Course Outline

MATH 2475: Differential Equations – spring 202110

Course format: Lecture 4 hours per week (online via Zoom): MW 1230 – 1420pm

Credits: 3

Course Description:

First order equations, special techniques and applications; second order linear equations - linear independence and completeness, homogeneous and nonhomogeneous equations, with applications; Laplace transform techniques; first order linear systems including matrix methods; phase plane and stability analysis. Non-linear systems (time permitting); numerical methods.

Prerequisite(s): Math 2362 or Math 1252, and 2371. (With instructor's permission, one of these courses may be taken concurrently). Prerequisites are valid for only three years.

Transfer Credit: For information regarding transfer and articulation, visit bctransferguide.ca

● Note that one on one help is available in the MSAC (Math and Stats Activity Centre) in room B154: faculty and peer tutors are available at posted hours (it’s online only these days).

See link here for Online MSAC Math & Stats Activity Centre

Learning Outcomes:

Upon successful completion of this course, students should be able to

● Classify differential equations by order, linearity, and homogeneity

● Solve first order linear DE and linear equations with constant coefficients

● Use separation of variables and integrating factors to solve differential equations

● Use variation of parameters and the method of undetermined coefficients to solveDE

● Determine whether a system of functions is linearly independent using theWronksian

● Model real-life applications using differential equations,

● Use Laplace transforms and their inverses to solve differential equations

● Solve systems of linear differential equations using matrix techniques and eigenvalues

● Use numerical methods to solve differential equations

Instructor: Dr. Bruce Aubertin

Office: B154a      Email: [email protected]      Phone: 604.323.5783

Office Hours: by appointment (email and/or on zoom) – email me first

Textbook and Course Materials:

● Elementary Differential Equations and Boundary Value Problems, by William E. Boyce and Richard C. DiPrima (11th Edition ebook or Loose-leaf version - Wiley) - Required.

IMPORTANT: Due to the move to online delivery, you will also need:

● Access to a computer, reliable internet access, and a webcam

● Access to Zoom using your Langara student account (sign-in here: https://langara.zoom.us/)

● Access to a camera or scanner in order to submit multi-page solutions as a single pdf file

(the simplest way to do this is to use your mobile phone along with a free scanning app such as Adobe Scan, CamScanner or similar)

Assignment Weighting:

● Assignments                                          20%

● Midterm 1 (50 minutes)                          20%

● Midterm 2 (50 minutes)                          20%

● Final Examination (1hour 55 minutes)      40%

Test Dates: (tentative)

Midterm 1: Wed February 10 at 1230pm

Midterm 2: Wed March 31 at 1230pm

Final exam will be comprehensive over the term and occur in the period April 9 – 16 (TBA)

Grading Guideline:

GRADE	F	D	C –	C	C +	B –	B	B +	A –	A	A +
% RANGE	0-47	48-52	53-57	58-62	63-67	68-72	73-76	77-79	80-84	85-95	≥96

Note: Last day to withdraw from regular semester courses is March 13 (Saturday) before 2100 hrs.

As a student at Langara, you are responsible for familiarizing yourself and complying with the following policies:

College Policies:

E1003 - Student Code of Conduct      F1004 - Academic Integrity

E2008 - Academic Standing - Academic Probation and Academic Suspension

E2006 - Appeal of Final Grade

F1002 - Concerns about Instruction

E2011 - Withdrawal from Courses

Departmental/Course Policies:      Math & Stats Department Policies

Further notes and links:

This course will be run using email, Brightspace by D2L, and Zoom classes with no videos or recordings.

Assessments will be made from assignments and exams only (no quizzes).

A PDF of each class (lecture) will be posted to Brightspace after the class.

It is fine to discuss or ask help with assignments if needed, they are for learning. But what you submit should be your own hand-written work. Exams on the other hand are assessments and it is on your honour that these be done independently and all submissions be completely your own work. Our exams will be designated closed book with a basic-only scientific calculator as an aid.

● If a midterm exam is missed -- due to illness or other reason -- provide a valid reason/explanation in advance or as soon as possible if an emergency, so you don’t get zero. No make-up exam will be given.

All of your work (assignments and exams) should be handwritten or presented on plain white 8½ x 11 inch paper and submitted as a single PDF to the correct submission folder found under Assessments/Assignments on Brightspace. Only in an emergency or technical issue can you email me photos of your work. Please keep in mind, especially in assignments, that you are communicating your work to be read in the beautiful language of mathematics; this will help you write more carefully and clearly. Good writing in any language is not easy!

Help with Brightspace and Zoom: https://iweb.langara.ca/lts/

Zoom basics by Ben Finio      https://www.youtube.com/watch?v=l-NgrIxQVf4

Academic integrity          https://langara.ca/student-services/academic-integrity/index.html

https://langara.ca/student-services/academic-integrity/resources.html

The “bad bet” video at the very bottom of this last link is kind of cute and worth a look I think.

Detailed Course Schedule:

The topics schedule is tentative; use it as a guide in preparing for classes.

Recommended Problems

from11th ed. text

(not for handing in)

1.3 [1 - 4, 7, 10, 15, 18]

2.1     [1, 5, 6, 10, 11, 18, 20, 22, 25]

2.2     [5, 11, 12, 19, 26, 28]

2.3     [2, 4, 6, 7, 9, 12, 20]

2.4     [1, 3, 5, 8, 9, 12, 15, 17, 18, 23, 24]

2.5     [1 - 6, 16, 19 - 22]

2.6     [2, 3, 7, 12, 15, 18, 19]

2.7     [2, 6, 7, 15, 17]

2.8     [3, 5]

3.1     [3, 11, 12, 13, 16, 17]

3.2     [4, 9, 10, 11, 13, 17, 20]

3.3     [3, 4, 9, 12, 13, 21]

3.4     [7, 9, 11, 12, 18, 21]

3.5     [6, 13, 14]

3.6     [2, 3, 8, 12, 13]

3.7     [3, 17]

6.1     [5, 16, 19 – 21]

6.2     [2, 4, 10, 16, 17, 22]

6.3     [5, 7, 10, 12, 14, 15, 17, 19, 22, 23]

6.4     [6, 9]

6.5     [6]

7.1     [1, 6]

7.5 [2, 4, 7, 11, 23]

7.6 [2, 5]

7.8     [1, 4, 6]

7.9     [1, 2, 5]

8.1     [3, 13, 16]

8.2     [8]

9.1 [1, 5, 10] (Only the matrices A are given here for the system dx/dt = Ax)