UBC Math 257: Partial Differential Equations
January-April 2014

This page provides official background information for all sections of two courses running this term:

There are two instructors involved; details are at the bottom of this page.

Details about the course layout are available on the Unified Outline Page.

Daily Updates (Most Recent First)

The most recent additions to this list of resources appear at the top. See the Draft Course Outline for policies and contact information.

Code Due Details Last Change
PP   Practice Assignment 11 is not to be handed in, but students may find these six sample problems on the Sturm-Liouville theory helpful as guides when studying. Solutions will be posted a few days before the final exam. 09 Apr 2014
RR   Office Hours for Exam Prep
The scheduled final exam is on Thursday 24 April, 15:30-18:00, room CIRS 1250. (CIRS, the Centre for Interactive Research on Sustainability, is at 2260 West Mall.) All students in both sections write the same test.
Students from either section are invited to discuss the material with either instructor. The dates and times below are firm, but the locations may change a little:
  • 14 Apr (Mon): 13:00–15:00 with K. M. Paton, room MATX 1118.
  • 15 Apr (Tue): 13:00–15:00 with K. M. Paton, room MATX 1118.
  • 16 Apr (Wed): 14:00–16:00 with P. D. Loewen, room MATH 207.
  • 17 Apr (Thu): 14:00–16:00 with P. D. Loewen, room MATH 207.
  • 18 Apr (Fri)—21 Apr (Mon): UBC Closed.
  • 22 Apr (Tue): 13:00–15:00 with K. M. Paton, room MATX 1118,
         OR           13:00–15:00 with P. D. Loewen, room MATH 207.
  • 23 Apr (Wed): 10:00–12:00 with P. D. Loewen, room MATH 207.
  • 24 Apr (Thu): Exam Day! No scheduled office hours.
07 Apr 2014
RR   Extended Sturm-Liouville Example
Studying Sturm-Liouville eigenvalue problems gives a nice review of how the Big Four eigenfunction series really work, and how the ideas that drive them can be extended. Here is an extended example that illustrates the full Sturm-Liouville story, from finding the eigenfunctions to solving some PDE's. Students may find it helpful in confronting Question 5 on Assignment 10.
02 Apr 2014
RR   Resources for Final Exam Preparation
A side benefit of Assignment 10 is supposed to be the “discovery” of a large number of real final exams to study from. Here's a more complete catalogue of helpful resources in this style:
31 Mar 2014
HW 04 Apr 2014
(FRI)
For Assignment 10, start on the Math Department's web page showing past final exams. Solve the following five final exam questions and hand in your results.
  1. 2012WT2 Question 3 (damped wave equation with Neumann BC's)
  2. 2012WT1 Question 5 (nonhomogeneous heat problem with time-varying left BC)
  3. 2011WT2 Question 2 (heat problem with mixed BC's, with numeric discussion)
  4. 2011WT1 Question 4 (nonhomogeneous heat problem, with numeric discussion)
  5. 2010WT1 Question 5 (Sturm-Liouville classic)
NOTE: The first 4 questions listed above should be accessible immediately. The Sturm-Liouville problem shown last will be the topic of classes in the last full week of term, so don't worry about it until closer to the due date.
Posted later: Solutions (PDF).
04 Apr 2014
RR   Excel Worksheets and Supporting Notes
Our classroom presentations this week were largely based on some more thorough notes by UBC's Professor Anthony Peirce. You can find all kinds of good related material on Peirce's MATH 257/316 page, including (but not limited to) the items linked directly from here:
28 Mar 2014
RR   Maple Worksheets
The computer algebra system Maple will make helpful intuition-builders with each of the following. Explore them in the order shown here:
  • Big 4 Eigenfunction Series—do the integrals and graph the partial sums for your choice of a Fourier Sine Series (FSS), Fourier Cosine Series (FCS), Half-Period Sine Series (HPSS), or Half-Period Cosine Series (HPCS).
  • Wave Equation: Modes and Movies—solve the classic wave equation for your choice of boundary conditions, leading to series-form solutions based on any of the FSS, FCS, HPSS, or HPCS.
  • Heat Equation: Modes and Movies—solve the classic heat equation for your choice of boundary conditions, leading to series-form solutions based on any of the FSS, FCS, HPSS, or HPCS.
27 Mar 2014
HW 28 Mar 2014
(FRI)
Here is Assignment 9 (PDF). Don't let the long statements that set up the questions scare you: some of the wordiest problems have short solutions.
Posted later: Solutions (PDF).
02 Apr 2014
HW 21 Mar 2014
(FRI)
Here is Assignment 8 (PDF). Please note that the hand-in deadline is Friday, a change from our usual Wednesday-to-Wednesday rotation. The last few assignments of the term will also be due on Fridays.
Posted later: Solutions (PDF).
21 Mar 2014
RR   Happy Nowrouz! Here are the solutions for Midterm 2 in Section 201 (11:00) and Section 202 (09:00). 20 Mar 2014
PP 12 Mar 2014

In Boyce and DiPrima, Elementary Differential Equations and Boundary Value Problems (10th ed), some relevant sections and practice problems include

  • 10.2 - Fourier Series: 13-18
  • 10.3 - The Fourier Convergence Theorem: 1-6
  • 10.6 - Other Heat Conduction Problems: 1-8, 10-14, 21-23
  • 10.7 - The Wave Equation: 23
  • 11.3 - Nonhomogeneous Boundary Value Probl
    Posted later: Solutions (PDF).ems: 19-26
11 Mar 2014
PP   Midterm Notes:

In class on Friday 14 March, we will have a 50-minute test. This is strictly closed-book: calculators and formula sheets are not allowed. There will be questions about eigenfunction series, separation of variables, and boundary-value problems. Students can benefit by memorizing the eigenvalue problems code-named FSS, FCS, HPSS, HPCS, and FFS and their associated series. Another useful source for guidance is the handout sheet distributed in class on Wednesday 5 March.

The tests in the two sections will be similar enough to be fair, but different enough to give no advantage to the students who have a later sitting. Later on this page, students can find a wealth of suggested practice problems, starting with Assignment 7.

12 Mar 2014
HW 12 Mar 2014
(WED)
Here is Assignment 7 (PDF). Please hand in solutions for the first 5 questions only, and treat the rest as practice for the upcoming midterm.
Posted later: Solutions (PDF).
12 Mar 2014
PP 12 Mar 2014

In the Trench textbook just mentioned, try some of these problems:

  • 12.1 - The Heat Equation: 10, 11, 13, 43-46, 48-53.
  • 12.2 - The Wave Equation: 2, 8, 17, 20, 28, 35, 56.
  • 12.3 - Laplace's Equation in Rectangular Coordinates: 7, 10.
03 Mar 2014
RR   Good Textbook Free Online:

The American Institute of Mathematics sponsors an Open Textbook Initiative that makes high-quality materials available free. A very good text for our course would be William F. Trench, Elementary Differential Equations with Boundary Value Problems. The document is nearly 800 pages long, and it contains over 400 exercises for practice. Go get your own free copy! Then read Chapters 11-12.

03 Mar 2014
HW 05 Mar 2014
(WED)
Here is Assignment 6 (PDF).
Posted later: Solutions (PDF).
05 Mar 2014
RR   Midterm Solutions:

Here are the solutions for Midterm One, for Section 202 (09:00) and for Section 201 (11:00).

26 Feb 2014
PP   Midterm Notes:

In class on Wednesday 12 February, we will have a 50-minute test. This is strictly closed-book: calculators and formula sheets are not allowed. There will be questions about ODE's, power series, eigenfunction series, and some separation of variables. The tests in the two sections will be similar enough to be fair, but different enough to give no advantage to students who have a later sitting. Later on this page, students can find a wealth of suggested practice problems, starting with Pretend Assignment 5.

08 Feb 2014
PP   Suggestions for Practice:

If you have access to the 9th edition of the text, Elementary Differential Equations and Boundary Value Problems, by Boyce and DiPrima, you could sharpen your skills by trying some problems from the list below. Of course you can't solve all these problems, and nobody expects you to try. What you can do, however, is make sure that you know how to solve all these problems, and build up your strength and skill by doing a selection of them that you find most appealing.

  • 5.1 - Review of Power Series: 19-28 (index-shifting practice).
  • 5.2 - Series Solutions Near an Ordinary Point, Part I: 1-14 [parts (a)(b) only].
  • 5.3 - Series Solutions Near an Ordinary Point, Part II: 5-9 [predict radius of convergence without finding the series].
  • 5.4 - Euler Equations; Regular Singular Points: 1-12 (solve Euler equations); 17-33 (make Euler-type approximations to distinguish regular from irregular); 35-39 (show qualitative understanding of solution behaviour).
  • 5.5 - Series Solutions Near a Regular Singular Point, I: 1-14.
  • 5.6 - Series Solutions Near a Regular Singular Point, II: 1-12 (find exponents); 13-17 (find series, but not both---handle the larger exponent only).
  • 10.1 - Two-Point Boundary Value Problems: 1-20.
  • 10.4 - Even and Odd Functions: 14-30 (compute some sine and cosine series).
  • 10.5 - Separation of Variables; Heat Conduction in a Rod: 1-6 (separation of variables as a general method); 7-12 (specific heat problem examples).
  • 10.7 - The Wave Equation: Vibrations of an Elastic String: 1-4 (examples where the initial velocity is 0); 5-8 (examples where the initial displacement is 0).
11 Feb 2014
PP (none) Here is Pretend Assignment 5 (PDF). This is not a real assignment because you never have to hand it in. However, it should provide excellent practice to help you prepare for the in-class test scheduled for Wednesday 12 Febuary 2014.
Posted later: Solutions.
10 Feb 2014
RR   Here, for your reference, are some formal notes on eigenfunction series. These cover all the examinable material for the test next week, and should mostly be familiar from our time together in class. 08 Feb 2014
RR   Here are some pictures showing all “Big 4” expansions for a certain piecewise-defined function. 07 Feb 2014
RR   Here is a handout describing the Big 4 Eigenproblems (PDF). Actual paper copies will be distributed in class on 7 Feb 2014. 06 Feb 2014
HW 05 Feb 2014
(WED)
Here is Assignment 4 (PDF). Posted later: Solutions (PDF). 06 Feb 2014
HW 27 Jan 2014 Here is Assignment 3 (PDF). Posted later: Solutions (PDF). 21 Jan 2014
HW 20 Jan 2014 Here is Assignment 2 (PDF). Posted later: Solutions (PDF). 21 Jan 2014
RR 13 Jan 2014 UBC's own Professor Anthony Peirce taught MATH 257/316 last term, and his course page is still serving a full set of very nice lecture notes. Relevant items for us include his PDF documents on the topics listed below. 10 Jan 2014
RR 13 Jan 2014 Here are some nice lecture notes about Infinite series, improper integrals, and Taylor series (PDF), by UBC's own Professor Leah Edelstein-Keshet. The notes come from UBC MATH 103; something similar is presented in every good first-year Calculus course. The ideas here are important prerequisites for the Math 257 material in Week Two. 10 Jan 2014
HW 13 Jan 2014 Here is Assignment 1 (PDF). Posted later: Solutions (PDF). 21 Jan 2014
RR   Here is a copy of the final exam from December 2012. The Math Department has a whole page of past final exams, including many from this course.
Sometimes the instructors allow or provide a formula sheet for the final exam, and sometimes they don't. The policy for 2014 has not yet been finalized.
06 Sep 2013

Codes: RR = reading/reference; PP = practice problems (not to hand in); HW = homework problems (to be submitted); EXAM = midterm or final exam materials.

Instructor Contact Information

Section 201, MWF 11:00-11:50, in room MATH 100

Kelly M. Paton

Office MATX 1110
Email kmpaton@math.ubc.ca (best option for contact)
Office phone 604-822-6754 (often unattended...)
URI http://www.math.ubc.ca/~kmpaton/
Office Hours Drop-in hours are shown below. Meetings outside these hours can also be arranged, but please reserve a time by email beforehand. Unexpected visitors often cannot be accommodated. If you expect to need more than 15 minutes, please make an appointment.

Jan–Mar 2014*

Mon Tue Wed Thu Fri
by appt by appt by appt by appt by appt

*See "Daily Specials" below for any irregularities.

Daily Specials There are multiple office hours scheduled during the exam period, and they are offered by both myself and Dr. Loewen; please see the April 7 update to the main webpage for the schedule. The regular hours do NOT apply.
Section 202, MWF 09:00-09:50, in room CHEM B250

Dr. Philip D. Loewen

Office Mathematics Building, room 207
Email loew@math.ubc.ca (try this first)
Office phone 604-822-3082 (urgent cases only, please)
URI http://www.math.ubc.ca/~loew/
Office Hours Drop-in hours are shown below. Meetings outside these hours can also be arranged, but please reserve a time by email beforehand. Unexpected visitors often cannot be accommodated. If you expect to need more than 15 minutes, please make an appointment.

April 2014*

Mon 14 Tue 15 Wed 16 Thu 17 Fri 18
by appt by appt 14:00-16:00 14:00-16:00 by appt

NOTE: Math 257/316 students should check the course home page for other support resources this month.

* I will be unavailable on some days. Please check “Daily Specials” below before trekking to MATH 207.

Daily Specials NONE: This week looks normal so far.

Last update: 09 Apr 2014 (Wed), 11:12:25. Valid HTML 5! Valid CSS! (Click a graphic to recheck.)