# Math 302, Section 1 - Ordinary Differential Equations - Spring 2016

## General Information:

Meeting Time: MWF, 11:00 - 11:50 Jones 301 Ryan Vinroot Office: Jones 130 Office Hours: Wed 1-2 and Thurs 3-5 (also by appointment). All announcements and course information will be on this webpage. In particular, I will not be using Blackboard. Differential Equations, Second Edition, by John Polking, Albert Boggess, and David Arnold 2 Midterms - 20% each, Homework and Quizzes - 25%, Final Exam - 30%, Class Participation - 5%. The grading scale will be based on the standard 10-point scale, as follows: A: 93-100, A-: 90-92, B+: 87-89, B: 83-86, B-: 80-82, C+: 77-79, C: 73-76, C-: 70-72, D+: 67-69, D: 63-66, D-: 60-62, F: 0-59. It is expected that you attend all lectures, with exceptions minimized. It is greatly appreciated when you are on time. Please do your best to stay awake and attentive during lecture, please do not email or text during lecture, and keep all cell phones/hand held devices/laptops put away during lecture. While it is understandable that you may miss a lecture here and there, or be sleepy in class once in awhile, repeated absences, late arrivals, naps, or general non-attentiveness will negatively affect your class participation score. Any legitimate absence for a test or quiz must be discussed with me (or the Dean of Students office) *prior* to the test or quiz date. Calculators will not be needed or allowed on quizzes or exams. Calculators could potentially be useful on some homework problems, but there is no requirement to buy any particular calculator for this purpose. Online tools will serve you the same (or better). Linear Algebra (Math 211) and Multivariable Calculus (Math 212 or 213).
Course Summary: Differential equations are (systems of) equations involving a function and its derivatives. These are at the heart of essentially all mathematical models, whether they are from physics, population biology, or finance. The main topic of this course are ordinary differential equations, which involve only the derivatives with respect to a single independent variable (as opposed to partial differential equations, where there could be many independent variables). There are some types of differential equations for which a precise solution can be written down through mathematical methods, while other (and most) differential equations cannot be solved directly. For the latter situation, one must use qualitative (or numerical) methods to understand the differential equations. Given all of their variations and applications, the study of differential equations is a huge area of mathematics, and we can only touch on a few topics in this course.

We will begin in Chapters 2 and 3, which after introducing some of the basic ideas (Section 2.1), covers some of the types of differential equations for which we can write down a precise solution (Sec. 2.2, 2.4, and 2.6), and a few examples of models using differential equations (2.3, 2.5, and Chapter 3, although we won't cover all of these). In Sections 2.7 and 2.8, we will discuss a crucial theorem asserting when there is the existence and uniqueness of a solution to a differential equation, and the dependence of the initial conditions.

After these introductory sections, we will focus on Chapter 4, which focuses on second-order differential equations, which occur frequently in models, and which we can often solve using precise methods. After Chapter 4, we will move on to linear systems of differential equations (from Sections 8.4, 8.5, and 9.1-9.4). With the remaining time in the semester, we will learn a few topics about nonlinear systems (Chapter 10) and either the method of Laplace transforms (Chapter 5) or the method of series solutions (Chapter 11), depending on time.

## Dates & Course Announcements:

Midterm and Final Exams:

There will be two midterm exams, one in February/March and one in April (exact dates to be determined later). Both of these exams will be 50 minutes, and will be given during class. The final exam is already scheduled to be on Thurs, May 5, 9 AM-12 Noon.

Exam Calendar (Tentative):

 Exam Date Time/Due Location Midterm 1 Fri, Mar 4 In Class Jones 301 Midterm 2 Fri, Apr 15 In Class Jones 301 Final Exam Thurs, May 5 9 AM-12 Noon Jones 301
• All relevant announcements will be listed here. Check back frequently (don't forget to refresh your browser) for updates.
• Important Dates and Class Holidays:
• Sat, Mar 5 - Sun, Mar 13: NO CLASS (Spring Break)
• Fri, Mar 18: WITHDRAW DEADLINE
• Thurs, May 5, 9 AM - 12 Noon: FINAL EXAM
• (1/20) My office hours during the first short week of class are as follows: Wed Jan 20: 1-2 and 4-5, Thurs Jan 21: 2-3, Fri Jan 22: 2-3.
• (1/20) Between our first and second meetings of class, you should read Sections 1.1 and 2.1 in the book (Sections 1.2 and 1.3 also, if you want to review a bit of Calculus).
• (1/21) I have to shift (but extend) my office hours today (Thurs, Jan 21). They will be 2:30-4.
• (1/25) Due to class being cancelled on Mon, Jan 25, HW 1 will now be due on Mon, Feb 1.
• (1/25) My office hours today, Mon, Jan 25, will be 2:30-4.
• (1/27) My office hours for the rest of this week are: Wed, Jan 27 (today), 1-2, and Thurs, Jan 28, 3-5.
• (2/1) My regular weekly office hours will be Wed 1-2 and Thurs 3-5, and I will have an extra office hour either on Fridays (if HW is due on Mon) or on Mondays (if HW is due on Fri).
• (2/8) Quiz 1 is scheduled for next Mon, Feb 15. It will cover exact differential equations, and will be at the *beginning* of class, for about 15 min.
• (2/10) I have to shift my office hours to 3:30-4:30 today (Wed), instead of 1-2. I apologize for any inconvenience. I will have my normal 3-5 office hours on this Thurs.
• (2/19) Midterm 1 will be on Fri, Mar 4, in class. It will cover the material through Homework 4. If you will already be out of town by class on Fri, Mar 4 (due to necessary travel), please let me know as soon as possible, and we can work out a time for you to take the midterm on Thurs, Mar 3.
• (2/22) I will have an extra office hour today (Mon, Feb 22), 1-2.
• (3/4) It was just pointed out to me that I had a typo in the last equation line of the solutions to Quiz 1. There was a cos that should have been a sin. It has been fixed.
• (3/14) Other than my normal office hours this week, I will also have open-door office hours tomorrow, Tues Mar 15, from 10:30 to 2:30.
• (3/16) There was a typo in Problem 2 of the handout problems of HW5. In the angle-sum formula for cosine, I mistakenly had a cos instead of a sin in the second term. This error has been fixed, and thank you to those of you who pointed this out.
• (3/23) Quiz 2 will be on Wed, Mar 30, and will cover the method of undetermined coefficients (Sec. 4.5).
• (3/28) I will have extra office hours tomorrow, Tues Mar 29, 12:30-3:00.
• (4/4) Midterm 2 will be on Fri, Apr 15, in class. The material covered is exactly that material covered in the Midterm 2 review problems listed in the HW below. Please note that HW 8, covering Section 9.2, is due on Mon, Apr 11.
• (4/11) I will have extra office hours today, Mon Apr 11, 1-2, and tomorrow, Tues Apr 12, 10-12. I will also have my usual office hours on Wed (1-2) and Thurs (3-5).
• (4/11) In the review problems, Sec. 4.3 should be the first 2 problems listed, *not* Section 4.4. Section 4.4 is not covered on Midterm 2.
• (4/18) The last HW of the semester has been posted, and is due next Mon, Apr 18. The last quiz, Quiz 3, will also be next Mon, Apr 18, and will cover nullclines and equilibrium points (from Sec. 8.3), and the phase plane for linear systems (Sec. 9.3).
• (4/20) My office hours today will be shifted, but extended, 2-3:30. My office hours on Thurs, Apr 21, will be 10-11:30 in addition to the regular 3-5.
• (4/27) My office hours this week are as follows: Today (Wed, Apr 27) 4-5, and tomorrow (Thurs, Apr 28) 10-11 and 3-5.
• (4/28) My office hours during the first week of exams, leading up to our final exam (Thurs, May 5, 9 AM, Jones 301), are as follows:
Mon, May 2: 12:30-4
Tues, May 3: 11-2 and 3-5
Wed, May 4: 10-2 and 3-5

## Homework & Quizzes:

Homework problems and quizzes will be a very important part of the course, and there will be homework assigned most weeks. Completion of all homework problems is required, and your grade on a homework assignment will be based on completeness, as well as on the details of the solutions of the problems graded. Solutions should be written carefully and neatly, with attention paid to the completeness and clarity of the steps of your solution. You may work with other students when you are figuring out how to do homework problems. However, you should be alone when you write up these solutions. That is, working with other students is only allowed when discussing the problems, but not when you are writing the solutions themselves. You should not, under any circumstances, attempt to look up solutions or hints to problems online. I will consider this plagiarism, an honor offense. You are always welcome to come to my office hours or to email me if you need any hints or help on homework problems.

Homework is due at the beginning of class on the due date of the assignment. Homework turned in by 5 PM on the due date, but after the start of class, will be allowed once without penalty, and after once will be marked of 10%. Homework turned in after 5 PM the due date will be marked off 20% for each day late. Any homework turned in late can be turned in on my office door, and please write down the date and time you turned in the work on your paper. If there are serious reasons for you not getting homework in on time (severe illness, injury, or family issues, for example), you should go through the Dean of Students office so that they can let me know. Please feel free to ask me about this policy if it is not clear.

Homework (and Quiz, see below) scores will each be out of 50 points. Some of the assigned problems will be scored in detail, others for completeness. Your lowest HW or Quiz score will be dropped at the end of the semester.

 Assignment Problems Due Date 1 2.1 #24, 2.2 #6, 10, 14, 16, 18, 20 3.1 #2, 10, 12 Mon, Feb 1 2 2.3 #10, 2.4 #6, 8, 12, 16, 18, 22, 25, 32 2.5 #12 Mon, Feb 8 3 2.6 #10, 14, 20, 22, 26 2.7 #4, 6, 14, 22, 2.8 #16 Fri, Feb 19 4 2.9 #20, 22, 24, 4.1 #14, 16 4.3 #4, 6, 18, 22, 32 Fri, Feb 26 Midterm 1 Review 2.2 #9, 11, 13, 15, 17 2.4 #5, 7, 11, 15, 21, 33 2.6 #11, 13, 17, 19, 21, 23 2.7 #3, 5, 7, 9, 27, 2.8 #17 2.9 #7, 9, 17, 19, 4.1 #13, 15 4.3 #3, 7, 17, 19, 25, 35 Not Due 5 4.3 #10, 16, 34 4.4 #4, 8, 14, 16 The problems on this handout. Mon, Mar 21 6 4.5 #2, 8, 14, 18, 26, 38 4.6 #6, 12, 14, 4.7 #10 Mon, Mar 28 7 8.1 #8, 16, 8.4 #8, 16, 20 8.5 #8, 10, 9.1 #4, 6, 8 Mon, Apr 4 8 9.2 #4, 6, 10, 14, 16, 18, 22, 30, 32, 46 Mon, Apr 11 Midterm 2 Review 4.3 #11, 15, and these problems. 4.5 #1, 7, 19, 21, 25, 27, 39 4.6 #7, 9, 8.1 #11, 13 8.4 #3, 5, 9, 11, 15 8.5 #3, 5, 9, 17, 9.1 #3, 5, 7 9.2 #41, 43, 45, 47, 51, 53 Not Due 9 8.2 #14, 16, 8.3 #2, 6 9.3 #10, 12, 14, 18, 20, 22 Mon, Apr 25 Final Review (to be added to) 10.1 #1, 3, 5, 7, 9.4 #1, 3, 5, 7, 9 9.3 #1, 11, 13, 17, 19, 21, 23 8.3 #1, 3, 5, 9.1 #1, 17, 21, 23 9.2 #17, 19, 21, 29, 31, 33, 46, 48, 8.1 #3, 9, 148.5 #7, 23, 25, 8.4 #4, 6, 7, 16, 4.6 #2, 114.5 #3, 5, 23, 24, 37, 4.3 #27, 29, 31, 33 4.1 #3, 5, 7, 26, 27, 2.9 #13, 15, 16, 18 2.7 #1, 2, 8, 10, 29, 2.6 #9, 12, 15, 16, 25 2.4 #3, 4, 13, 14, 2.2 #3, 5, 7, 19 Not Due

Quizzes: There will be 3 in-class quizzes during the semester, each 15-20 min in length, and each will count the same weight as a homework score. Quizzes will be announced the week before they are given, along with what material they will cover. Quizzes will typically be given at the beginning of class. There will be no make-up quizzes, unless your absence is discussed with me prior to the quiz, or there is a serious issue which is reported through the Dean of Students. The quiz solutions will be posted below throughout the semester, following each quiz:
• Quiz 1 solutions.
• Quiz 2 solutions.
• Quiz 3 solutions.