Math 2326 Quiz 7
You may use a calculator and your homework, but not your books or notes. There are two problems
worth 10 points each. Show all work to receive full/partial credit.
1) Consider the linear system
dY 2 0
El? (1 1) Y"
a) Show that the two
Section 1.9
The method of the integrating factor:
For a nonhomogeneous differential equation of the form
the integrating factor
is found with the formula
Multiplying both sides of the differential equation by
gives
The integrating factor
is chosen in this
Section 1.2
First-order differential equation: An equation for an unknown function in terms of its derivative. A
solution of the differential equation is a function of the independent variable that, when substituted
into the equation as the dependent vari
Section 1.5
Existence Theorem: Suppose
an
and a function
is a continuous function in a rectangle of the form
in the -plane. If
is a point in this rectangle, then there exists
defined for
that solves the initial-value problem
This theorem says that as long
Section 1.1
First-order differential equation: An equation that only contains the first derivative of the independent
variable.
Ordinary differential equation: An equation that only contains ordinary derivatives and no partial
derivatives.
Equilibrium sol
Section 1.6
Phase Line: A vertical line that helps determine the behavior of solutions to an initial-value problem.
Equilibrium points: Points on a phase line that represent constant solutions to an initial-value problem.
1) Draw phase lines for the follo
Section 1.7
Bifurcation: A change in the long-term behavior of solutions to an ODE resulting from a slight change in
a parameter.
Bifurcation diagram: A picture (in the
-plane) of the phase lines near a bifurcation value.
Notation:
When an autonomous diff
Math 2326
Practice Exam 2
There will be 6-8 problems on the actual test. All of them will be similar to the problems shown here.
1) Use the guess and test method to find two solutions
and
to the second-order differential equation for the damped harmonic
o
Math 2326
Practice Final
There will be 10-12 problems on the actual test. The final exam will be comprehensive, so in addition to
these problems you should study the problems from the previous exams and practice exams.
1) Consider the following competing
Math 2326
Practice Exam 1
There will be 6 to 8 problems on the actual test. All of them will be similar to the problems shown here.
For problems 1-3, solve the differential equations. If you cannot solve for the independent variable,
leave the solution de
Section 1.4
Summary of Eulers Method
Eulers method is used to approximate a solution to a first-order initial-value problem
Given the initial condition
preceding point
as follows:
and the step size
, compute the point
1. Use the differential equation to c
Section 1.3
Slope field: A graphical representation of the solutions of a first-order differential equation.
1) Draw a slope field for the differential equation
. Draw small slope lines on each of
the dots in the graph to the right (it doesnt have to be e
Section 1.8
Linear: A first-order differential equation is linear if it can be written in the form
where
and
are arbitrary functions of .
If
for all , then the equation is said to be homogeneous or unforced. Otherwise it is
nonhomogeneous or forced.
A fir
WW,
1 4° .
Math 2326 Quiz 8 Name A: L g
DUE THURSDAY, 7/25, NO EXCEPTIONS!
There are two problems worth 10 points each. Show all work to receive full/partial credit.
1) For the harmonic oscillator with mass m = 1, spring constant k = 10, and damping co
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Math 2326 Quiz 9 Name
DUE FRIDAY, 7/26, NO EXCEPTIONS!
There are two problems worth 10 points each. Show all work to receive full/partial credit.
1) The linear system has one line of eigenvectors.
dY
E 2(31 All) Y'
8)
er l
MK Lias-k "
Find the
Math 2326 Quiz 1 Name Z
You may use a calculator and your homework, but not your books or notes. There are three problems
worth 5 points each. Show all work to receive full/partial credit.
1) Assume that bacteria in a culture grows according to an expo