Here are the quizzes and their associated problem sets (Quiz 1, Quiz 2, Quiz 3, Quiz 4, Quiz 5):

- Introduction:
- Date taken: July 23 Monday.
- 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 3 Friday.
- Problems from §3.1 (pages 147&148, note that Exercises 2–6 have accidentally been printed in the right-hand column): 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, 39.
- 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.
- Extra credit:
- Simpler problem:
Exercise 3.5.54:
Find the general solution of the differential equation
*g*″(*x*) +*g*(*x*) = csc^{2}*x*for 0 <*x*< π, using variation of parameters. (Either show what equations you solve to find the parameters or show what integrals you take to use a formula. Or show lots of work; you'll probably want to do that anyway.) - Original problem:
Following the development of Theorem 3.5.1 on page 194 of the textbook,
find a general formula for
*y*=*g*(*x*), given*g*‴(*x*) +*P*(*x*)*g*″(*x*) +*Q*(*x*)*g*′(*x*) +*R*(*x*)*g*(*x*) =*f*(*x*), assuming that*P*,*Q*,*R*, and*f*are continuous. Assume that you are given independent solutions*y*_{1}=*g*_{1}(*x*),*y*_{2}=*g*_{2}(*x*), and*y*_{3}=*g*_{3}(*x*) for the corresponding homogeneous linear differential equation (in which*f*(*x*) has been replaced by 0); your answer will include some indefinite integrals that cannot be evaluated (much as Theorem 3.5.1 does).

- Simpler problem:
Exercise 3.5.54:
Find the general solution of the differential equation

- Systems of differential equations:
- Date taken: August 15 Wednesday.
- Problems from §4.1 (pages 235–237): 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.

- Numerical methods and applications:
- Date taken: August 27 Monday.
- Problems from §2.1 (pages 82–84): 2, 7, 9, 18, 21, 24.
- Problems from §2.2 (pages 91–93): 6, 10, 20, 21.
- Problems from §2.3 (pages 100–102): 1, 2, 4, 13, 14, 20.
- Problems from §2.4 (pages 113&114): 5, 8, 12, 14, 16, 19, 22, 23, 30.
- Problems from §6.1 (pages 380&381): 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 2.5 of the textbook to approximate the same value. Which is closer to the actual value, e^{3}≈ 20.1? (Show at least the numerical results at each step.)

- Laplace transforms:
- Date taken: September 12 Wednesday.
- Problems from §7.1 (pages 445&446): 1, 8, 19, 21, 29, 32.
- Problems from §7.2 (pages 456&457): 1, 2, 3, 5, 6, 9, 11, 13, 16, 19.
- Problems from §7.3 (pages 464&465): 1, 3, 4, 6, 7, 8, 9, 11, 12, 15, 19, 27.
- Problems from §7.4 (pages 473&474): 1, 3, 5, 7, 9, 15, 17, 19, 22, 23, 26, 29.
- Problems from §7.5 (pages 482&483): 1, 2, 3, 5, 6, 9, 11, 13, 16, 19.
- Extra credit:
Refer to Exercise 7.1.36 on page 446.
Is the Laplace transform of
*f*(*t*) = sin(exp(*t*^{2})) defined anywhere? (Explain why or why not.) Is the Laplace transform of*f*′ defined anywhere? (Explain why or why not.)

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