Math 2250 - 002
Midterm #2 Review
Chapter 4:

Determine whether a set of vectors is
linearly independent or linearly dependent.

Describe the span of a finite set of vectors


Find the specific solution to a homogenous
linear DE with constant coefficients given a
set of initial conditions.

Use the method of undetermined
coefficients to find the particular solution of
a non-homogenous linear DE with constant
coefficients.

Use variation of parameters to find the
particular solution of a non-homogeneous
linear DE with constant coefficients.

Fine the complimentary solution of a nonhomogeneous linear DE with constant
coefficients.

Given a mass-spring-dashpot system, or a
pendulum system, find the
o general solution
o period of motion
o frequency of motion
o amplitude of motion
o whether the system is over-damped,
under-damped, or critically damped.
Given a mass-spring-dashpot system with
external forcing, find the
o natural frequency
o forcing frequency
o general solution
o transient solution
o stable periodic solution
o amplitude of stable periodic solution
Vector addition, subtraction, scalar
multiplication.


Fall 2011
11/10/11
Determine whether a set of vectors is a
subspace
o Closed under addition
o Closed under scalar multiplication
Determine whether or not a finite set of
vectors is a basis.

Determine the dimension of a vector space.

Determine the solution space of a linear
system.

Determine whether two functions are
linearly independent.

Chapter 5:

Given two linearly independent solutions to
a second order homogeneous DE, and a set
of initial conditions, find a solution that
satisfies the initial conditions using the
principle of super position.

Calculate the Wronskian of a set of
functions. Use this information to
determine whether the functions are
linearly dependent or independent.
Chapter 10:

Find the Laplace Transform of a basic
functions.
Find the general solution for a
homogeneous linear DE with constant
coefficients.
o Distinct Roots
o Duplicated Roots
o Complex Roots

Find the inverse Laplace Transform of basic
functions

Apply the Laplace Transform to an IVP.

Math 2250 - 002
Midterm #2 Review
Practice Problems:
Note: I would suggest trying out at least one of
each type of problem. If you need the
additional practice then work through
additional examples of the same problem type.
Problem types are separated by commas.
Section 4.1:
13 - 18, 19 - 24, 29 - 32, 33 - 37
Section 4.2:
1 - 14, 15 - 18
Section 4.3:
9 - 16, 17 - 22
Section 4.4:
1 - 8, 12 - 14, 15 - 26
Section 4.7:
13 - 18
Section 5.1:
1 - 16, 20 - 26
Section 5.2:
7 - 12, 13 - 20
Section 5.3:
1 - 20, 21 - 26, 27 - 32
Section 5.4:
1 - 4, 8, 13, 14, 15 - 21
Section 5.5:
1 - 20, 31 - 40, 44 - 46, 47 - 56
Section 5.6:
1 - 6, 7 - 10, 11 - 14, 15 - 18
Section 10.1:
1 - 6, 11 - 22, 23 - 32
Section 10.2:
1 - 16, 17 - 24
Fall 2011
11/10/11