Math 302, Sections 2/4 - Ordinary Differential Equations - Fall 2020

General Information:

Meeting Time: MWF, 11:00 - 11:50 Zoom/Jones 301 Ryan Vinroot Office Hours: On Zoom, Tues. 10:30-11:30, Wed. 2:30-3:30, Thurs 1:30-2:30 (or by appt) 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 Midterm - 30%, Homework and Quizzes - 35%, 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 (whether on Zoom or in the classroom), 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).

Dates & Course Announcements:

Midterm and Final Exams:

There will be one midterm exam, some time in mid-October (the exact date and details to be determined later). The final exam is already scheduled to be on Thurs, Nov 19, 9 AM-12 Noon.

• All relevant announcements will be listed here. Check back frequently (don't forget to refresh your browser) for updates.
• Important Dates and Class Holidays:
• Mon, Oct 12: WITHDRAW DEADLINE
• Thurs, Nov 19, 9 AM - 12 Noon: FINAL EXAM
• (8/19) My regular weekly office hours will be determined after the add/drop period has ended. I will have a Zoom office hour this week, Thurs Aug 20, 1-2 pm. I will email the Zoom link to the class. You can always email me questions or to request a Zoom meeting as well.
• (9/7) For next Monday, there is not a HW set due, but rather a quiz will be due (see Blackboard for details). Below I have listed problems from Section 2.6 to do in preparation for the quiz, which will cover Exact Differential Equations.
• (9/16) The solutions to Quiz 1 have been posted below. I will plan on having it graded by Friday. Also remember that Friday class is entirely on Zoom.

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 to me as a pdf through email. If there are serious reasons for you not getting homework in on time (severe illness, injury, or family issues, for example), you should contact 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. For each HW assignment, there will be some problems to turn in, and others to do but not turn in. Your lowest HW or Quiz score will be dropped at the end of the semester.

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 Assignment Problems Due Date 1 2.1 (pg. 26) #24, 2.2 (pg. 35) #8, 10, 16, 18 3.1 (pgs. 115-116) #10, 12 Mon, Aug 31 2 2.3 #10, 2.4 #6, 8, 14, 16, 18, 30 2.5 #12 Mon, Sept 7 Quiz prep 2.6 #10, 13, 14, 20, 23, 26, 29 NOT DUE 3 2.7 #4, 6, 14, 22 2.8 #18, 2.9 #20, 22, 24 Mon, Sept 21 4 4.1 #26, 4.3 #4, 6, 16, 18, 26, 28, 32 Mon, Sept 28 5 4.4 #8, 12 4.5 #18, 20, 22 The problems on this handout. Mon, Oct 5 Midterm Review 2.2 #11, 13, 15, 17 2.4 #7, 11, 21, 33 2.6 #11, 13, 19, 23 2.7 #3, 5, 7, 9, 27, 2.8 #17 2.9 #7, 9, 17, 19, 4.1 #17, 19 4.3 #7, 15, 19, 25, 35 These problems (solutions are on pg. 2 of the pdf) 4.5 #1, 7, 19, 25, 27, 31 Not Due 6 8.1 #8, 16, 8.4 #16, 20 8.5 #8, 10, 9.1 #4, 8 Mon, Oct 19 7 9.2 #2, 16, 20, 30, 42, 46, 48, 56 Mon, Oct 26 8 8.2 #26, 8.3 #2, 6, 8 9.3 #10, 12, 18 Mon, Nov 2 Quiz prep 9.4 #1-6, 10.1 #1-4, 9-12 NOT DUE Extra Credit (Optional) 9.4 #14, 15, 16, and Describe the phase plane solutions for any scalar matrix A Fri, Nov 13 by 5pm (optional) Final Review 10.1 #5-8 9.4 #7-12 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, 8.1 #3, 9, 148.5 #7, 23, 25, 8.4 #4, 6, 7 4.5 #3, 5, 23, 24, 37, 4.3 #27, 29, 31, 33 4.1 #3, 5, 7, 4.2 #1, 3, 5, 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 several 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.

Student Accessibility Services:

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