Mathematics 45, Spring 2017

Differential Equations for Science and Engineering

Lectures:

Section 07: MWF 8-8:50am, Room 156, Alpine Hall

Section 08: MWF 11-11:50am, Room 201, Brighton Hall



Instructor: Michael VanValkenburgh.

Office: Room 140, Brighton Hall
Office Hours: Mondays and Wednesdays 9-10am and Thursdays 10:30-11:30am.


A description of the course: Math 45, Spring 2017 (pdf)

Drop Policy


Announcements:

We will be using the following textbook:
A First Course in Differential Equations with Modeling Applications (10th edition) by Dennis Zill.
We will cover the sections listed in the lecture schedule below.



Final Exam Schedule. Please take this into account when registering for classes:
Section 07: Monday, May 15, 8-10am
Section 08: Monday, May 15, 10:15am-12:15pm
(Note how it overlaps with the regular lecture time.)

One of your classmates found this online slope field calculator: desmos.com slope field calculator


Homework:


You will not turn in the homework. Instead, we will have occasional quizzes, with the problems taken from the homework.

Quiz 1: Monday, January 30. Based on the Sections 1.1, 1.2, and 1.3 homework of this book: Differential Equations, by András Domokos.

Quiz 2: Monday, February 6.
Section 1.1 (7, 8, 12, 13, 16, 17, 21, 22, 23, 30, 32, 38)
Section 1.2 (1, 2, 3, 4, 8, 9, 12, 13, 26, 27)

For the Exam on Monday, February 13.
Section 2.1 (2, 15, 21, 24, 26, 30)
Section 2.2 (5, 6, 7, 8, 17, 24, 25)

Quiz 3: Friday, February 24.
Section 2.3 (5, 6, 9, 10, 18, 19, 20, 26, 27)
Section 2.4 (4, 5, 12, 13, 22, 23, 27, 28, 31, 32, 37, 38)

For the Exam on Wednesday, March 8.
Section 2.4 (35, 36)
Section 2.5 (11, 12, 15, 16, 23, 24)
Section 2.6 (1, 2, 3, 4)
Section 4.1 (1, 2, 3, 4, 5, 13, 14, 35, 36)

Quiz 4: Friday, March 17.
Section 4.1 (15, 16, 17, 18, 25, 26, 33, 34)
Section 4.2 (3, 4, 7, 8, 11, 12, 19, 20)

Quiz 5: Wednesday, March 29.
Section 4.3 (2, 3, 8, 9, 11, 12, 16, 17, 21, 24, 29, 30, 38, 39)
It's all about factoring and finding roots of polynomials. It's just algebra!

Quiz 6: Wednesday, April 5.
Section 4.4 (3, 4, 8, 10, 11, 14, 15, 18, 19, 20)

Quiz 7: Friday, April 14.
Section 4.5 (6, 7, 12, 13, 18, 20, 44, 45, 48, 50)
Section 4.6 (2, 3, 9, 10, 12, 13, 16)
(Note: Exam 3 is on Friday, April 21)

For the Exam on Friday, April 21.
Section 4.7 (1-24) [the first 24 problems]
It's good review of auxiliary equations, variation of parameters, etc.!

Quiz 8: Friday, April 28.
Section 7.1 (3-6, 9, 10, 13-16, 21, 22, 25-28, 31, 32, 35-38)
We'll devote some of class-time to working on them.

Quiz 9: Friday, May 5.
Section 7.2 (5, 6, 9, 10, 15-20, 31, 32, 35, 36)
Section 7.3 (3, 4, 7, 8, 11-16, 21, 22, 25, 26)
It might look like a lot, but most of them are short (once you get the hang of it).
You can use my list of formulas during the quiz.

Quiz 10: with open notes, on Wednesday, May 10.
Section 7.3 (49-54, 61-68)
Section 7.4 (7-10, 19-22)
For this quiz, you can work together in class, and I can help you if you need it.

For the Final Exam.
Section 7.5 (1-12)




Exams:

Exams and Solutions are posted on Sac CT.




Lecture Schedule

I may occasionally type lecture notes.
DateTopicsBookNotesCode
1. M 1/23 Introduction.
2. W 1/25 Calculus Review, I.
3. F 1/27 Calculus Review, II.
4. M 1/30 Definitions and Terminology of DEs. § 1.1
5. W 2/1 Initial Value Problems. § 1.2
6. F 2/3 Direction Fields. § 2.1.1
7. M 2/6 Autonomous First-Order DEs. § 2.1.2
8. W 2/18 Separable Equations. § 2.2
9. F 2/10 Review.
M 2/13 EXAM 1
10. W 2/15 Linear Equations, I. § 2.3
11. F 2/17 Linear Equations, II. § 2.3
12. M 2/20 Exact Equations, I. § 2.4
13. W 2/22 Exact Equations, II. § 2.4
14. F 2/24 Solutions by Substitutions. § 2.5
15. M 2/27 A Numerical Method. § 2.6
16. W 3/1 Higher-Order DEs, I. § 4.1
17. F 3/3 Higher-Order DEs, II. § 4.1
18. M 3/6 Review.
W 3/8 EXAM 2
19. F 3/10 Higher-Order DEs, III. § 4.1
20. M 3/13 Reduction of Order. § 4.2
21. W 3/15 Homog. Linear Eqs with Constant Coeffs, I. § 4.3
22. F 3/17 Homog. Linear Eqs with Constant Coeffs, II. § 4.3
M-F 3/20-24 NO CLASS (Spring Break)
23. M 3/27 Undetermined Coeffs, I. § 4.4
24. W 3/29 Undetermined Coeffs, II. § 4.4
F 3/31 NO CLASS (Cesar Chavez Day)
25. M 4/3 Undetermined Coeffs, III. § 4.5
26. W 4/5 Undetermined Coeffs, IV. § 4.5
27. F 4/7 Variation of Parameters, I. § 4.6
28. M 4/10 Variation of Parameters, II. § 4.6
29. W 4/12 The Cauchy-Euler Equation, I. § 4.7
30. F 4/14 The Cauchy-Euler Equation, II. § 4.7
31. M 4/17 The Laplace Transform. § 7.1
32. W 4/19 Review.
F 4/21 EXAM 3
33. M 4/24 The Laplace Transform, II. § 7.1
34. W 4/26 The Inverse Laplace Transform, I. § 7.2
35. F 4/28 The Inverse Laplace Transform, II. § 7.2
36. M 5/1 Properties of the Laplace Transform, I. § 7.3
37. W 5/3 Properties of the Laplace Transform, II. § 7.3
38. F 5/5 Properties of the Laplace Transform, III. § 7.4
39. M 5/8 The Dirac Delta Function. § 7.5
40. W 5/10 Homework in Class. Chapter 7.
41. F 5/12 Review.
FINAL EXAM: 5/15, 8-10am (Section 7), 10:15-12:15 (Section 8)