction field of a 1st order DE.
P47#13,14,15,21,23
2.2 - 2.5 Find the general solution to first order DE's and solve first order IVP's of the following varieties:
a. Separation of variables (2.2) P54#1,3,5,7,11,23,27
b. First order linear (2.3) P65#1,3,5,25
c. Exact equations (2.4) P73#1,3,5,21
d. Integrating factors (2.4) P73#31,33,37
e. Homogeneous (2.5) P78#1,3,5,11
f. Bernoulli (2.5) P78#15,17,19
2.6 Use Euler's Method to find a numerical solution to a first order IVP. P84#1,3