Fall 2012: Math 265, Section 103: Linear Differential Equations

http://www.math.ubc.ca/~coombs/tch/265.html
Instructor: Dr. Daniel Coombs.
Office hours: Mathematics Annex, Room 1109. Monday 1pm-2.30pm and Wednesday 1pm-2.30pm.
Math department tutoring centre is located in LSK 100.

Email: coombs (at) math (dot) ubc (dot) ca
Office phone: 604-822-2859

Text: Our main reference will be the online textbook Diffy Qs by Lebl. You can download the book (for free) or order a copy (for cheap) to be sent to you from this page: http://www.jirka.org/diffyqs.
Additional free online notes are available at the following sites:
http://tutorial.math.lamar.edu/Classes/DE/DE.aspx
http://www.math.ust.hk/~machas/
http://www.springerlink.com/content/p78848/?MUD=MP (for the last link you will need to be accessing from UBC, either directly or via VPN: http://www.it.ubc.ca/service-catalogue/internet-and-telephone/network-management/myvpn)
You can also consult physical textbooks. Some favourites are Boyce and DiPrima (any recent edition) and Edwards and Penney. Boyce and DiPrima has often been used at UBC.
  • Clickers will be used in this course. Everyone needs to get a clicker (available from the bookstore).

    Important Dates:

  • Midterm test 1: Weds, October 10th 7pm-8pm in ESB 1013 (new Earth Sciences Building on main mall).
  • Midterm test 2: Weds, November 14th 7pm-8pm in ESB 1013.
  • Final exam: TBA
    Note: You must inform me on or before Sept 14th if you will have any problem with attending the midterms on these dates and times.

    Grading

  • The breakdown of marks between course elements will be as follows: Final exam: 50%. Midterms: 15% each. HW, clicker questions, quizzes and other activities: 20%.
  • Missing a midterm normally results in a mark of 0. Exceptions may be granted in two cases: prior consent of the instructor or a medical emergency. In the latter case, the instructor must be notified within 48 hours of the missed test, and presented with a doctor's note immediately upon the student's return to UBC. No make-up midterms will be given.
  • Term marks may be scaled up or down on a classwide basis, depending on performance on the final exam. This is to ensure fairness across both sections of the course.
  • Final Exam:
  • WHEN: December 11th, 3.30pm-6pm
  • WHERE: CIRS 1250 (2260 West Mall)
  • Bring: pen/pencil, eraser, ruler.
  • NO CALCULATOR, CELL PHONE, NOTES, etc
  • Bring your student ID and put it on your desk
  • The exam will include this page of Laplace Transforms: [LTTable]
  • Information on topics for the final exam: [PDF]
  • Old final exams are available from the math department site. Math 265 exams are most relevant, but other courses with similar topics are Math 215, 255 and 256. The best (most relevant to this term) 265 exams are from 2008, 2010 and 2011.
  • UBC Math Club is selling exam packages with solutions for Math 215. Math 265 is quite similar to Math 215. The following questions from the exam package are relevant: [2011Dec] 1a,3,4,5,6 [2010Apr1] 1a,2,3,4 [2010Apr2] 1a,1b,3a,3c,4,5,7 [2009Apr] 1,2,3,4,5,6 [2007Dec] 1,4,5,6abd. The package is on sale from the math club room, Math Annex 1119.

    Homework

  • Homework will be regularly assigned.
  • Homework 1 [PDF]: Due in class on Sept 19. Solutions [PDF].
  • Homework 2 [PDF]: Due in class on Oct 3. Solutions [PDF].
  • Homework 3 [PDF]: Due in class on Oct 17 or at my office before 4pm on Oct 19. Solutions [PDF].
  • Homework 4 [PDF]: Due in class on Oct 31. Solutions [PDF].
  • Homework 5 [PDF]: Due in class on Nov 19. Solutions [PDF].
  • Homework 6 [PDF]: Due in class on Nov 28 or to my office by Nov 30. Solutions [PDF].

    Reading and practise questions (complete before indicated class)

  • Mon, Sept 24: Read Lebl 2.2. Do exercises 2.2.4-10.
  • Wed, Sept 26: Read: Lebl 2.3.2, 2.4.1, 2.4.2, 2.4.3. Do exercises: 2.3.1, 2.3.2, 2.4.1, 2.4.2, 2.4.102.
  • Mon, Oct 1: Read: Lebl 2.5.1, 2.5.2. Do exercises 2.5.1, 2.5.2, 2.5.3.
  • Mon, Oct 15: Read: Lebl 2.5.3 and 2.6. Do exercise 2.5.7.
  • Mon, Oct 29: Read: Lebl 6.1, 6.2. Do exercises 6.2.2, 6.2.6.

    Course notes (selected)

  • Classes 1-4 [PDF]
  • Classes 5-6 [PDF]
  • Classes 6-8 [PDF]
  • Notes on theory of 2nd order equations [PDF]
  • 2nd order equations with complex roots [PDF]
  • 2nd order equations with repeated roots [PDF]
  • Undamped oscillator [PDF]
  • Method of undetermined coefficients [PDF]
  • Variation of parameters [PDF]
  • Frequency response of a damped oscillator [PDF]
  • Beats in an undamped oscillator [PDF]
  • Laplace transform introduction [PDF]
  • Step and delta functions [PDF]
  • Delta functions and convolutions [PDF]
  • Transfer and impulse response functions [PDF]
  • 2x2 linear systems [PDF]
  • 2x2 linear systems, part deux [PDF]

    Midterm information

  • Midterm 1:
  • WHEN: October 10th, 7pm-8pm.
  • WHERE: ESB Room 1013. (New earth science building on main mall).
  • Bring: pen/pencil, eraser, ruler.
  • NO CALCULATOR, CELL PHONE, NOTES, etc
  • Bring your student ID and put it on your desk
  • List of topics [PDF]
  • Old midterm 2008: [PDF] Solutions: [PDF]
  • Old midterm 2010: [PDF] Solutions: [PDF]
  • Midterm 2012 with solutions: [PDF]
  • Midterm 2:
  • WHEN: November 14th, 7pm-8pm.
  • WHERE: ESB Room 1013. (same as midterm 1)
  • Bring: pen/pencil, eraser, ruler.
  • NO CALCULATOR, CELL PHONE, NOTES, etc
  • Bring your student ID and put it on your desk
  • The exam will include this page of Laplace Transforms: [LTTable]
  • List of topics for midterm 2: [Topics]
  • Old midterm 2008: [PDF] Solutions: [PDF]
  • Old midterm 2010: [PDF] Solutions: [PDF]
  • Another old midterm 2004: [PDF]
  • Midterm 2012 with solutions: [PDF]

    Other sections

    Section 101 (Zwiers)

    Approximate Schedule of Topics

    Date Day Note Topics  Book Section (Lebl)
    05-Sep Wed Linear vs nonlinear, 1st vs 2nd, etc. Direction fields for 1st order 1.1,1.2
    10-Sep Mon Integrating factor method, separable equations 1.3,1.4
    12-Sep Wed Separable equations (brief) and examples/applications of 1st order 1.4
    17-Sep Mon Examples and applications of 1st order
    19-Sep Wed Second order constant coefficient with examples (mass-spring/LCR) 2.1/2.4
    24-Sep Mon Superposition, existence, Wronskian (briefly) 2.1/2.2 (minimal treatment)
    26-Sep Wed Complex roots 2.2
    01-Oct Mon Repeated roots and higher-order problems 2.1, 2.3
    03-Oct Wed Nonhomogeneous equations: undetermined coefficients solution 2.5
    08-Oct Mon NO CLASS
    10-Oct Wed TEST 1 (EVENING) Examples and applications: SHO, damping 2.6
    15-Oct Mon Examples and applications: forcing, resonance, frequency response 2.6
    17-Oct Wed Laplace transform: definition, examples 6.1
    22-Oct Mon Solution of ODE with LT; properties of LT 6.2
    24-Oct Wed LT: step response 6.2
    29-Oct Mon Delta function forcing, LT solution 6.2
    31-Oct Wed Examples/review/catch-up
    05-Nov Mon Systems of ODE, examples 3.1,3.2,3.3
    07-Nov Wed Basic solution of x'=Ax 3.4
    12-Nov Mon NO CLASS
    14-Nov Wed TEST 2 (EVENING) Phase plane analysis, complex eigenvalues examples 3.5
    19-Nov Mon Complex and repeated eigenvalues, examples 3.7
    21-Nov Wed Nonhomogeneous systems: undetermined coefficients solution 3.9
    26-Nov Mon Examples/review/catch-up
    28-Nov Wed Examples/review/catch-up
    Daniel Coombs / Department of Mathematics / University of British Columbia