MATH 275 ORDINARY DIFFERENTIAL EQUATIONS
SPRING 2011
REVIEW TOPICS FOR THE FINAL EXAM
The exam is cumulative and consists of 10 problems covering the main
concepts in the course.
You may bring two 4”x 6” information cards for use during the exam.
A calculator may be handy.
You should bring some scratch paper.
You will have the entire class period for the exam.
The following is a list of topics that you should be familiar with for the final
exam. Exam problems will cover some subset of these topics.
Chapter 1
9 Be able to solve 1st order differential equations by separation of
variables.
9 Be able to interpret slope/direction fields.
9 Be able to apply Euler’s method for 1st order differential equations.
9 Be able to find equilibria and be able to draw associated phase lines.
9 Be able to draw and label bifurcation diagrams.
9 Be able to solve, analytically, 1st order linear differential equations by
the method of guessing (undetermined coefficients) and by the
method of integrating factors.
Chapter 2
9 Be able to find equilibrium solutions and interpret direction fields.
Chapter 3
9 Be familiar with properties of linear systems, vectors, matrices, etc.
9 Be able to find straight line solutions.
9 Be familiar with phase planes, how they are constructed and how they
are interpreted.
Skyline College Math 275 1
