Home
Notes
Homework
Midterms
Final Exam
UBC Math 257/316: Course Notes
Here is a set of lecture notes from an earlier version of this course, courtesy of Dr. Anthony Peirce:
Lecture 1
: Review of ODE
Lecture 2
: Series Solutions to ODE
Lecture 3
: Regular Singular Points
Lecture 4
: Frobenius Series
Lecture 5
: Example: Bessel's Equation & Bessel Functions
Lecture 6
: Introduction to PDE (Part I)
Lecture 7
: Introduction to PDE (Part II)
Lecture 8
: Finite Difference Methods for PDE
Lecture 9
: Separation of Variables and Fourier Series
Lecture 10
: Fourier Sine Series
Lecture 11
: Fourier Cosine Series
Lecture 12
: Heat Equation on a Circular Ring
Lecture 13
: Full Range Fourier Series
Lecture 14
: Half Range Fourier Series
Lecture 15
: Convergence of Fourier Series
Lecture 16
: Bessel's Inequality and Parseval's Theorem
Lecture 17
: Heat Conduction with Inhomogeneous BCs (Part I)
Lecture 18
: Heat Conduction with Inhomogeneous BCs (Part II)
Lecture 19
: Heat Conduction with Distributed Sources
Lecture 20
: Heat Conduction with Time Dependent BCs
Lecture 21
: Wave Equation on the Line: D'Alembert's Solution
Lecture 22
: Wave Equation on the Line: interpreting D'Alembert's Solution
Lecture 23
: Wave Equation on Finite Domains: Separation of Variables
Lecture 24
: Laplace's Equation
Lecture 25
: Laplace's Equation: Neumann, Mixed-BC, and Semi-Infinite Strip Problems
Lecture 26
: Laplace's Equation: Circular Domains
Lecture 27
: More Circular Domain Problems
Lecture 28
: Sturm-Liouville Eigenvalue Problems
Lecture 30
: Heat and Laplace Problems Involving Euler Equations
Supplementary Notes:
A more complicated
eigenvalue problem
Short note on
Radius of Convergence
Finite difference schemes: some
notes
, some
slides
.
Spreadsheet computations:
Obtaining a spread sheet
Basic Excel tutorial
,
Basic Calc tutorial
Using Excel to evaluate a Fourier series
Using Excel to solve the heat equation by finite differences
Comparing the finite difference solution of the heat equation with the Fourier series solution
Using Excel to solve the wave equation - including how to construct a slider