Math 181: Differential Equations - Fall 2009
Instructor Information
- Instructor:
Dr. Doreen De Leon
- Office: PB 350
- Office telephone: (559) 278-4009
- Office hours: M 10-10:45 a.m., W 4-5:15 p.m., Th 2-4 p.m., or by appointment.
Course Information
- Class meeting time: MWF 3:00-3:50 p.m. in S2 108
- Furlough days (no class): September 4, September 28
- Furlough days (no e-mail availability): August 25, October 6, October 13,
November 10, November 24
- Syllabus (in .pdf form) - posted 08-21-09
Announcements
- 09-02-09: Furlough day (09-04-09) assignment: Read Section 1.6, a
discussion of separable equations and do exercies given on 09-02-09.
Make sure to do Homework #2c) - Section 1.6, problem 11 - in addition
to the other Homework #2 problems assigned. (See HomeworkAssignments below.)
- 09-21-09: Furlough day (09-28-09) assignment: Exercise given in class
(Solve the IVP y''-5y'+6y=0, y(0)=0, y'(0)=2); work
on Homework #5a) posted below; read Section 3.4 for Wednesday's lecture.
- 10-07-09: Office hours on 10-07 will be from
4-5:30 p.m. and office hours on 10-08 will be from 1-2:30 p.m. due to
academic commitments.
- 10-20-09: Office hours in 10-22-09 will be from
2-3:45 p.m. due to commitment.
- 11-02-09: Extra credit opportunity! Work on the
Department of Mathematics
November problem of the month, a copy of which can be found outside of my
office. If you correctly complete the problem, which is due to Adnan
Sabuwala or Oscar Vega by November 24, 2009, you will earn 10 points extra
credit.
- 11-04-09: Office hours for 11-05-09 cancelled
due to a meeting.
12-03-09: Extra credit towards homework! Attend the presentation on "Having fun with Numb3rs and other Mathematical Recreations" by Ed Pegg, Jr., write up a brief (1-2 page) report, and earn 10 points extra credit. You must find me at the talk and let me know that you are there to
get the credit.
Exam Information
- Midterm I Information
- Exam is on Wednesday, September 23, 2009
- Location: S2 108 (the regular classroom).
- The exam covers Chapters 1 and 2
- Bring your student ID.
- Calculators are not permitted.
- The exam is closed note and closed book.
- Midterm Topics
- Extra office hours: Tuesday, 09-22-09, 1:30-3:00 p.m.
- Midterm II Information
- Exam is on Wednesday, October 28, 2009
- Location: S2 108 (the regular classroom).
- The exam covers Chapter 3, Section 8.3, the method of finding a particular
solution to Euler-Cauchy equations using an undetermined-coefficients like
method (discussed in class), and Sections 8.1-8.2
- Bring your student ID.
- Calculators are not permitted.
- The exam is closed note and closed book.
- Midterm Topics
- Extra Office Hours: Tuesday, 10-27-09, 1 p.m.-2:30 p.m.
- Midterm III Information
- Exam is on Wednesday, December 2, 2009 during the regularly scheduled
class time.
- Location: S2 108 (the regular classroom).
- The exam covers Section 8.4; Sections 4.1-4.7; Sections 6.1-6.3
- Bring your student ID.
- Calculators are not permitted.
- The exam is closed note and closed book.
- Midterm III Topics
- Extra Office Hours: Tuesday, 12-01-09, 1 p.m.-2:30 p.m.
- Final Exam Information
- Date: Monday, December 14, 2009
- Time: 3:30-5:30 p.m.
- Location: S2 108 (the regular classroom).
- Bring your student ID.
- Calculators are not permitted.
- The exam is closed note and closed book.
- The exam is cumulative, covering Section
6.6 (type of equilibrium point and
the associated phase portraits for
constant coefficient systems of two equations), and the
material you were responsible for on all midterms except the following:
- Direction fields for autonomous first order equations
- Exact first order equations
- Euler-Cauchy equations
- The method of reduction of order (except the use of the results for
linear equations with repeated roots)
- Extra office hours (consultation day):
Thursday 1-4 (in PB 350)
Reading Assignments
- 08-24-09: Read Sections 1.1-1.3; start reading Section 2.1
- 08-26-09: Read Sections 2.1-2.2; start reading Section 2.3
- 08-28-09: Read Sections 2.3-2.4
- 08-31-09: Read Section 2.5
- 09-02-09 and 09-04-09: Read Section 2.6
- 09-09-09: Read Section 2.7; start reading Section 2.8
- 09-11-09: Finish reading Section 2.8; start reading Section 2.9
- 09-14-09: Finish reading Section 2.9; read Sections 2.10-3.1
- 09-16-09: Read Section 3.2; start reading Section 3.3
- 09-18-09: Finish reading Section 3.3
- 09-21-09: Study for midterm
- 09-30-09: Read Section 3.5
- 10-02-09: Read Section 8.3
- 10-05-09: Read Section 3.6
- 10-07-09: Read Sections 3.7-3.8
- 10-09-09: Read Section 3.9
- 10-12-09: Read Section 3.10
- 10-14-09: Read Sections 3.11-3.12
- 10-16-09: Read Section 3.13 and Section 8.1
- 10-19-09: Read Section 8.2
- 10-21-09: Read Section 8.4
- 10-23-09 and 10-26-09: Study for Midterm II
- 11-02-09: Read Sections 4.1-4.2
- 11-04-09: Read Section 4.3
- 11-06-09: Read Section 4.4-4.5
- 11-09-09: Read Section 4.6
- 11-13-09: Read Sections 4.7, 6.1-6.2
- 11-16-09: Read Section 6.3
- 11-18-09: Read Section 6.4
- 11-20-09: Read Section 6.5
- 11-23-09: Read Section 6.6 (for after midterm)
Homework Assignments
Your homework solutions should follow the format set forth in
Communicating
Mathematics through Homework.
- Homework #1, Due Wednesday, September 9, 2009 by 3:00 p.m.
- Homework #2, Due Friday, September 11, 2009 by 3:00 p.m.
- 08-31-09 - Section 2.3: 11, 18; Section 2.4: 9, 15
- 09-02-09 - Section 2.5: 6, 9, 11, 16
- 09-04-09 - Section 2.6: 11
- Homework #2 Solutions -- Please note that
in the solution to Section 2.5, problem 16b), the interval of existence
should be
[½ ln(½), ∞) (so, the
solution is defined for t >= ½).
- Homework #3, Due Friday, September 18, 2009 by 3:00 p.m.
- Homework #4, Due Friday, September 25, 2009 by 3:00 p.m.
- 09-14-09 - Section 2.9: 2, 6
- 09-16-09 - Section 2.9: 11, 15; Section 2.10: 3; Section 3.1: 4, 5
- 09-18-09 - Section 3.2: 9, 22; Section 3.11: 11
- Homework #4 solutions
- Homework #5, Due Friday, October 9, 2009 by 3:00 p.m.
- 09-28-09 - Section 3.3: 8, 11
- 09-30-09 - Section 3.4: 2, 7, 14, 18
- 10-02-09 - Section 3.5: 6, 10, 18
- Homework #5 solutions
- Homework #6, Due Friday, October 16, 2009 by 3:00 p.m.
- Homework #7, Due Friday, October 23, 2009 by 3:00 p.m.
- 10-12-09 - Revised Homework #7a
- 10-14-09 - Section 3.10: 9, 16
- 10-16-09 - Section 3.11: 6, 9, 15; Section 3.12: 5, 16, 25
- Homework #7 solutions. Please note there
is an error in Section 3.11: 6 with the derivative of
ln|-t|. The derivative should be 1/t.
- Homework #8, Due Friday, October 30, 2009 by 3:00 p.m.
- 10-19-09 - Section 3.13: 2, 7, 22; Section 8.1: 5, 10
- 10-21-09 - Section 8.1: 31, 23; Section 8.2: 5, 10, 24
- 10-23-09 - Section 8.2: 15, 29 (for part (d), just find
H2(t) and H3(t))
- Homework #8 solutions
- Homework #9, Due Friday, November 13, 2009 by 3:00 p.m.
- Homework #10, Due Friday, November 20, 2009 by 3:00 p.m.
- 11-09-09 - Section 4.4: 7, 12; Section 4.5: 2, 6
- 11-13-09 - Section 4.6: 18, 20; Section 4.7: 2, 9
- Homework #10 solutions
- Homework #11, Due Monday, November 30, 2009 by 3:00 p.m.
- 11-16-09 - Section 6.2: 5, 14, 16
- 11-18-09 - Homework #11b)
- 11-20-09 - Section 6.4: 6, 15, 16, 20
- 11-23-09 - Section 6.5: 2, 8
- Homework #11 solutions
- Please note that there are two minor errors in the solutions.
In Section 6.2: 14, the equilibria should also include
(5*pi/6+2k*pi, 0, 0), where k = 0, -1, 1, ...
In Section 6.2: 16, when checking (-2, -2), I had -2-(-2)(-2) = 2, instead of -6.
- Extra Credit, Due Thursday, December 10, 2009 by 4:00 p.m.
- 12-07-09 - Section 6.6: 6, 10, 14. For each exercies, also sketch
the phase portrait, making sure to show the direction of motion along
trajectories.
- 12-10-09 - Extra Credit Solutions
Handouts and Examples