MATH 256 (Section 202)
This was the course webpage for the JanMay 2018 edition of Section 202 of MATH 256 at the University of British Columbia.
Course Description
This course is an introduction to differential equations, how to solve them, and how to model physical situations with them. (This course is based on the textbook of Boyce and DiPrima, but the focus and emphasis given to the topics in the lectures will often be different to that given in the textbook. The textbook is a good source of extra worked examples and problem sets.)
Office Hours
Office hours will be located in LSK 203C at the following times:

Mondays 2.15pm  3.45pm

Thursdays 10.00am  11.30am
Assessment
The course will be graded as follows:

10%: Homework (5% Assignments and 5% Webwork)

40%: Two midterm exams (20% each)

Feb 9

Mar 28


50%: Final Exam
Notes

Review Notes

Lecture Notes
Course Outline
The following is an outline of the course. Numbers in square brackets [] show the relevant section number in Boyce and DiPrima.

Linear, firstorder, ordinary differential equations (ODEs)

Homogeneous, linear, constant coefficient, firstorder ODEs

Inhomogeneous, linear, constant coefficient, firstorder ODEs

Integrating factors for nonconstant coefficient, linear, firstorder ODEs [2.1]


Nonlinear, firstorder ODEs

Separable firstorder ODEs [2.2]

Bernoulli ODEs

Homogeneous ODEs

Existence and uniqueness (linear vs nonlinear ODEs) [2.4]

Autonomous firstorder ODEs and stability [2.5]


Linear, secondorder ODEs

Homogeneous, linear, secondorder ODEs [3.1, 3.4, 3.5]

The Wronskian [3.2, 3.3]

Inhomogeneous, linear, secondorder ODEs [3.6, 3.7]

Beating, resonance, and damping [3.8, 3.9]

Euler equations [5.5]


Systems of firstorder ODEs

Homogeneous systems of linear, firstorder ODEs [7.5, 7.6]

Inhomogeneous systems of linear, firstorder ODEs [7.9]


Laplace Transforms

Properties of the Laplace transform [6.1]

Solving linear ODEs with the Laplace transform [6.2]

Step functions and discontinuous forcing [6.3, 6.4]

Impulses [6.5]

Convolutions [6.6]


Fourier Series

Properties of sine and cosine [10.2]

Writing periodic functions as Fourier series [10.2, 10.4]


Separation of variables for partial differential equations (PDEs)

Heat equation for a conducting rod with homogeneous boundary conditions [10.5]

Heat equation for a conducting rod with inhomogeneous boundary conditions [10.6]

Wave equation for an elastic string [10.7]

Laplace equation [10.8]

Handouts

Final

Midterm 2

Midterm 1

Written Assignments