Math 3161
Ordinary Differential Equations II

Winter, 2026

Instructor:	Dr. Xiaoqiang Zhao, HH-2009, zhao@mun.ca
Time:	MWF 14:00-14:50
Classroom:	SN-3060
Office Hours:	Monday 10:30-12:00, Friday 15:00-16:30, or by appointment
Course Website:	http://www.math.mun.ca/~zhao/course/Y2025/math3161.html

Text Book:

1. "Differential Equations: An introduction to Modern Methods and Applications", by J.R. Brannon and W.E. Boyce, third edition, Wiley, 2021. Note that Chapters 9 and 10 of this book are freely available from the publisher online.

2. "Differential Equations with Applications and Historical Notes", by G. F. Simmons, third edition, CRC Press, 2017.

Prerequisites: Math 2260 and Math 3202

Course Contents:

Series Solutions to Initial Value Problems (Chapter 9, Book 1)
- Regular singular points
- Series solutions near a regular singular point (I & II)
- Bessel's equation
Boundary Value Problems and Sturm-Liouville Theory (Chapter 10, Book 1)
- Elementary two-point boundary value problems
- General Sturm-Liouville boundary value problems
- General Fourier series and eigenfunction expansions
- Singular Sturm-Liouville boundary value problems
The Calculus of Variations (Chapter 12, Book 2)
- Introduction
- Euler's differential equation for an extremal
- Isoperimetric problems
- Variational problems for double integrals
The Existence and Uniqueness of Solutions (Chapter 13, Book 2)
- The method of successive approximsations
- Picard's theorem
- Systems of first order equations
- Peano's theorem

Evaluation:

Homework	20%
Midterm test	30%
Final exam	50%

Leture Notes:

Lecture 1 Lecture 2 Lecture 3 Lecture 4 Lecture 5 Lecture 6 Lecture 7 Lecture 8 Lecture 9 Lecture 10 Lecture 11 Lecture 12 Lecture 13 Lecture 14 Lecture 15 Lecture 16 Lecture 17 Lecture 18

Assignments: Please drop your finished assignments in the mail box 41 beside the departmental general office before and on the due date.

Assignment 1, Due time: 6:00pm, Friday, Jan. 23

Problems (Section 9.2): 4, 6, 18

Problems (Section 9.3): 6, 8

Problems (Section 9.4): 6, 10, 30

Solution to HW1

Assignment 2, Due time: 6:00pm, Friday, Jan. 30

Problems (Section 9.5): 2, 4, 8

Problems (Section 9.6): 2, 6, 14, 16

Problems (Section 9.7): 2

Solution to HW2

Assignment 3, Due time: 6:00pm, Friday, Feb. 6

Problems (Section 10.3): 10, 12, 22, 24

Problems (Section 10.4): 2, 20

Solution to HW3

Assignment 4, Due time: 6:00pm, Monday, Feb. 16

Problems (Section 10.5): 6, 10, 16, 20

Problems (Section 10.6): 2 (a) and (b)

Note that in Problem 6 of Section 10.5, there is a typo: y^n should be y''

Solution to HW4

Assignment 5, Due time: 6:00pm, Monday, March 2

Problems (Section 67): 1, 2, 3

Midterm Test (in class): Monday, March 2

This test covers all contents which were selected from Chapters 9 and 10 in Book 1. To review all examples we discussed in the classes and all problems from HW1, HW2, HW3 and HW4 should be very helpful. Here is a brief review for the midterm test.

Final Exam: (to be annouced)

Note that this syllabus is tentative and should not be considered definite. The instructor reserves the right to modify it (including the dates of tests) to meet the needs of the class. It is the student responsibility to attend class regularly and to make note of any change.

Math 3161 Ordinary Differential Equations II