MATH 256 (Section 202)

This is the course webpage for the 2017 edition of Section 202 of MATH 256, given by Tom Eaves. For Section 201, given by Prof. Eric Cytrynbaum, please visit here.

Office Hours

Office hours will be located in LSK 203C at the following times:

Piazza. Also linked via connect.

Assessment

The course will be graded as follows:

Webwork. Also linked via connect.

The mid-term exams will be on Wed 1st Feb and Wed 15th March.

Handouts and Lecture Notes

Course Outline

This course is an introduction to differential equations, how to solve them, and how to model physical situations with them. The following is an outline of the course. Sections marked with ** will be covered in class if time permits, but will not be examined. Numbers in square brackets [] show the relevant section number in Boyce and DiPrima. (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.)

Our progress through the course is marked by the completed, striked out sections.

  1. Introduction
    1. Terminology of differential equations [1.3]
  2. 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]
  3. Nonlinear, first-order ODEs
    1. Separable first-order ODEs [2.2]
    2. Autonomous first-order ODEs and stability [2.5]
    3. ** Discrete equations (the logistic map) [2.9]
    4. ** Existence and uniqueness (linear vs nonlinear ODEs) [2.4]
  4. Linear, second-order ODEs
    1. Homogeneous, linear, second-order ODEs [3.1, 3.4, 3.5]
    2. ** Linear-independence and 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]
  5. 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]
    3. ** The Lorenz equations, or, the most famous system of ODEs [9.8]
  6. 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]
  7. Fourier Series
    1. Properties of sine and cosine [10.2]
    2. Writing periodic functions as Fourier series [10.2, 10.4]
  8. 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. ** Similarity solutions for the heat equation
    4. Wave equation for an elastic string [10.7]
    5. ** Propagation of waves on an infinite elastic string
    6. Laplace equation [10.8]
    7. ** Potential flow around a cylinder

Contacts

Office: LSK 203C
Email: tse23@math.ubc.ca