Mathematics 45, Spring 2016

Differential Equations for Science and Engineering

Lectures:

Section 05: MWF 8-8:50am, Room 218, Alpine Hall

Section 06: MWF 11-11:50am, Room 110, Douglass Hall



Instructor: Michael VanValkenburgh.

Office: Room 140, Brighton Hall
Office Hours: MWF 9-9:50am, Tuesdays and Thursdays 4-5pm, and also by appointment. Please come visit!


A description of the course: Math 45, Spring 2016 (pdf)

Drop Policy


Announcements:

We will be using the following free textbook:
Differential Equations, by András Domokos


Final Exam Schedule. Please take this into account when registering for classes:
Section 05: Monday, May 16, 8-10am
Section 06: Monday, May 16, 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, February 1: Chapter 1.

Quiz 2. Monday, February 8: Sections 2.1, 2.2, 2.3.


The Exam on Monday, February 15, will cover everything up to and including Section 3.1.


Quiz 3. Friday, February 26: Sections 3.2 and 3.3.


The Exam on Wednesday, March 9, will cover everything up to and including Section 4.1.


Quiz 4. Friday, March 18: Sections 4.1 and 4.2.


Quiz 5. Monday, April 4: Sections 4.3 and 4.4 (excluding Runge-Kutta and error estimates).


Quiz 6. Monday, April 11: Sections 5.1 and 5.2.


Quiz 7. Wednesday, May 4: Sections 6.1 and 6.2.


Quiz 8. Wednesday, May 11: Sections 6.3 and 6.4.



Exams:

Exams and Solutions are posted on Sac CT.




Lecture Schedule

I may occasionally type lecture notes.
DateTopicsBookNotesCode
1. M 1/25 Calculus Review: Derivatives. § 1.1 (pdf) (latex)
2. W 1/27 Calculus Review: Indefinite Integrals. § 1.2
3. F 1/29 Calculus Review: Definite Integrals. § 1.3 (pdf) (latex)
4. M 2/1 Intro to Differential Equations. § 2.1
5. W 2/3 Initial Value Problems. § 2.2 (pdf)
6. F 2/5 Classifying Differential Equations. § 2.3
7. M 2/8 Real-life Examples. § 2.4
8. W 2/10 Separable Equations. § 3.1
9. F 2/12 Review.
M 2/15 EXAM 1
10. W 2/17 First-order Linear Diff. Eq.s., I. § 3.2
11. F 2/19 First-order Linear Diff. Eq.s., II. § 3.2
12. M 2/22 Bernoulli's Diff. Eq. § 3.3
13. W 2/24 Non-linear Homog. Diff. Eq.s. § 3.4
14. F 2/26 a Special Form, and Second-order Reducing to First-Order. § 3.5, 3.6
15. M 2/29 Slope Fields, I. § 4.1
16. W 3/2 Slope Fields, II. § 4.1 (pdf)
17. F 3/4 Slope Fields, III. § 4.1
18. M 3/7 Review.
W 3/9 EXAM 2
19. F 3/11 Existence and Uniqueness, I. § 4.2 (pdf)
20. M 3/14 Existence and Uniqueness, II. § 4.2
21. W 3/16 Existence and Uniqueness, III. § 4.2
22. F 3/18 Successive Approximations. § 4.3
M-F 3/21-25 NO CLASS (Spring Break)
23. M 3/28 Numerical Methods, I. § 4.4
24. W 3/30 Numerical Methods, II. § 4.4
25. F 4/1 Higher-order: General Theory, I. § 5.1
26. M 4/4 Higher-order: General Theory, II. § 5.1
27. W 4/6 Homogeneous D.E.s with Constant Coeff.s, I. § 5.2
28. F 4/8 Homogeneous D.E.s with Constant Coeff.s, II. § 5.2
29. M 4/11 Inhomogeneous D.E.s with Constant Coeff.s, I. § 5.3
30. W 4/13 Inhomogeneous D.E.s with Constant Coeff.s, II. § 5.3
31. F 4/15 Inhomogeneous D.E.s with Constant Coeff.s, III. § 5.3
32. M 4/18 Review.
W 4/20 EXAM 3
33. F 4/22 the Laplace Transform, I. § 6.1
34. M 4/25 the Laplace Transform, II. § 6.1
35. W 4/27 the Laplace Transform, III. § 6.2
36. F 4/29 the Laplace Transform, IV. § 6.2
37. M 5/2 Homework in Class. § 6.1-2
38. W 5/4 the Inverse Laplace Transform. § 6.3
39. F 5/6 Solving I.V.P.s with the Laplace Transform. § 6.4
40. M 5/9 Homework in Class. § 6.4
41. W 5/11 Review.
42. F 5/13 Review.
FINAL EXAM: 5/16, 8-10am (Section 5), 10:15-12:15 (Section 6)