UBC Math 257: Partial Differential Equations
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 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.

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):


Last update: 07 Aug 2014 (Thu), 11:47:48. Valid HTML 5! Valid CSS! (Click a graphic to recheck.)