May–August 2014

This page provides official background information for two courses running side-by-side:

- UBC Math 257 — Partial Differential Equations, and
- UBC Math 316 — Elementary Differential Equations II.

An overview of the plan for the term is provided separately, on the MATH 257/316 Course Outline.

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

Code | Due | Details | Last Change |

RR | 07 Aug 2014 |
Here is a copy of the Math 257/316 final exam from April 2014. For more practice problems, visit Professor Peirce's UBC M257/316 course page for Sep-Dec 2013. See also the Math Department's central collection of past exams. |
07 Aug 2014 |

RR | 05 Aug 2014 |
Here are some notes from your instructor's personal files on Laplace's equation. |
05 Aug 2014 |

RR | 05 Aug 2014 |
Links for Chladni patterns: |
05 Aug 2014 |

RR | 31 Jul 2014 |
Here are some notes from your instructor's personal files on the wave equation. |
01 Aug 2014 |

HW | 05 Aug 2014 |
Here is Assignment 11 (PDF).
For Question 5, search for clues in the final section of the
notes on the wave equation posted after
class on Thursday 31 July.
Added later: detailed solutions for Assignment 11. |
07 Aug 2014 |

RR | 24 Jul 2014 |
Here are some notes from your instructor's personal files on the heat/diffusion equation. |
24 Jul 2014 |

HW | 29 Jul 2014 |
Here is Assignment 10 (PDF).
Added later: detailed solutions for Assignment 10. |
30 Jul 2014 |

RR | 17 Jul 2014 |
Here are some notes from your instructor's review of prerequisite ODE material. The exponential shift is described on pages 4–7. For more information and examples on this material, please read Section 5.4 in the Trench textbook. Trench recalculates the exponential shift in every single example, instead of using the convenient formula shown in a box on page 5 of the notes provided here. |
17 Jul 2014 |

HW | 22 Jul 2014 |
Here is Assignment 9 (PDF).
Added later: detailed solutions for Assignment 9. |
24 Jul 2014 |

RR | 12 Jul 2014 |
Here are some lecture notes on eigenfunctions. Please report any typos or unclear elements to the instructor. Elements that may be helpful for Assignment 8 appear throughout, but pages 3-4 are relevant for Question 4(b), and there are a few words following the sketch on page 8 that may clarify the desired elements in Questions 2(ii) and 3(ii). For more information and examples on this material, please read Section 13.2 in the Trench textbook. |
Updated 17 Jul 2014 |

RR | 11 Jul 2014 |
Here are your instructor's semi-polished notes on separation of variables. Treat this as the companion writeup for the 6-step recipe distributed earlier. |
11 Jul 2014 |

NEWS | 10 Jul 2014 | UBC Enrolment Services has just released the Summer Exam Schedule. Our final exam will be on Wednesday 13 August in the evening, 19:00–21:30. Please rely on the official site just mentioned as your definitive source for details about the time and place. | 10 Jul 2014 |

HW | 15 Jul 2014 |
Here is Assignment 8 (PDF).
In addition to the classroom discussion of the key topics here,
there is support in Section 13.2 of the official Trench textbook.
(There is a nasty typo in textbook line (13.2.2), where the first
y' should actually
be y''.)
Added later: detailed solutions for Assignment 8. |
16 Jul 2014 |

RR | 08 Jul 2014 |
In class today, we discussed modes of vibration (another word for eigenfunctions) and their characteristic frequencies, as revealed by the Wave Equation. The computer-generated animations came from the software package Maple, using the script file here: wavemode.mws. A similar script provides animations for the Heat Equation: heatmode.mws. |
10 Jul 2014 |

VID | 08 Jul 2014 |
This is weird, but relevant, for reasons discussed in class today: Nestor Kornblum presents Amazing Grace in overtones. Interested? Follow Kornblum's channel. Or, watch ordinary-looking guy Alexander Glenfield demonstrate seven styles of Tuvan throat-singing. |
08 Jul 2014 |

RR | 04 Jul 2014 |
Here is a one-page summary sheet that presents a systematic recipe for solving boundary-value problems. Most of our work for the final month of the course will concern Steps 1 and 2 shown here. The rest should already be familiar. |
04 Jul 2014 |

HW | 08 Jul 2014 |
Here is Assignment 7 (PDF).
In honour of the short deadline, it has only 3 questions.
Added later: detailed solutions for Assignment 7. |
09 Jul 2014 |

HW | 03 Jul 2014 |
Here is Assignment 6 (PDF).
Question 1 requires some computer work, based on the functions
for which pairs of
(x,y)
values are given in the files
Students unfamiliar with computers may find that
the spreadsheet
described in the next entry of this table helps with Question 1.
Added later: detailed solutions for Assignment 6. |
19 Jun 2014 |

RR | 24 Jun 2014 |
Here is an Excel spreadsheet that illustrates the Fourier Sine Series “machines” discussed in class. The document has two tabs: “synthesizer” and “analyzer”. - The synthesizer calculates the signal generated by a sum of terms like bn*sin(n*pi*x/L) for given coefficients bn. You enter the value of L in row 1, the values of bn in row 2, and the corresponding values of n in row 3. Then the formulas in column B automatically generate the y-values that correspond to the x-values appearing in column A, and the system automatically updates the given plot of the resulting function.
- The analyzer looks at the (x,y) pairs laid out in columns A and B and uses the Trapezoidal Rule to estimate the FSS integral that defines each coefficient bn. You tell it the n-values you like in row 3, and scroll down to the bottom of the column to recover bn. The method for each bn is the same, so the system is happy to compute five coefficients at the same time. The number L is important in this formula; you enter that in row 1, as for the synthesizer.
Students unfamiliar with computers may find this spreadsheet useful in tackling Assignment 6. There is still plenty of room for learning: the value of L and the number of (x,y) pairs in this spreadsheet are different from the corresponding values on the assignment, and the spreadsheet only handles the FSS, whereas the assignment mentions several others of the Big Four eigenfunction series. Finally, the spreadsheet given here deals with just 5 terms at once in both the synthesizer and the analyzer; it is perfectly possible to increase this number. Students with programming experience may prefer to write some simple code instead of modifying the given spreadsheet. Both approaches are fully acceptable. |
24 Jun 2014 |

BREAK | 03 Jul 2014 |
Good News! There will be no class meetings in the week of 23-27 June, because this is the official exam week for courses that run only in Summer Term One. The next Tuesday following exam week is Canada Day, 1 July, another holiday. So our next meeting after the midterm will be on Thursday 3 July. Bad News: Assignment 6 will be due on Thursday 3 July, the day we come back, and then the Tuesday-to-Tuesday homework rotation will resume with Assignment 7 due on Tuesday 8 July. |
17 Jun 2014 |

TEST | 19 Jun 2014 |
Here is a page showing
Examinable Topics for the Midterm.
Some sample problems from the textbook are listed there.
Added later: a blank copy of the question booklet, and the instructor's detailed solutions. |
16 Jun 2014 |

TEST | 19 Jun 2014 | On Thursday 19 June 2014 we will have a test for the full 110-minute class period, from 14:00-15:50. This activity will account for about 40% of your grade in the course. Please bring your UBC ID and writing tools (including a ruler), and nothing else. Calculators, formula sheets, and other resources are not allowed. Please see the course outline for more details on policies and expectations, and come to class for further study tips. | 11 Jun 2014 |

RR | Here is a copy of the paper handout describing the Big Four Eigenvalue Problems we will use heavily in this course. It is nicely illustrated by this triangle-wave example. | 11 Jun 2014 | |

HW | 17 Jun 2014 |
Here is Assignment 5 (PDF).
The first question relies heavily on Assignment 4.
Note that
detailed solutions for Assignment 4
are now available.
Posted later: detailed solutions for Assignment 5. |
07 Jun 2014 |

RR | Under the general heading of Eigenfunction Series [Part 3] (PDF), here is the final collection of material relevant for next week's in-class test. (More details about that celebration of learning will follow soon.) | 10 Jun 2014 | |

RR | Here is a fresh installment of notes on Eigenfunction Series [Part 2] (PDF). The ideas they contain may help with Question 3 on Assignment 4 (PDF). | 06 Jun 2014 | |

HW | 10 Jun 2014 |
Here is Assignment 4 (PDF).
NOTE: After class on Thursday 6 June, I updated this posting by dropping the last question. Please solve only Questions 1–3 as shown here for submission on Tuesday 10 June. NOTE: On Saturday 7 June at 09:32 PDT, I corrected a minor one-character typo in the formulation of Question 3, Part II(c). Posted later: detailed solutions. |
07 Jun 2014 |

RR | Here are the instructor's personal notes on Eigenfunction Series Part 1 (PDF). The ideas they contain may help with Assignment 4 (PDF). | 06 Jun 2014 | |

RR | Here are the instructor's personal notes on Series Solutions for ODE's (PDF). The ideas they contain may help with Assignment 3 (PDF). Preparing these for posting triggered some revisions to the previously-posted notes on Introduction and Power Series (PDF). | 29 May 2014 | |

HW | 03 Jun 2014 |
Here is Assignment 3 (PDF).
Posted later: detailed solutions. |
12 Jun 2014 |

HW | 27 May 2014 |
Here is Assignment 2 (PDF).
Posted later: detailed solutions. |
28 May 2014 |

RR | It's fair to know what protocols are used to assess your work. Here are your instructor's guidelines for the grading of homework. Rubrics for the marking of midterm and exam questions are typically more detailed than this, but the same ladder of priorities applies also in those high-stakes situations. | 20 May 2014 | |

RR | 19 May 2014 | Here is a writeup that closely resembles our course's Introduction and Power Series (PDF). The ideas in it may help with Assignment 1 (PDF). | 29 May 2014 |

HW | 20 May 2014 |
Here is Assignment 1 (PDF).
The “optional” label on Question 5
means that it will not be marked when your homework
is graded. But the concepts in that question are
not optional:
you should make a serious attempt to solve it,
and pay close attention to the instructor's solution
when it is released.
Posted later: detailed solutions. |
20 May 2014 |

RR | 15 May 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 316 material in Week One. | 13 May 2014 |

TUT | The Math Department has hired some undergraduate TA's to hang out in room LSK 300 and help drop-in visitors with questions. For details, check out the Math Learning Centre Schedule. | 13 May 2014 | |

RR |
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 summer 2014 is strictly minimalistic: there will be NO CALCULATORS and NO FORMULA SHEET on any midterm or final exam. |
11 May 2014 |

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

Dr. Philip D. Loewen

Office | Mathematics Building, room 207 |

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 | I'm happy to meet individuals or small groups in room MATH 207, but advance planning is essential. To schedule a conversation, email loew@math.ubc.ca, including your course number (e.g., “264” or “211”) in the subject line. |

Last update: 07 Aug 2014 (Thu), 17:02:14. (Click a graphic to recheck.)