Mathematics 241A, Fall 2019

Methods of Applied Mathematics

Lectures:

Section 1:
Tuesdays and Thursdays, 4-5:15pm, Room 227, Alpine Hall




Instructor: Michael VanValkenburgh

Office: Room 140, Brighton Hall

Tentative Office Hours:
Mondays and Wednesdays, 12-2pm. Also by appointment.

A description of the course: Math 241A, Fall 2019 (pdf)

Drop Policy


Announcements:

We will be using the following textbook:
Applied Mathematics (Fourth Edition), by J. David Logan.


Final Exam:
Thursday, December 12, 3-5pm




Homework:



Instructions for Formatting Homework

Homework 1, due Thursday, September 5:
p.8, #1
p.8, #3 (there is more than one correct answer!)
pp.27-29, #2, 5, 8, 11, 13 (instructions: use the ``Pi'' notation from class)
Extra problem: Find a fun example using dimensional analysis to solve a ``real life problem''


Homework 2, due Tuesday, September 17:
p.41-46 (the section on Scaling): #2, 3, 7, 8, 10, 15, 16
#16 is the only problem without hints/solutions online.
REMINDER: the first exam is also on Tuesday, September 17.



Homework 3, due Tuesday, October 1:
p.72-75 (the section on Stability and Bifurcation): #2, 5, 6, 10, 12
The solutions might not be available online...



Homework 4, due Thursday, October 10:
Section 2.1, p.87: #5
Section 2.2, p.93-94: #1bcf, 2, 6
The solutions might not be available online...



Homework 5, for review (you don't need to turn it in).
Usually I do all the book problems and assign the "best" ones, but there are too many in this section. For now try:
Section 2.3, 2.4, p.107-112: #1, 2, 4, 5, 6, 10.
Section 3.1, p.165-169: #7, 9. Very similar to the easy problem we did in class.
Hints:
#1ab: I could only find the obvious critical point (0,0).
#1c: Let z=y' to get a separable ODE. See p.52 for details.
#1d: I'm not sure how to solve analytically.
#1e: Why is the last problem the easiest one?
#2: Change to polar coordinates, like Example 2.21.
#3: Skip for now (?).
#4: I haven't done them all yet.
#5: One way is to change to polar coordinates. You don't need to solve the ODEs to understand the behavior near (0,0).
#6, 10: I didn't do them yet, but they look fun.



Homework 6, due Thursday, November 7 (postponed by request):
Section 3.1, p.165-169: #12, 13, 17
Section 3.2, p.178: #1ab, 2, 4
I added one more:
Section 3.4, p.201: #7
There are some hints/solutions online, but beware of errors! (Boo!)



Homework 7, due Tuesday, December 3:
Section 4.3, p.243-245: #2ab, 8ac, 12, 13
Section 4.5, p.263-266: #3, 4, 9, 12
There are some hints/solutions online, but beware of errors!


Exams:

Exams and Solutions are posted on Sac CT.




Lecture Schedule

DateTopicsBook
Week 11. T 8/27 Dimensional Analysis. § 1.1
2. R 8/29 Dimensional Analysis. § 1.1
Week 23. T 9/3 Dimensional Analysis. § 1.1
4. R 9/5 Scaling. § 1.2
Week 35. T 9/10 Scaling. § 1.2
6. R 9/12 Spruce Bud Worms. § 1.2
Week 4T 9/17 EXAM 1
7. R 9/19 Stability and Bifurcation. § 1.3
Week 58. T 9/24 Stability and Bifurcation. § 1.3
9. R 9/26 Intro to Two-Dimensional Systems. § 2.1
Week 610. T 10/1 Linear Systems. § 2.2
11. R 10/3 Nonlinear Systems. § 2.3
Week 712. T 10/8 Bifurcations. § 2.4
13. R 10/10 Regular Perturbation. § 3.1
Week 814. T 10/15 Regular Perturbation. § 3.1
R 10/17 EXAM 2
Week 915. T 10/22 Singular Perturbation. § 3.2
16. R 10/24 Singular Perturbation. § 3.2
Week 1017. T 10/29 Boundary Layer Analysis. § 3.3
18. R 10/31 Initial Layers. § 3.4
Week 1119. T 11/5 Variational Problems. § 4.1
20. R 11/7 Necessary Conditions for Extrema. § 4.2
Week 1221. T 11/12 Review
R 11/14 EXAM 3
Week 1322. T 11/19 the Simplest Problem. § 4.3
23. R 11/21 Hamilton's Principle. § 4.5
Week 1424. T 11/26 Hamilton's Principle. § 4.5
R-F 11/28-29 NO CLASS (Thanksgiving)
Week 1525. T 12/3 Isoperimetric Problems. § 4.6
26. R 12/5 To be determined.
FINAL EXAM: Thursday, December 12, 3-5pm