Dr. Neil Balmforth
COURSES
ODEs
This course provides an introduction to solution
methods for ODEs.
Anouncements:
The video
replacing lectures on Friday Nov 22 and Monday Nov 25
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 1:30-2:30, Friday 2:00-3:00 (in my office, Math 229C)
The TAs (for sections 101 and 102):
Deven Shidfar (devenshidfar@math)
Xinyang Li (xy35li@math)
TA office hours: TBA
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
Lecture notes I
Lecture notes II
Lecture notes III
Lecture notes IV
Lecture notes V
Lecture notes VI
Lecture notes VII
Laplace transform table
Additional notes on systems and Laplace transforms (LTs):
Systems,
systems and LTs,
more LTs,
and yet more
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)
Midterm-1 date: TBA
Sample midterm 1
Sample midterm 2
Solutions
Another year's midterm
A midterm without a solution...
A midterm and its solution
THE midterm and its solution
Midterm-2 date: TBA
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
A midterm without a solution...
A midterm, plus solution (typo fixed 1/11)
THE midterm and its solution
Two sample finals,
some quick solutions
More finals
Another final
And another
One last one
Please note that if the solution is not provided, you can always check your answer by substituting it back into the differential equation and any ICs/BCs
to verify that it does indeed satisfy the problem
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