MATH 256 (Section 202)

This was the course webpage for the Jan--May 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 mid-term exams (20% each)

    • Feb 9​

    • Mar 28

  • 50%: Final Exam​

Notes

Course Outline

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

  1. Linear, first-order, ordinary differential equations (ODEs)

    1. Homogeneous, linear, constant coefficient, first-order ODEs

    2. Inhomogeneous, linear, constant coefficient, first-order ODEs

    3. Integrating factors for non-constant coefficient, linear, first-order ODEs [2.1]

  2. Nonlinear, first-order ODEs

    1. Separable first-order ODEs [2.2]

    2. Bernoulli ODEs

    3. Homogeneous ODEs

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

    5. Autonomous first-order ODEs and stability [2.5]

  3. Linear, second-order ODEs

    1. Homogeneous, linear, second-order ODEs [3.1, 3.4, 3.5]

    2. The Wronskian [3.2, 3.3]

    3. Inhomogeneous, linear, second-order ODEs [3.6, 3.7]

    4. Beating, resonance, and damping [3.8, 3.9]

    5. Euler equations [5.5]

  4. Systems of first-order ODEs

    1. Homogeneous systems of linear, first-order ODEs [7.5, 7.6]

    2. Inhomogeneous systems of linear, first-order ODEs [7.9]

  5. Laplace Transforms

    1. Properties of the Laplace transform [6.1]

    2. Solving linear ODEs with the Laplace transform [6.2]

    3. Step functions and discontinuous forcing [6.3, 6.4]

    4. Impulses [6.5]

    5. Convolutions [6.6]

  6. Fourier Series

    1. Properties of sine and cosine [10.2]

    2. Writing periodic functions as Fourier series [10.2, 10.4]

  7. Separation of variables for partial differential equations (PDEs)

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

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

    3. Wave equation for an elastic string [10.7]

    4. Laplace equation [10.8]

Handouts