# Introduction to Differential Equations

Faculty
Science & Technology
Department
Mathematics
Course Code
MATH 2421
Credits
3.00
Semester Length
15
Max Class Size
35
Method Of Instruction
Lecture
Tutorial
Typically Offered
Winter
Campus
New Westminster

## Overview

Course Description
This course is an introduction to ordinary differential equations. Topics include the solution of first- and higher order differential equations, power series solutions, Laplace transforms, linear and non-linear systems, stability and applications.
Course Content
1. First-Order Differential Equations: linear, separable, autonomous and exact, existence and uniqueness of solutions, numerical methods and applications.
2. Higher Order Differential Equations: reduction of order, homogeneous linear equations with constant coefficients, nonhomogenous equations and undetermined coefficients, variation of parameters
3. Equations with Variable Coefficients: Cauchy-Euler equations and power series solutions about ordinary and singular points, Bessel and Legendre Equations
4. Laplace Transforms and applications
5. Systems of Linear Differential Equations: systems of homogeneous and nonhomogeneous first-order equations, reduction of higher-order linear equations to normal form
6. Non-linear Systems and Stability:  solutions and trajectories of autonomous systems, stability of critical points
Methods Of Instruction

Lectures, problems sessions, assignments (written and/or Maple).

Means of Assessment

Evaluation will be carried out in accordance with Douglas College policy.  The instructor will present a written course outline with specific evaluation criteria at the beginning of the semester.  Evaluation will be based on some of the following criteria:

Tutorials: 0-10%
Tests: 20-70%
Assignments/Group work: 0-20%
Attendance: 0-5%
Final exam: 30-40%

Learning Outcomes

Upon completion of MATH 2421 the student should be able to:

• identify an ordinary differential equation and classify it by order or linearity
• determine whether or not a unique solution to a first-order initial-value problem exists
• understand differences between solutions of linear and non-linear first-order differential equations
• recognize and solve linear, separable and exact first-order differential equations
• use substitutions to solve various first-order differential equations (optional)
• recognize and solve autonomous first-order differential equations, analyze trajectories, and comment on the stability of critical points
• use the Euler method to approximate solutions to first-order differential equations
• model and solve application problems using linear and non-linear first-order differential equations, including, but not limited to, topics such as: growth and decay, series circuits, Newton’s Law of Cooling, mixtures, logistic growth, chemical reactions, particle dynamics
• determine whether or not a unique solution to a linear nth-order initial-value problem exists
• determine whether or not a set of solutions to a differential equation are linearly dependent or independent using the Wronskian
• use reduction of order to find a second solution from a known solution
• solve homogeneous linear equations with constant coefficients
• express linear differential equations in terms of differential operators (optional)
• use the method of undetermined coefficients to solve nonhomogeneous linear differential equations for which the nonhomogeneous term can be annihilated
• solve nonhomogeneous linear differential equations using variation of parameters
• solve nonhomogeneous linear differential equations using Green’s functions (optional)
• model, solve and analyze problems involving mechanical and electrical vibrations using second-order linear differential equations
• determine ordinary and singular points of linear differential equations
• recognise and solve Cauchy-Euler equations
• use power series techniques to solve linear differential equations in the neighbourhood of ordinary points
• use the method of Frobenius to solve linear differential equations about regular singular points
• use series methods to solve Bessel, modified Bessel and Legendre equations (optional)
• state the definition of the Laplace transform of a function and the sufficient conditions for its existence
• determine the Laplace transforms for basic functions, derivatives, integrals and periodic functions and find inverse transforms
• use the convolution theorem and translation theorems to find Laplace transforms and their inverses
• use Laplace transforms to solve initial value problems, integral equations and integro-differential equations
• solve systems of differential equations using differential operators or Laplace transforms (optional)
• reduce higher-order linear differential equations to first-order systems in normal form
• solve systems of homogeneous first-order linear differential equations using matrix methods
• solve systems of nonhomogeneous linear first-order differential equations
• model and solve application problems using systems of first-order linear differential equations, including, but not limited to, topics such as: parallel circuits, mixtures, chemical reactions, particle dynamics, competition models
• find trajectories associated with, determine critical points of, and perform phase plane analyses for simple autonomous linear and non-linear systems of equations
Textbook Materials

Consult the Douglas College bookstore for the current textbook. Examples of textbooks under consideration include:

A First Course in Differential Equations with Modeling Applications, Zill, Dennis G., Brooks-Cole, current edition

Elementary Differential Equations, Johnson and Kohler, Pearson, current edition

Elementary Differential Equations and Boundary Value Problems, Boyce and DiPrima, Wiley, current edition

## Requisites

### Prerequisites

MATH 1220 and MATH 2232 or instructor permission

### Corequisites

No corequisite courses.

### Equivalencies

No equivalent courses.

## Course Guidelines

Course Guidelines for previous years are viewable by selecting the version desired. If you took this course and do not see a listing for the starting semester / year of the course, consider the previous version as the applicable version.

## Course Transfers

Institution Transfer Details Effective Dates
Camosun College (CAMO) CAMO MATH 225 (3) 2013/01/01 to 2018/04/30
Coquitlam College (COQU) COQU MATH 215 (3) 2004/09/01 to -
Kwantlen Polytechnic University (KPU) KPU MATH 2421 (3) 2004/09/01 to 2006/08/31
Kwantlen Polytechnic University (KPU) KPU MATH 3421 (3) 2006/09/01 to -
Langara College (LANG) LANG MATH 2475 (3) 2004/09/01 to -
Okanagan College (OC) OC MATH 225 (3) 2005/09/01 to -
Simon Fraser University (SFU) SFU MATH 310 (3) 2004/09/01 to 2020/08/31
Simon Fraser University (SFU) SFU MATH 260 (3) 2020/09/01 to -
Thompson Rivers University (TRU) TRU MATH 224 (3) 2004/09/01 to 2010/08/31
Thompson Rivers University (TRU) TRU MATH 2240 (3) 2010/09/01 to -
Trinity Western University (TWU) TWU MATH 3XX (3) 2018/09/01 to -
Trinity Western University (TWU) TWU MATH 2XX (3) 2006/05/01 to 2016/12/31
Trinity Western University (TWU) TWU MATH 321 (4) 2004/09/01 to 2006/04/30
University of British Columbia - Okanagan (UBCO) UBCO MATH 225 (3) 2005/05/01 to -
University of British Columbia - Vancouver (UBCV) UBCV MATH 215 (3) 2004/09/01 to -
University of Northern BC (UNBC) UNBC MATH 230 (3) 2004/09/01 to -
University of the Fraser Valley (UFV) UFV MATH 255 (3) 2004/09/01 to -
University of Victoria (UVIC) DOUG MATH 2421 (3) & DOUG MATH 2440 (3) = UVIC MATH 204 (1.5) & UVIC MATH 2XX (1.5) 2017/09/01 to -
University of Victoria (UVIC) UVIC MATH 204 (1.5) 2015/09/01 to 2017/08/31
University of Victoria (UVIC) UVIC MATH 2XX (1.5) 2017/09/01 to -
University of Victoria (UVIC) UVIC MATH 201 (1.5) 2004/09/01 to 2015/08/31
Vancouver Community College (VCC) VCC MATH 2310 (3) 2017/05/01 to -
Vancouver Island University (VIU) VIU MATH 251 (3) 2004/09/01 to -

## Course Offerings

### Fall 2021

There aren't any scheduled upcoming offerings for this course.