Math 81, Applied Analysis - 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
  • Section 3: MWF 11:00-11:50 a.m. in S2 206
  • Section 5: MWF 12:00-12:50 p.m. in S2 206
• Syllabus (in .pdf format) - posted 08-21-09
• Relational Syllabus (Word document) - posted 08-21-09
• Introduction to WeBWorK
• Furlough days (no class): September 4, September 28
• Furlough days (no e-mail availability): August 25, October 6, October 13, November 10, November 24

Announcements

• 09-02-09: Furlough day (09-04-09) assignment: Review Chapter 1 and do suggested problems on page 76 (see suggested problems below).
• 09-22-09: There is an error in the solutions to the suggested problems for Section 3.2: 23. I goofed in my Gaussian elimination, and the second row of the matrix should be (0 0 | k - 2). Therefore, the correct answers are: (b) no solution for k - 2 not equal to 0, so for k not equal to 2, and (c) infinitely many solutions for k = 2. I apologize for my error.
• 09-21-09: Furlough day (09-28-09) assignment: Do suggested problems for Sections 4.1 and 4.2 assigned below in preparation for homework assignment; review notes so far on Sections 4.1.
and 4.2
• 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.
• 11-20-09: There is a minor error on Quiz #5. In problem 3, the initial condition for the second equation should read x2(0) = 2.
• 12-04-09: The Extra Credit assignment has been posted on WeBWorK. It will be due on Thursday, December 10, 2009 at 4:30 p.m.

Exam Information

• Midterm I Information
  • Exam is on Wednesday, September 23, 2009 during the regularly scheduled class time.
  • Location: the regular classroom, S2 206
  • The exam covers Chapters 1 and 3.
  • 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 during the regularly scheduled class time.
  • Location: the regular classroom, S2 206
  • The exam covers Sections 4.1-4.4 and 4.7, and Sections 5.1-5.6
  • Bring your student ID.
  • Calculators are not permitted.
  • The exam is closed note and closed book.
  • Midterm II Topics
  • Extra Office Hours: Tuesday, 10-27-09, 1-2:30 p.m.
• Midterm III Information
  • Exam is on Wednesday, December 2, 2009 during the regularly scheduled class time.
  • Location: the regular classroom.
  • The exam covers Sections 6.1, 7.1-7.3, 7.5, 10.1-10.3
  • 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, 1:00-2:30 p.m.
  • Test Preparation and Test-Taking Tips
• Final Exam Information
  • Date and time:
    • Section 3 - Monday, December 14, 2009, 11:00 a.m.-1:00 p.m.;
    • Section 5 - Wednesday, December 16, 2009, 1:15 p.m.-3:15 p.m.
  • Location: S2 206 (the regular classroom).
  • Calculators are not permitted.
  • The exam is closed note and closed book.
  • Make sure to bring your student ID to the exam.
  • The exam is cumulative, covering the material you were responsible for in all three midterm exams, as well as the new material from Sections 10.4-10.5.
  • Final Exam topics list: Final Exam Topics.
  • Extra Office Hours (consultation day): Thursday 1-4 (in PB 350)

Partial Notes

Partial notes will be posted before each lecture for which they are to be used so that you may print and bring them to class, as required in the syllabus.

• 08-24-09: Introduction to Differential Equations
• 08-26-09: Separable Equations
• 08-28-09: Linear Equations
• 08-31-09: Substitution Methods
• 09-02-09: Exact Equations
• 09-09-09: Matrix Basics
• 09-11-09: Solution of Linear Systems of Equations
• 09-16-09: Determinants
• 09-18-09: Introduction to Vector Spaces and Subspaces
• 10-02-09: Linear Combinations and Independence of Vectors
• 10-05-09(?): Basis and Dimension for Vector Spaces
• 10-12-09: Homogeneous Higher Order Differential Equations
• 10-16-09: Nonhomogeneous Differential Equations
• 10-21-09: Modelling Oscillations: The Mass-Spring System
• 10-23-09: Eigenvalues and Eigenvectors
• 11-02-09: Introduction to Systems of Linear Differential Equations
• 11-13-09: Laplace Transform and Inverse Transform (an introduction to the Laplace transform)
• 11-16-09: Transformation of Initial Value Problems
• 11-20-09: Translation and Partial Fractions
• 11-30-09: Convolution and Discontinuous Functions

Reading Assignments

• 08-24-09: Read Sections 1.1, 1.2, and 1.4
• 08-26-09: Read Section 1.5
• 08-28-09: Read Section 1.6 to p. 65
• 08-31-09: Finish reading Section 1.6
• 09-02-09 and 09-04-09: Review Chapter 1
• 09-09-09: Read Sections 3.4 and 3.1-3.2
• 09-11-09: Read Sections 3.3 and 3.5
• 09-14-09: Read Section 3.6
• 09-16-08: Read Section 3.6, paying close attention to the affect of elementary row operations on the determinant of a matrix.
• 09-18-09: Read Sections 4.1-4.2
• 09-21-09: Review for midterm
• 09-30-09: Read Section 4.3
• 10-05-09: Read Sections 4.4 and 4.7
• 10-09-09: Read Sections 5.1-5.2
• 10-12-09: Read Section 5.3
• 10-14-09: Finish reading Section 5.3 if not finished, and read Section 5.5 to p. 343
• 10-16-09: Finish reading Section 5.5
• 10-19-09: Read Sections 5.4 and 5.6
• 10-21-09: Start reading Section 6.1
• 10-23-09: Review for midterm; finish reading Section 6.1 for 11-02-09
• 11-02-09: Read Sections 7.1 and 7.2
• 11-04-09: Read Section 7.3 to p. 420
• 11-06-09: Finish reading Section 7.3; read Section 7.5 through p. 443
• 11-09-09: Finish reading Section 7.5; start reading Section 10.1
• 11-13-09: Finish reading Section 10.1
• 11-16-09: Read Section 10.2, p. 578-9, 584-5
• 11-18-09: Finish reading Section 10.2, read Section 10.3
• 11-20-09: Finish reading Section 10.3
• 11-23-09: Read p. 599-601
• 11-30-09: Read Section 10.5

Homework Assignments (posted on WeBWorK)

Please note that if you would like to to additional problems similar to your WeBWorK assignment, additional practice logins have been created. Since each problem in WeBWorK is generated using random numbers, or in some cases, random sets of problems, this may be helpful to you when you are studying. The practice logins are practice1, practice2, practice3, and practice4. No password is necessary for these login ids.

• Set 0 - Due Friday, August 28, 2009 by 4:30 p.m.
• Set 1 - Due Friday, September 4, 2009 by 4:30 p.m.
• Set 2 - Due Friday, September 11, 2009 by 4:30 p.m.
• Set 3 - Due Friday, September 18, 2009 by 4:30 p.m.
• Set 4 - Due Friday, September 25, 2009 by 4:30 p.m.
• Set 5 - Due Friday, October 9, 2009 by 4:30 p.m.
• Set 6 - Due Friday, October 16, 2009 by 4:30 p.m.
• Set 7 - Due Friday, October 23, 2009 by 4:30 p.m.
• Set 8 - Due Friday, October 30, 2009 by 4:30 p.m. (Please note that this assignment only contains problems on material for Midterm II.)
• Set 9 - Due Friday, November 13, 2009 by 4:30 p.m.
• Set 10 - Due Friday, November 20, 2009 by 4:30 p.m.
• Set 11 - Due Monday, November 30, 2009 by 4:30 p.m.

Suggested Problems

• 08-24-09 - Section 1.1: 5, 9, 22, 35
• 08-26-09 - Section 1.4: 12, 25, 40, 47
• 08-28-09 - Section 1.5: 5, 22
• 08-31-09 - Section 1.5: 36; Section 1.6: 8, 19, 20, 27
• 09-02-09 - Section 1.6: 70, 34, 38
• 09-04-09 - p. 76: 1, 3, 10, 17, 35, 38 (p. 78 in the 3rd edition)
• 09-09-09 - Section 3.4: 3, 8, 27
• 09-11-09 - Section 3.2: 11, 15, 17, 23
• 09-14-09 - Section 3.3: 21, 25, 27
• 09-16-09 - Section 3.5: 15, 22; Section 3.6: 5
• 09-18-09 - Section 3.6: 19
• 09-28-09 - Section 4.1: 30, 31, 34, 35; Section 4.2: 5, 6, 7, 10, 14
• 09-30-09 - Section 4.2: 15, 20; Section 4.7: 1, 6, 7, 9-11
• 10-02-09 - Section 4.3: 1, 10
• 10-05-09 - Section 4.3: 20; Section 4.7: 13, 14, 16, 18
• 10-07-09 - Section 4.4: 2, 4, 9, 10, 13
• 10-09-09 - Section 4.7: Find a basis of the subspaces in 1, 10; Section 4.4: 16, 20, 24
• 10-12-09 - Section 4.4: 16, 20, 24; Section 5.1: 3, 16, 20, 25; Section 5.2: 21, 7, 16
• 10-14-09 - Section 5.3: 2, 4, 7, 23
• 10-16-09 - Section 5.3: 15, 25
• 10-19-09 - Section 5.5: 32, 33, 39
• 10-21-09 - Section 5.5: 53, 54
• 10-23-09 - Section 5.4: 4, 22; Section 5.6: 23
• 11-02-09 - Section 6.1: 3, 13, 22; Section 7.1: 1, 3
• 11-04-09 - Section 7.2: 3, 6, 16, 25
• 11-06-09 - Section 7.3: 3, 21 (omit the graphs)
• 11-09-09 - Section 7.3: 9, 13
• 11-13-09 - Secion 7.5: 5, 9; Section 10.1: 3, 8
• 11-16-09 - Section 10.1: 23, 29, 31
• 11-18-09 - Section 10.2: 2, 8, 10, 12
• 11-20-09 - Section 10.3: 1, 3, 7
• 11-23-09 - Section 10.3: 9, 10, 27, 30
• 11-30-09 - Section 10.4: 3, 12
• 12-07-09 - Section 10.5: 6, 8, 10, 11, 14

Solutions to Suggested Problems

• Solutions to Sections 1.1 through 1.5
• Solutions to Section 1.6 and p. 76 (p. 78 in 3rd edition)
• Solutions to Sections 3.2 through 3.6
• Solutons to Sections 4.1-4.2 and part of 4.7
• Solutions to Sections 4.3-4.4, 4.7
• Solutions to Sections 5.1-5.3
• Solutions to Section 5.5
• Solutions to Sections 5.4 and 5.6
• Solutions to Sections 6.1 and 7.1-7.2
• Solutions to Sections 7.3 and 7.5
• Solutions to Sections 10.1 and 10.2
• Solutions to Section 10.3
• Solutions to Sections 10.4 and 10.5

Quizzes

All quizzes are handed out at the end of a lecture and are due at the beginning of the next class.

Your quiz solutions should follow the format set forth in Communicating Mathematics through Homework.

• 09-02-09: Quiz #1 handed out, due Wednesday, 09-09-09 by the beginning of class
  Quiz #1 Solutions
• 10-02-09: Quiz #2 handed out, due Monday, 10-05-09 by the beginning of class.
  Quiz #2 Solutions
• 10-09-09: Quiz #3 handed out, due Monday, 10-12-09 by the beginning of class.
  Quiz #3 Solutions
• 10-16-09: Quiz #4 handed out, due Monday 10-19-09 by the beginning of class.
  Quiz #4 Solutions
• 10-20-09: Quiz #5 handed out, due Monday 11-23-09 by the beginning of class.
  Quiz #5 Solutions