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*f*_{1},*f*_{2}, and*f*_{3}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.

- 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, e^{3}≈ 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(*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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