MTH 311: Introduction to Ordinary Differential Equations

University of Miami, Fall 2019

Instructor: Christopher Scaduto
Email: c.scaduto @ math.miami.edu
Office: Ungar 525
Office hours: 11:15-12:15 MF, 2:30-3:30 W, or by appointment

I am teaching two sections for this course:

MTH 311 C 10:10-11:00 MWF @ Dooly Memorial 102
MTH 311 F 1:25-2:15 MWF @ Mahoney Pearson 118

The course syllabus can be found here.

Course Schedule

Date	Lecture Content	Reading
8/19/19	Syllabus overview, "What is an ODE?", Separation of variables	1.1, 1.2, 1.4
8/21/19	Separation of variables (cont.), Application: physics problems	1.4
8/23/19	Applications: population growth, radioactive decay, heating and cooling	1.4
8/26/19	Linear 1st order differential equations	1.5
8/28/19	Applications: mixing problems, electrical circuits	1.5
8/30/19	Class canceled (hurricane prep)
9/2/19	Labor day (no class)
9/4/19	Slope fields	1.3
9/6/19	Euler's method, Existence and Uniqueness	2.4, 1.3
9/9/19	Existence and Uniqueness (cont.)	1.3
9/11/19	Population Models	2.1
9/13/19	Population Models (cont.)	2.2
9/16/19	Substitution methods	1.6
9/18/19	Linear ODE of higher order	3.1, 3.2
9/20/19	Second order linear ODE and the Wronskian	3.1, 3.2
9/23/19	More Wronskians: higher order case	3.1, 3.2
9/25/19	Review for midterm 1. Here is a practice exam: pdf
9/27/19	Midterm 1 (in class) Solutions: pdf
9/30/19	Nonhomogeneous linear equations	3.1, 3.2
10/2/19	Constant coefficient equations	3.1, 3.2
10/4/19	Constant coefficient equations: complex roots	3.3
10/7/19	Spring models (without external forces)	3.4
10/9/19	Spring models (cont.), Method of undetermined coefficients	3.4, 3.5
10/11/19	Method of undetermined coefficients (cont.)	3.5
10/14/19	Resonance, Variation of parameters	3.6, 3.5
10/16/19	Variation of parameters (cont.)	3.5
10/18/19	Fall recess (no class)
10/21/19	Introduction to systems of ODE	4.1
10/23/19	Matrix operations, eigenvalues and eigenvectors	5.1, 5.2
10/25/19	Finding eigenvalues and eigenvectors	5.1, 5.2
10/28/19	Review for midterm 2. Here is a practice exam: pdf Solutions: pdf
10/30/19	Midterm 2 (in class) Solutions: pdf
11/1/19	Solving linear systems using eigenvalues and eigenvectors	5.2
11/4/19	Intro to phase portraits	5.3
11/6/19	Phase portraits: complex eigenvalues	5.3
11/8/19	More phase portraits	5.3
11/11/19	Non-linear systems: predator-prey model	6.1, 6.3
11/13/19	Non-linear systems: method of linearization	6.2
11/15/19	Linearization of non-linear systems (cont.), Laplace transform	6.2, 7.1
11/18/19	Laplace transforms: definition and basic properties	7.1, 7.2, 7.4
11/20/19	More Laplace transforms; method of partial fractions	7.3
11/22/19	Laplce tranforms and discontinuous functions	7.5, 7.6
11/25/19
11/27/19	Thanksgiving break
11/29/19
12/2/19	Power series methods	8.1, 8.5
	Practice problems for the final exam: pdf Solutions: pdf

Homework Assignments

All homeworks are worth the same, even if graded out of different totals.

Assignment	Due Date	Remarks
Homework 1	~~8/30/19~~ ~~9/4/19~~ 9/6/19	Out of 30; 5 problems graded (1,4,6,7,10), 5 pts each, + 5 pts for completeness
Homework 2	~~9/6/19~~ 9/9/19	Out of 30; 5 problems graded (1-5), 5 pts each, + 5 pts for completeness
Homework 3	9/13/19	Out of 20; all 4 problems graded, 5 pts each. Solutions: pdf
Homework 4	9/20/19	Out of 30; 5 problems graded (1-4, 6), 5 pts each, + 5 pts for completeness. Solutions: pdf
Homework 5	10/11/19	Out of 25; 4 problems graded (1, 2, 4, 6), 5 pts each, + 5 pts for completeness. Solutions: pdf
Homework 6	10/21/19	Out of 25; ~4 problems graded (1, 2, 3(a,b), 5), 5 pts each, + 5 pts for completeness. Solutions: pdf
Homework 7	10/28/19	Out of 10; all problems graded. Solutions: pdf
Homework 8	11/11/19	Out of 30; all problems graded but the last, 5 pts each, + 5 pts for completeness. Solutions: pdf
Homework 9	11/20/19	Out of 20; both problems graded for 10 pts. Solutions: pdf
Homework 10	12/2/19	Solutions: pdf