Form A
Math 24 Castroconde
Exam 1A (Chapters 1 and 2)
Name:
I.D.#:
This paper MUST be attached to your work when submitting it for grading.
Number the work for each question clearly.
1. Verify that y = 10 cos(3x) is a solution of the differential equation
Mathematics 24 Castroconde
Exam 3B (Chapters 5-8)
Name:
I.D.#:
Do your work on separate sheets of paper. You MUST attach this page to your
work before submitting it for grading. This exam has 12 question.
Maple may be used for the entire test to help with
Math 24 Castroconde
Worksheet 4 (Chapter 4)
Name:
I.D.#:
Do your work on separate sheets of paper. Attach this page to your work before
submitting it for grading.
1.
Show that y = c1 + c2 cos( x) + c3 sin( x) is a family of solutions of the equation
y + y
Form B
Math 24 Castroconde
Exam 1B (Chapters 1 and 2)
Name:
I.D.#:
This paper MUST be attached to your work when submitting it for grading.
Number the work for each question clearly.
1. Verify that y = 12sin(5 x) is a solution of the differential equation
Mathematics 24 Castroconde
Exam 2A (Chapters 3 and 4)
Name:
I.D.#:
Technology may be used for the entire test when appropriate.
Make sure to show enough work to justify your answers.
The dsolve command can be used only for application problems.
Attach thi
Mathematics 24 Castroconde
Exam 2B (Chapters 3 and 4)
Name:
I.D.#:
Technology may be used for the entire test when appropriate.
Make sure to show enough work to justify your answers.
The dsolve command can be used only for application problems.
Attach thi
Mathematics 24 Castroconde
Exam 3A (Chapters 5 -8)
Name:
I.D.#:
Do your work on separate sheets of paper. You MUST attach this page to your
work before submitting it for grading. This exam has 12 questions.
Maple may be used for the entire test to help wi
The Laplace Transform
TABLE 6.2.1 Elementary
f(t)
Laplace Transforms
= 2 -1 cfw_F(s)
F(s)
\.
1.
s
,
s>o
s3. tn,n = positive integer
= ' cfw_f(tJ
5>a
a'
n!
5> 0
5>0
a
5. sin at
5>0
s
6. cos at
o
s
lal
s
8. cosh at
b
eacsinbt
s>a
s- a
10.eaccosbt
11. tneae,
Project 1 Getting Started
In the Maple Tutorials section of Blackboard find the Getting Started Tutorial and study
it carefully. Then complete the assignments below using in each case the appropriate
Maple commands illustrated in the tutorial.
To earn ful
Math 24 Castroconde
Worksheet 5 (Chapter 5)
Name:
I.D.#:
Do your work on separate sheets of paper. Attach this page to your work before
submitting for grading.
Our agreement: down is positive
1. A 4-lb weight is attached to a spring whose constant is 16 l
Math 24 Castroconde
Frobenius Method (6.4)
Name:
I.D.#:
For the equation xy + 2 y + xy = 0 , do the following:
Show that = 0 is a regular singular point.
Use the method of Frobenius to find the indicial equation and the indicial roots.
Find the recursi
Math 24 Castroconde
Worksheet 6 (Chapter 6)
Name:
I.D.#:
Do your work on separate sheets of paper. Attach this page to your work before
submitting it for grading.
1. Solve: xy y = 0
2. Solve: x 2 y 5 xy + 8 y = 0, y (2) = 32, y (2) = 0
3. Find the radius
Math 24 Castroconde
Worksheet 7 (Chapter 7)
Name:
I.D.#:
Start your work after the last question. Attach more paper, if needed.
1.
Use the definition of Laplace transform to find the Laplace transform of
f (t ) = e t 2
2.
Use the table of Laplace transfor
Math 24 Castroconde
Worksheet 8 (8.1, 8.2)
Name:
I.D.#:
Start your work after the last question. Attach more paper, if needed.
1.
Solve the system below using elimination.
dx
= 2x y
dt
dy
=x
dt
2.
Solve the system below using determinants.
dx
= y + t
dt
d
Section 5.3 - Problem 9
After reading the problem carefully, I applied Hooke's Law to the system. Since the oscillation of the
support starts after the mass the mass reaches equilibrium, this is what we get:
Force = -k(displacement form equilibrium) = -k[
Review of Convergence Tests
Test
Statement
Comments
Geometric Series
If
, converges for
the sum is
Divergence Test
Let
.
If
Integral Test
, the series diverges
and
, then
If the limit is 0, the series may or
may not converge.
diverges.
Use this test when
Math 24 Castroconde
Review of Power Series
Determine whether the series converges or diverges. Name all test used.
5n
1.
n =1
2
3
+n+2
ln(n 2 )
n
n =1
1
3n 1
n =1
2.
3.
4.
3n 2 + 2n
n =1
4 + n5
Find the radius and interval of convergence of each power s
Math 24 - Castroconde
Preliminary Theory for Chapter 4
Part 1: Initial Value Problems and Boundary Value Problems
An initial value problem consists of a differential equation and a set of values for the
unknown function and its derivatives at a fixed poin
Project 2 Solving ODEs
In the Maple Tutorials section of Blackboard find the Solving ODEs Tutorial and study it
carefully. Then complete the assignments below using in each case the appropriate
Maple commands illustrated in the tutorial.
To earn full cred
Project 3 Eulers Methods
In the Maple Tutorials section of Blackboard find the Eulers Methods Tutorial and study
it carefully. Then complete the assignments below using in each case the appropriate
Maple commands illustrated in the tutorial.
To earn full
Project 4 Power Series Methods
In the Maple Tutorials section of Blackboard find the Power Series Methods Tutorial and
study it carefully. Then complete the assignments below.
To earn full credit, text must be inserted correctly to answer questions and to
A Few More Things
Laplace Transforms
Maple can be used to find Laplace transforms and inverse Laplace
transforms. The package inttrans is needed.
>
(1)
>
(2)
>
(3)
Notice that f was defined as an espression, not a function and that the
command for the tra
Project 4 A Few More Things
In the Maple Tutorials section of Blackboard find the A Few More Things Tutorial and study it
carefully. Make sure to read carefully the instructions about submitting work for grading. Then
complete the assignments below using
Project 3 Numerical Approximations
In the Maple Tutorials section of Blackboard find the Numerical Approximations Tutorial and
study it carefully. Make sure to read carefully the instructions about submitting work for grading.
Then complete the assignment
(1)
Getting Started
This tutorial will teach you some of the basic Maple commands you will
need through out the course. It would be a good idea for you to practice
the commands as you read the tutorial. Find a computer that has access
to Maple. Computers
Solving Differential Equations with Maple
This tutorial will teach you the basic Maple commands for solving
Ordinary Differential Equations (ODEs).
The most important thing to remember is to always use function
notation.
The package needed is DEtools.
We