Mathematics 3113-001 - Introduction to ODE - Fall 2003
Information about Exam I
Exam I will be in the usual classroom on September 23, 2003.
Only a basic, non-graphing calculator may be used. Actually, there is no
need to use a calculator. Scratch paper will be available, so all you will
need is something to write with.
The exam will be worth 53 points, and will cover sections 1.1-1.6, 3.1, and
3.2. The approximate point breakdown by section of the text is as
follows:
| 1.2 | 2
|
| 1.3 | 4
|
| 1.4 | 3
|
| 1.5 | 12
|
| 1.6 | 7
|
| 3.1 | 15
|
| 3.2 | 10
|
| Total | 53
|
The following topics will definitely be covered (of course, the exam is not limited to
these topics):
| 1.
| initial value problems, nonuniqueness of solutions for some
equations
|
| 2.
| separation of variables, solving first-order linear equations using
an integrating factor
|
| 3.
| the theory of linear equations as summarized on the handouts
|
| 4.
| solving second-order linear equations with constant coefficients and
with initial conditions of the form y(a)=b_0, y'(a)=b_1
|
You do not need to know about "exact" equations (section 1.6). There are no
problems similar to 1.2 #19-22 or the word problems in section 1.2.
You will need to know the integrating factor method for first-order linear
equations from memory. If there is an equation of Bernoulli type to solve,
you will be given the formula v=y^{1-r}. If there is a first-order equation
that can be put in the form y' = F(y/x), you will be given the substitution
v = y/x. If there is a second-order equation that can be put in the form
F(y,v,dv/dy), you will be given the substitution v=dy/dx.
You should know the general form for a linear equation, the definition of
homogeneous linear DE, the definition of linear dependence and how to use
it to show that a collection of functions is linearly dependent, and the
meaning of particular solution and complementary solution. There is no
question involving the Wronskian (of course, there is always the final exam...).
There is no start-from-scratch word problem, but there are problems
involving the thinking processes used in solving some of the word problems
we have had.
Remember that you can find exams that I wrote for this course in previous
semesters, on the Course Pages From Previous Semesters page. For some
students, these are a useful study aid. But the lectures, homework, and
above description are your best guide to what is likely to be on our exam
this semester.