APMA 2130
First Exam
September 19th, 2012
STUDENT NAME:
Please write clearly and legibly. Show all of your work in order to receive full credit,
and circle or box your nal answer. No books, notes or calculators are allowed.
On my honor as a student, I hav

APMA 2130
Third Exam
November 14th, 2012
STUDENT NAME:
Please write clearly and legibly. Show all of your work in order to receive full credit,
and circle or box your nal answer. No books, notes or calculators are allowed.
On my honor as a student, I have

APMA 2130
Second Exam
October 17th, 2012
STUDENT NAME:
Please write clearly and legibly. Show all of your work in order to receive full credit,
and circle or box your nal answer. No books, notes or calculators are allowed.
On my honor as a student, I have

Practice Qs for nal exam:
Dierential equations & Fourier series
Math 21b, Fall 2009
Below are some questions on dierential equations and Fourier series, the main topics
covered in class after Midterm 2. As you attempt them, try to make connections with
th

APMA 2130
Undetermined Coecients
Worksheet
Heres the big picture:
g (t) = p(t)et cos t = Y (t) = tn et p1 (t) cos t + p2 (t) sin t .
a. The functions p(t), p1 (t), p2 (t) are polynomials.
b. The number n is an integer: n = 0, 1, or 2.
c. Replacing the cos

Solving the non-homogeneous equation ay + by + cy = g (t) is a 3-step process:
(1) Solve the homogeneous equation ay + by + cy = 0. This requires you to nd a fundamental set of solutions cfw_y1 , y2 ; the general solution to the homogeneous equation can
t

APMA 213
Wronskian & Linear Independence
October 15, 2007
If W (y1 , . . . , yn )(x0 ) = 0 for any x0 in the interval I = (, ), then y1 , . . . , yn are
linearly independent on I . However, even if W (y1 , . . . , yn )(x) = 0 for all < x < , this
does not

Math 14 Differential Equations Sample Exam Questions
1. Find all solutions of the IVP, describe their domain of validity, and make a reasonably
accurate sketch of the solution(s):
2y + y 3 = 0,
y (0) = 1
2. Find and sketch all solutions of the IVP, and de

Math 115 Exam #4 Practice Problem Solutions
1. Solve the initial-value problem
y + 8y + 16y = 0,
y (0) = 3,
y (0) = 6.
Answer: The characteristic equation is
r2 + 8r + 16 = 0,
which factors as
(r + 4)2 = 0,
so r = 4 is the only solution of the equation. T

Dierential Equations Final Exam Practice
Solutions
1. A tank originally contains 10 gal of water with 1/2 lb of salt in solution.
1
Water containing a salt concentration of 200 (10 t)2 (sin(t) + 1) lb per gallon
ows into the tank at a rate of 1 gal/ min,

Practice Midterm Exam #1 Math 211 Ordinary Differential Equations and Linear Algebra Summer 2009 Instructions: This is a 2 hour exam. You may not consult any notes or books during the exam, and no calculators are allowed. 1. Find a general solution for ea

Name:
Math 246 - Dierential Equations, Summer 2012, Practice Exam 2
INSTRUCTIONS: All work must be shown to receive credit. Use one answer sheet per
problem. One page of notes, typed or handwritten, front and back, is allowed, but nothing
else. Make sure

Name:
Math 246 - Dierential Equations, Summer 2012, Practice Exam 2
INSTRUCTIONS: All work must be shown to receive credit. Use one answer sheet per
problem. One page of notes, typed or handwritten, front and back, is allowed, but nothing
else. Make sure

Dierential Equations: Final Exam Practice Questions
The
You
You
You
You
Page 1 of 5
nal exam will include 8 questions, one of which will be several True/False.
will answer all questions (unlike the midterm, where you had choice).
will have 120 minutes to

Math 308 Dierential Equations
Practice Exam 2
Fall 2002
1. The plot below shows a direction eld for an autonomous system of two rst order
dierential equations dx/dt = f (x, y ), dy/dt = g (x, y ). The solid curve corresponds to
a solution (x(t), y (t) to

APMA 213
Second Exam
July 17, 2007
STUDENT NAME:
Answer each question in the space provided. Please write clearly and legibly.
Show all of your work in order to receive full credit, and clearly identify your
nal answer. No books, notes or calculators are