Problem sets and quizzes
Almost every Thursday, there will be a quiz,
based on an associated problem set.
(However, the last quiz will be on June 5 Monday.)
Unless otherwise specified,
all problems
are from the 5th Edition
of Differential Equations and Boundary Value Problems
by Edwards et al published by Prentice-Hall (Pearson).
Here are the quizzes and their associated problem sets
(Quiz 1, Quiz 2, Quiz 3,
Quiz 4, Quiz 5):
- Introduction:
- Date taken: July 21 Friday.
- Problems from §1.1 (pages 8&9): 3, 9, 16, 22, 25, 30, 36.
- Problems from §1.2 (pages 15–17): 3, 6, 10, 14, 22, 25, 30.
- Problems from §1.3 (pages 24–27): 2, 8, 12, 15, 21, 27.
- Problems from §1.4 (pages 40–44):
5, 10, 16, 17, 24, 31, 35, 39, 49, 61.
- Problems from §1.5 (pages 53–55): 3, 9, 16, 22, 30, 33, 37.
- Problems from §1.6 (pages 69–71): 7, 14, 29, 37, 47.
- Extra-credit essay question:
Explain your background in mathematics
and what you are going to use this course for.
(Or just tell me if anything has changed since last term.)
- Linear differential equations:
- Date taken: August 2 Wednesday.
- Problems from §3.1 (pages 147&148):
3, 6, 9, 16, 18, 20, 22, 27, 33, 37, 40.
- Problems from §3.2 (pages 159&160):
3, 5, 8, 12, 14, 18, 21, 24, 26, 29.
- Problems from §3.3 (pages 170–172):
3, 7, 18, 19, 23, 26, 34, 37, 40, 43, 44.
- Problems from §3.5 (pages 195&196):
3, 4, 5, 10, 13, 22, 28, 31, 40, 43, 49, 53.
- Extra credit:
Following the development of Theorem 3.5.1 on page 194 of the textbook,
find a general formula for the function f,
given f″′(x) +
P(x) f″(x) +
Q(x) f′(x) +
R(x) f(x) = F(x),
assuming that P, Q, R, and F are continuous,
using integrals and given solutions
f1, f2, and f3
of the corresponding homogeneous linear differential equation
(where F(x) is replaced by 0).
- Systems of differential equations:
- Date taken: August 16 Wednesday.
- Problems from §4.1 (pages 235&236):
3, 5, 11, 12, 14, 19, 21.
- Problems from §5.1 (pages 279–281):
2, 4, 6, 12, 18, 21, 24, 26.
- Problems from §5.2 (pages 293&294): 2, 5, 10, 29, 38.
- Problems from §5.5 (pages 346–348): 2, 4, 6, 23, 27, 30.
- Extra credit:
Consider this system of differential equations and initial values:
- f′(t) =
5 f(t) − 4 g(t),
- g′(t) =
2 f(t) − g(t),
- f(0) = 3,
- g(0) = −1.
Calculate the exponential of the coefficient matrix of this system
and use it to solve the system.
- Numerical methods and applications:
- Date taken: August 30 Wednesday.
- Problems from §2.1 (pages 82—): 2, 7, 9, 18, 21, 24.
- Problems from §2.2 (pages 91—): 6, 10, 20, 21.
- Problems from §2.3 (pages 100—): 1, 2, 4, 13, 14, 20.
- Problems from §2.4 (pages 113—):
5, 8, 12, 14, 16, 19, 22, 23, 30.
- Problems from §6.1 (pages 380—):
1–8, 13, 15, 16, 19, 20, 23.
- Extra credit:
Use Euler's method with a step size of 1
to approximate f(3),
where f is the solution to the differential equation
f′(x) = f(x) with f(0) = 1.
Then use the improved Euler method described in Section 7.5 of the textbook
to approximate the same value.
Which is closer to the actual value,
e3 ≈ 20.1?
(Show at least the numerical results at each step.)
- Laplace transforms:
- Date taken: September 13 Wednesday.
- Problems from §7.1 (pages 445—): 1, 8, 19, 21, 29, 32.
- Problems from §7.2 (pages 456—):
1, 2, 3, 5, 6, 9, 11, 13, 16, 19.
- Problems from §7.3 (pages 464—):
1, 3, 4, 6, 7, 8, 9, 11, 12, 15, 19, 27.
- Problems from §7.4 (pages 473—):
1, 3, 5, 7, 9, 15, 17, 19, 22, 23, 26, 29.
- Extra credit:
Is the Laplace transform of
f(t) = sin(exp(t2))
defined anywhere?
(Explain why or why not.)
Is the Laplace transform of f′ defined anywhere?
(Explain why or why not.)
That's it!
Go back to the the course homepage.
This web page was written between 2003 and 2017 by Toby Bartels,
last edited on 2017 September 18.
Toby reserves no legal rights to it.
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http://tobybartels.name/MATH-2200/2017SU/quizzes/.
