UBC Math 316: Elementary Differential Equations II
May–August 2014

This page provides official background information for two courses running in parallel:

Daily readings, homework, and updates, are on the courses' Unified Home Page.


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.

2014 Summer Exam Week Prep*

Mon 11 Aug Tue 12 Aug Wed 13 Aug Thu 14 Aug Fri 8 Aug
14:00–15:30 14:00–15:30 [none] [none] 14:00–15:30

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

Daily Specials Office hours will be “by appointment only” starting on Wednesday 13 August and continuing through Friday 12 September.

Topic Outline

Topic Hrs Description
Review of Series 5
  • Convergence concepts
  • Geometric series and the ratio test
  • Error control and Shanks Transformation
  • Power series
  • Analytic functions, radius of convergence
Linear Ordinary Differential Equations 9
  • Power Series Solutions near an ordinary point
    • General Solutions
    • Initial-Value Problems
    • Non-homogeneous problems
  • Homogeneous ODE's with Constant Coefficients
  • Non-Homogeneous ODE with Constant Coefficients
  • ODE's of Euler type
  • Change of independent variable
  • Singular points: regular vs irregular
  • Series solutions near a regular singular point (Frobenius method)
Linear Operators and Eigenvalue Problems 6
  • The matrix case
  • Operators and eigenvalues in function space
  • Sample eigenvalue problems
  • Orthogonality and eigenfunction series
Eigenfunction-series solutions for Boundary-Value Problems 6
  • Separation of variables: eigenvalue problems, formal series
  • The Big Four standard eigenvalue problems
  • Propagating coefficients
  • Initialization
  • Special modes; superposition
  • Nonhomogeneous PDE
  • Nonhomogeneous BC
More General Eigenfunction Series 5
  • Eigenvalue Problems
  • Orthogonality and Eigenfunction Series
  • Sturm-Liouville Theory
  • Full Fourier Series
Heat Equation in Depth 3
  • Derivation; BC's and their meanings
  • Transient versus long-run behaviour
  • Splitting methods for nonhomogeneous boundary conditions
Laplace's Equation in Depth 4
  • Derivation and Interpretation
  • Superposition and splitting
  • Neumann problems and consistency conditions
  • Physical solutions are bounded functions
  • Problems in polar coordinates (Euler equations reappear)
Wave Equation in Depth 4
  • Derivation; BC's and their meanings
  • Travelling wave solutions
  • D'Alambert's solution
  • Signal speed; reflections
  • Forcing and resonance
Numerical Methods 2
  • Finite Differences
  • Spreadsheet Implementations
Total Hours on Outline 44
  • (44 lecture-hours + 2 test-hours = 46 meetings this term)

Course Details

Required Text:

Recommended Reading:

Watch the main course page for writeups customized for this term's experience. In addition, consult the following:

Other Nice Books:

Important Dates:



Course Web Page (daily details appear here):


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