Differential Equations - Math 3113
Section 001

Instructor

Garrett Alston
galston...math.ou.edu
Office: 528
Office Hours: M 1-2, F 10:30-11:20

Time and place:

MWF 11:30-12:20, Physical Sciences 0323

Text

Differential Equations and Boundary Value Problems: Computing and Modeling, Fifth Edition, Edwards, Penney and Calvis

Overview

We will cover some standard topics in ordinary differential equations such as linear equations and systems, geometry of equations and solutions, exact solution methods, Laplace transform, numerical solution methods, and applications.
We will try to do as many applications as possible to science. A big source of examples throughout the class will be Newton's law F=ma.
We will spend some time using computers to numerically solve equations and gain insight into the theory. We will use MatLab or similar programs for the computer work. MatLab is installed on some university computers and is available for free to students through OU IT Store. SciLab and Octave are two open-source alternatives to MatLab and can be found at www.scilab.org and www.gnu.org/software./octave. Octave is very similar to MatLab.
There will be three types of homework: Webwork, traditional written homework, and computer projects. Webwork is an online homework system, and Webwork problem sets will generally be due every Wednesday at 10 pm. The hand written assignments will be due on Fridays, one about every three weeks. They will be relatively short but the problems will be challenging. A computer project will be due about once every three weeks. Some amount of class time will be devoted to work on the computer projects.
There will be a short 10 minute in-class quiz on most Fridays. It will cover the material of the homework due that week.

Grades

10% Webwork
10% Written homework
10% Computer projects
10% Quizzes (lowest 2 quiz scores will be dropped)
15% Exam 1
15% Exam 2
30% Final Exam

Grading Policy

Each quiz and exam problem will be graded out of 3 points (except for multiple choice, true/false, fill in the blank). Here are the guidelines I will use to determine how many points you get on a problem:

3 points: complete, correct solution, a few small arithmetic errors or other minor errors are okay (A level work)
2 points: substantial progress towards a solution but still missing a key idea or step; or a mostly correct solution but with some more serious algebra/arithmetic errors that change the solution slightly (B,C level work)
1 points: a first step or steps toward a correct solution such as a correct formula or expression of a correct plan; an algebra mistake or other mistake that changes the solution significantly may result in this score (D level work)
0 points: no progress towards a correct solution (F level work)

You should write your solutions in a neat, step-by-step, orderly way. Basically, they should be clear enough that another student reading your solution would be able to follow each step and understand how the solution works. You don't need to write words (although sometimes a word or two can be helpful), but instead focus on using mathematical language and symbols to correctly express how your solution goes. Random non-applicable or incorrect formulas and calculations will also be penalized and may result in moving down the grade scale.

Your final letter grade will be based on a curve (to be determined).

Calculator Policy

Calculators are allowed on homework, exams and quizzes. It is recommended that you bring a scientific or graphing calculator for exams and quizzes. No cell phones allowed on quizzes and exams.

Exam Dates

Exam 1: Friday, Feb 17
Exam 2: Friday, Mar 24
Final Exam: Thursday, May 11, 1:30-3:30

Missed work policy

No late homework will be accepted. No makeup exams or quizzes, except in the case of excused absence (illness with doctor's note, etc.).

Academic misconduct statement

All cases of suspected academic misconduct will be referred to the Dean of the College of Arts and Sciences for prosecution under the University’s Academic Misconduct Code. The penalties can be quite severe. Don’t do it! For more details on the University’s policies concerning academic misconduct consult http://www.ou.edu/integrity/.

Students are also bound by the provisions of the OU Student Code, which can be found at http://judicial.ou.edu/.

Students with disabilities

The University of Oklahoma is committed to providing reasonable accommodation for all students with disabilities. Students with disabilities who require accommodations in this course are requested to speak with the instructor as early in the semester as possible. Students with disabilities must be registered with the Office of Disability Services prior to receiving accommodations in this course. The Office of Disability Services is located in Goddard Health Center, Suite 166: phone 405–325–3852 or TDD (only) 405–325–4173.

Webwork

Due on Wednesdays at 10 pm. The website for Webwork is https://webwork.math.ou.edu/webwork2/alston_math3113_001_spring2017/. To login, your username is your OU 4x4, and so is your password (this means username=password, for example username=alst1234, password=alst1234). Change your password after logging in for the first time.

Computer Projects

#	Due Date	Assignment	Solutions
1	2/10	Computer Project 1	slopefield.m graphslopefield.m slopefield.pdf
2	3/10	Computer Project 2	temp.m EulerMethod.m ImprovedEulerMethod.m
3	4/14	Computer Project 3	kepler.m
4	5/5	Computer Project 4 RungeKuttaMethod.m stringAnimation.m (files updated 5/3: string changed to string2)	string2.m stringAnimation2.m video of solution with delta function initial position

Written Homework

#	Due Date	Assignment	Solutions
1	1/27	Section 1.1: 43, 44, 45	solutions
2	2/3	Section 1.3: 25, 26, 29	solutions
3	3/3	Written Assignment 3	solutions
4	4/7	Section 4.1: 30, 32, 37, also, for 30 and 37, rewrite as a 1st order system of ODEs	solutions
5	4/28	Written Assignment 5	solutions

Daily Syllabus

1/18: Section 1.1: notation and conventions, examples of ordinary differential equations, modelling, general solutions, order, initial value problems, checking solutions, partial differential equations
1/20: Section 1.2: solutions to equations of the form y'=f(x), velocity and acceleration

1/23: Section 1.3: slope fields, graphical analysis of solutions, existence and uniqueness theorem
1/25: Section 1.4: exponential function, separable equations, Newton's law of cooling and heating, Webwork 1 due at 10 pm
1/27: Computer work, Matlab Handout 1, Quiz 1, solution, Written Assignment 1 due in class

1/30: Section 1.4 continued
2/1: Section 1.5: First order linear equations and the integrating factor technique, Webwork 2 due at 10 pm
2/3: Computer work, Quiz 2, solution, Written Assignment 2 due in class

2/6: Class Cancelled
2/8: Section 1.5 continued: mixture problems, Webwork 3 due at 10 pm
2/10: Section 1.6: Exact equations, Quiz 3, solution, Computer Project 1 due at 11:30 am (upload to Canvas)

2/13: Section 1.6 continued
2/15: Section 2.1: Logistic equation, Webwork 4 due at 10 pm
2/17: Midterm 1, solutions, covers Sections 1.1-1.5, Review Problems: Section 1.1: 27-31, Section 1.2: 6, 7, 10, 11, 19, Section 1.3: 1, 2, 3, Section 1.4: 1-28, 40, 45, 53, 65, 66, Section 1.5: 1-25, 33, 36, 42

2/20: Section 2.2: Autonomous equations and phase diagrams
2/22: Section 2.4, Section 2.5: Euler Method and Improved Euler Method, Webwork 5 due at 10 pm
2/24: Computer work, Quiz 4, solution

2/27: Section 3.3: Homogeneous Linear Equations
3/1: Section 3.1, 3.2: General Properties of Linear Equations, Webwork 6 due at 10 pm
3/3: Computer work, Quiz 5, solution, Written Assignment 3 due in class

3/6: Homogeneous linear equations continued
3/8: Section 3.4: Spring problems, Webwork 7 due at 10 pm
3/10: spring problems continued, Quiz 6, solution, Computer Project 2 due at 11:30 am (upload to Canvas)

Spring Break

3/20: Section 3.5: Nonhomogeneous equations, the method of undetermined coefficients
3/22: Section 3.5 continued, Webwork 8 due at 10 pm
3/24: Exam 2, solutions, covers exact equations (Section 1.6), logistic equation (2.1), autonomous equations and phase diagrams (2.2), Euler method but not improved Euler (2.4), homogeneous linear equations (3.1-3.3), spring problems (3.4)
Review problems: 1.6: 31-42, 2.1: 25, 2.2: 1-12 (just draw the phase diagrams and know how to analyze long term behavior), 2.4: 1-10, 3.1: 1, 16, 17, 33-42, 3.2: 1, 13, 3.3: 1-42, 3.4: 1-30

3/27: Section 3.5 continued
3/29: Section 4.1: First order systems, Webwork 9 due at 10 pm
3/31: Computer work, no quiz

4/3: Section 4.1: Continued, Matlab files for demonstration
4/5: Section 4.3: Numerical methods for systems, Webwork 10 due at 10 pm
4/7: Computer work, Matlab files for demonstration,Quiz 7, solution, Written Assignment 4 due in class

4/10: constructing integrals (conserved quantities), more substitution examples
4/12: Computer work, Matlab files for demonstration, Webwork 11 due at 10 pm
4/14: Section 5.1: matrix algebra, determinants, linear independence, eigenstuff, Quiz 8, solution, Computer Project 3 due at 11:30 am (upload to Canvas)

4/17: Section 5.1 continued
4/19: Section 5.1 continued Webwork 12 due at 10 pm
4/21: Section 5.2: linear systems in matrix notation, the eigenvalue method Quiz 9, solution

4/24: computer work: eigenstuff in Matlab, code from class
4/26: computer work continued, in class worksheet, Webwork 13 due at 10 pm
4/28: computer work continued, complex eigenstuff Quiz 10 (take home, due on Monday at beginning of class), solution, Written Assignment 5 due in class

5/1: Runge-Kutta method, computer work, worksheet solution
5/3: Computer work, Webwork 14 due at 10 pm
5/5: Computer work, Computer Project 4 due at 11:30 am (upload to Canvas)

Thursday 5/11 1:30-3:30 Final Exam Some review problems:
Section 1.2: 35, 40
Section 1.3: 1, 23, 24, 25 (use Computer Project 1 to generate the slope fields)
Section 1.4: 1-28, 41, 43, 68, 69
Section 1.5: 1-25, 29, 31, 33, 34, 39, 40
Section 1.6: 31-42
Section 2.1: 9, 25, 39
Section 2.2: 1-12, 22
Section 2.3: 2, 4
Section 2.4: 1-10, 26
Section 3.1: 32 (use W=y1*y2'-y1'*y2), 33-42
Section 3.2: 13-24, 31
Section 3.3: 1-36
Section 3.4: 1-38
Section 3.5: 1-40
Section 4.1: 1-16 and write the function to program into Matlab, 35-37
Section 4.2: 1-20 (use 5/1: worksheet solution code to graph vector fields and solutions for 1-6), 48
Section 4.3: 9-12, 13
Section 5.1: 1-45
Section 5.2: 1-50

Additional Materials

Matlab tutorials

Differential Equations - Math 3113Section 001