Dr. Neil Balmforth
COURSES

ODEs

This course provides an introduction to solution methods for ODEs.

Instructors:
Section 201 - Neil Balmforth,
Section 202 - Laurent MacKay,
Section 203 - Miranda Holmes-Cerfon

Anouncements: the course webpage on CANVAS provides more information and details about this course

Some video lectures:
Lecture 1 (linear, second-order, constant-coefficient ODEs)
Lecture 2 (sample ODE problems)
Lecture 3 (mechanical oscillators)
PDE example (material at the very end of the course)


The syllabus:
I. First-order ODEs (integrating factors, separable equations)
II. Second-order, constant coefficient ODEs (real, repeated and complex roots; homogeneous and inhomogeneous)
III. Systems of ODEs
IV. Laplace Transform methods
V. Fourier series
VI. Solution of partial differential equations by separation of variables


Assessment will involve coursework (homework problems) and examination.

Recommended texts:
Boyce and DiPrima, "Elementary differential equations and boundary value problems"
E. Kreiszig, "Advanced Engineering Mathematics"
On-line "Notes on Diffy Qs" by J. Lebl

Office hours: Monday at 1pm, Tuesday at 1pm


The TAs: Jiahao Gong (davidgong@math), Tuoxin Li (tuoxin@math), Fatemeh Saghafifar (fsaghafi@math) (email them for assistance with WebWork and more)

Extra problem, page 1, 2, 3, 4

Background knowledge
Fun with complex numbers
Notation and more
Some terse notes

Coursework involves Webwork, which must be accessed via Canvas: login using your CWL, then click on Assignments and Webworking

Midterm-1 date:
Sample midterm 1
Sample midterm 2
Solutions
Another year's midterm

Actual midterm, brief solution

Lecture notes I
Lecture notes II
Lecture notes III
Lecture notes IV
Lecture notes V

Laplace transform table

Midterm-2 date:
Sample midterm 1
Sample midterm 2
Terse solutions summary (there is a minor hiccup in question 3 of part 1 for the second sample, which is answering a slightly different question - the sign of a has switched)
Another year's midterm
And its solution

Lecture notes VI
Lecture notes VII

Two sample finals, some quick solutions
More finals