General Information:
Meeting Time: | MWF, 11:00 - 11:50 |
Location: | Jones 301
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Instructor: | Ryan Vinroot
Office: Jones 130
Office Hours: Wed 1-2 and Thurs 3-5 (also by appointment).
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Announcements: | All announcements and course information will be on
this webpage. In particular, I will not be using Blackboard.
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Textbook: | Differential Equations, Second Edition, by
John Polking, Albert Boggess, and David Arnold |
Grade Breakdown: | 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. |
Attendance & Lecture Policy: |
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.
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Calculator Policy: |
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). |
Prerequisites: | Linear Algebra (Math 211) and Multivariable
Calculus (Math 212 or 213). |
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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
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Midterm 1 |
Fri, Mar 4 |
In Class |
Jones 301
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Midterm 2 |
Fri, Apr 15 |
In Class |
Jones 301
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Final Exam |
Thurs, May 5 |
9 AM-12 Noon |
Jones 301
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- All relevant announcements will be listed here. Check back frequently (don't forget
to refresh your browser) for updates.
- Important Dates and Class Holidays:
- Fri, Jan 29: ADD/DROP DEADLINE
- 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
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Mon, Feb 1 |
2 | 2.3 #10, 2.4 #6, 8, 12, 16, 18, 22, 25, 32 2.5 #12
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Mon, Feb 8 |
3 | 2.6 #10, 14, 20, 22, 26 2.7 #4, 6, 14, 22, 2.8 #16
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Fri, Feb 19 |
4 | 2.9 #20, 22, 24, 4.1 #14, 16 4.3 #4, 6, 18, 22, 32
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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
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Not Due |
5 | 4.3 #10, 16, 34 4.4 #4, 8, 14, 16 The problems
on this handout.
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Mon, Mar 21 |
6 | 4.5 #2, 8, 14, 18, 26, 38 4.6 #6, 12, 14, 4.7 #10
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Mon, Mar 28 |
7 | 8.1 #8, 16, 8.4 #8, 16, 20 8.5 #8, 10, 9.1 #4, 6, 8
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Mon, Apr 4 |
8 | 9.2 #4, 6, 10, 14, 16, 18, 22, 30, 32, 46
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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
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Not Due |
9 | 8.2 #14, 16, 8.3 #2, 6 9.3 #10, 12, 14, 18, 20, 22
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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, 14 8.5 #7, 23, 25, 8.4 #4, 6, 7, 16, 4.6 #2, 11 4.5 #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
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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.
Resources:
- A few homework problems will ask for slope fields or other
computer-generated numerical or quantitative solutions. You may use any
package you like to generate images of these things, and print them out.
Free packages can be found on the web, here are a few that I like:
Nathan Grigg's slope field generator
Desmos slope field generator
WolframAlpha (for general
computation)
Vector
Field generator (for the phase plane of two equation systems).
Desmos graphing tool.
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