Math 2280 - Introduction to Differential Equations
University of Utah
Fall, 2013
Contact Information
Instructor - Patrick Dylan Zwick.
Telephone - 801-651-8768 (Cell).
Email - zwick@math.utah.edu .
Office - JWB Math Building Room 129.
Office Hours - 3:00 PM - 4:00 PM Mondays, 8:35 AM - 9:35 AM Thursdays
Class Location - Alfred Emery Building (AEB) Room 350 Mondays, Wednesdays, and Fridays. Behavioral Sciences Building (BEH S) Room 106 Thursdays.
Class Time - 8:35 AM - 9:25 AM Mondays, Tuesdays, Wednesdays, and Fridays.
All grades for the class are posted on canvas
Headline Announcements
- THANK YOU - Thank you all for what I hope was a good semester! Good luck in all you do. -Dylan
- FINAL GRADES POSTED - The final exam has been graded, as have all homework assignments, and all grades are available on canvas. The average score on the final exam was 74.26, with a median of 74 and a standard deviation of 15.96. The final exam and its solutions are posted below. The final grades for the class are also now available on canvas. The final grades broke down as follows:
A: 10
A-: 1
B+: 4
B: 6
B-: 2
C+: 2
C: 5
C-: 2
D+: 0
D: 1
D-: 0
E: 2
While your final grades are posted on canvas, I will not be posting your final grades to the university system until 5:00 PM this Monday, December 30th. I'll be in my office from 2:00 PM until 4:00 PM on Monday if you'd like to come by and pick up your final exam or any old exams or homework, and/or if you'd like to discuss your final grade. After this Monday you can pick up your old homework or exams from me at any time during next week. After that, you'll be able to pick up your final exam from the main office in the math building, and I'll be throwing out anything else that is unclaimed. If you can't come by or if there are any other issues, please send me an email.
Announcements
- December 13th - Today was the final day of class. So, all that remains is the final exam! I'll have office hours on Monday from 2:00 PM until 4:00 PM. I've posted the lecture notes with examples for lecture 47, the review lecture, below. Also, the solutions for assignment 13 are now posted below. Happy studying!
- December 12th - The room for tonight's review session has been reserved! The review session will be from 7:30 PM until 9:00 PM in LCB 215. Also, I've posted lecture 47, a review "lecture", below. It's actually just a sequence of three problems that you might want to work through. I'd be happy to go over any of them either tonight or tomorrow. I'll post the solutions to these problems, as lectures notes with examples, after class tomorrow. See you tonight!
- December 11th - The lecture notes with examples for lecture 46 are now posted below, along with assignment 15, the second extra credit assignment. Please note I've decided to make assignment 14 an extra credit assignment as well.
- December 9th - The lecture notes with examples for today's lecture, lecture 45, are now posted below, along with the lecture notes for tomorrow's lecture, lecture 46. Also posted below in assignment 14, our last assignment that is not extra credit. It will be due at the exam on Tuesday, December 17th.
- December 8th - The lecture notes with examples for lecture 44 are now posted below, along with the lecture notes for tomorrow's lecture, lecture 45. Please remember that assignment 13 is due tomorrow. See you then!
- December 4th - The solutions for assignment 12 are now posted below, as are the lecture notes with examples for lecture 43, and the lecture notes for tomorrow's lecture, lecture 44. See you tomorrow morning!
- December 3rd - Exam 3 has been graded, and the grades are now posted on canvas. The average on the exam was 76.67, the median was 77, and the standard deviation was 13.88. Remember you can drop an exam! The exam and its solutions are now posted below. Also posted below are the lecture notes with examples for lecture 42, and tomorrow's lecture, lecture 43.
- December 2nd - Assignment 11 has been graded, and your grades are now posted on canvas. I'll hand back the assignment tomorrow in class. Assignment 13 is now posted below, and is due on Monday, December 9th. The lecture notes with examples for lecture 41 are now posted below, as are the lecture notes for lecture 42. There have been some questions about the schedule for the rest of the semester. There will be one more required assignment, which will cover sections 9.5 through 9.7 and be due at the final exam. There will also be an extra credit assignment covering sections 6.1 through 6.3, which you can also hand in at the final exam. Note that we're now about a day behind schedule, so we'll be finishing section 9.6 tomorrow, and then covering section 9.7 on Wednesday. See you tomorrow in the behavioral sciences building!
- November 26th - Assignment 10 has been graded, and your grades are now posted on canvas. I'll hand back the assignment in class tomorrow. Please remember that exam 3 is tomorrow during class. The solutions to assignment 11 are now posted below, as is lecture 40 with examples. See you tomorrow!
- November 23rd - Today we went over the final example problem from lecture 39 again, and began lecture 40. We didn't get all that far in lecture 40, as class was cut short by a fire. Yes, that's right, it was an actual fire caused by an oven on the first floor. Everybody is fine. Also, assignment 12 is now posted below. It is due on Monday, December 2nd.
- November 21st - I did a godawful job of going through the example problem at the end of class yesterday, and so I'm going to take a mulligan. Tomorrow, at the start of class, I'll go through it again. I've modified the schedule to take into account our special election day lecture, and also to give us a little more time for section 9.5. The lecture notes with examples for lecture 39 are now posted below, as are the lecture notes for lecture 41. Please also note the headline announcement above regarding exam 3 on Wednesday, November 27th.
- November 19th - The lecture notes with examples for today's lecture, lecture 38, are now posted below. Also posted below are solutions for assignment 10. Also, I forgot to hand back assignment 9 in class today. Sorry. I'll do that tomorrow. Remind me if I forget!
- November 18th - The lecture notes with examples for today's lecture, lecture 37, are now posted below. Also posted below are the lecture notes for lectures 39 and 40. See you tomorrow in the other classroom.
- November 15th - The lecture notes with examples up through today's lecture, lecture 36, are now posted below. The lecture notes for lectures 37 and 38 are now posted below as well, along with assignment 11, which is due on Friday, November 22nd. Have a good weekend!
- November 14th - The lecture notes with examples up through lecture 35 are now posted below, along with tomorrow's lecture, lecture 36. Please remember that assignment 10 is due in class tomorrow.
- November 11th - The lecture notes with examples for lectures 32 and 33 are now posted below, along with the lecture notes for tomorrow's lecture, lecture 34. Also posted below are the solutions to assignment 9. Assignment 10 is posted below as well, and has been posted since last Friday.
- November 7th - The lecture notes with examples for lecture 31 are now posted below, along with the lecture notes for tomorrow's lecture, lecture 32. Assignments 7 and 8 have now been graded, and the grades are posted on canvas. I'll hand back the assignments in class tomorrow. Please remember the assignment 9 is due in class tomorrow. See you then!
- November 5th - Remember, remember... Today's lecture was a "for fun" lecture on the mathematics of voting. Unfortunately, I didn't have enough time to get into a proof of Arrow's theorem, but hopefully you still got something useful out of it. You can pick up the lecture notes for the lecture here. Tomorrow we'll cover lecture 31, and finish up chapter 7.
- November 4th - The lecture notes with examples for today's lecture, lecture 30, are now posted below. The solutions for assignment 8 are now posted below as well. I'll see you tomorrow in the behavioral sciences building. We might be having a special election day lecture!
- November 3rd - Exam 2 and its solutions are now posted below. Please note that there were two errors in the exam. The first error didn't affect the solutions, but the function cos(2x) in problem 1 should have been cos(2t), and as announced in class during the exam the unknown function in problem 2 should have been y, not x. Both of these mistakes have been corrected in the exam posted below. Also, the next two lectures, lectures 30 and 31, are now posted below. See you tomorrow morning!
- November 1st - Thank you to everybody who participated in the nerdy shirt contest on October 30th! The second exam has now been graded, and your grades are all posted on canvas. Scores were overall pretty good! The class average was 82.65, with a median of 82 and a standard deviation of 12.73. Assignment 9 is posted below, and is due next Friday. Also, the lecture notes with examples for lectures 28 and 29 are now posted below. Have a nice weekend!
- October 29th - The lecture notes with examples for today's lecture, lecture 27, are posted below, along with the lecture notes for lecture 29. Also, in honor of Halloween tomorrow in class we'll be having a nerdy shirt contest! So, please wear the nerdiest shirt you've got. Everybody who wears a nerdy shirt will receive 3 point of extra credit on the exam, and we'll have a contest for the nerdiest shirt, with first and second place receiving 5 points and 4 points of extra credit, respectively.
- October 28th - The lecture notes with examples for today's lecture, lecture 26, are now posted below, along with the lecture notes for lectures 27 and 28. The solutions to assignment 7 are now posted below as well.
- October 27th - I've decided in a change of schedule for the class. Instead of covering chapter 6 this week, I've moved chapter 6 back to the end of the course. So, we'll be starting chapter 7 tomorrow. The lecture notes for section 7.1 are now posted below. The syllabus and schedule on this website have been adjusted to reflect this change.
- October 25th - The second exam was given in class today. I'll try to get the exam graded over the weekend. Also, sorry I forgot to bring graded assignments 5 and 6 to class this morning. I'll bring them on Monday. Assignment 8 is now posted below. It is due on Friday, November 1st.
- October 23rd - Assignments 5 and 6 have been graded, and the grades are now posted on canvas. I'll hand back the assignments in class on Friday. If you'd like to pick up the assignments tomorrow during office hours, you may. I'll be having office hours at my regular time tomorrow, and there will be a review for exam 2 tomorrow evening from 7:00 PM until 8:00 PM. The room is not yet determined, but when it is I'll send out an email and post it on this website. Oh, and don't forget our second exam is this Friday in class.
- October 15th - The solutions for assignment 6 are now posted below. I hope everybody is enjoying the break!
- October 11th - The lecture notes with examples for lectures 21, 22, and 23 are now posted below, along with the lecture notes for lectures 24 and 25. Please note that our second exam is on Friday, October 25th. The exam will cover sections 3.1 through 3.8, sections 4.1 and 4.2, and sections 5.1, 5.2, and 5.4. Also, assignment 7 is now posted below. Please remember that next week is fall break, so there will be no classes. Enjoy the break! I'll see you when we get back.
- October 7th - The lecture notes for lectures 22 and 23 are now posted below, along with the lecture notes with examples for today's lecture, lecture 20. Also posted below are the solutions to assignment 5. Assignment 4 has been graded, and your grades are now posted on canvas. I'll hand back assignment 4 in class tomorrow. See you then!
- October 4th - The lecture notes and lecture notes with examples for today's lecture, lecture 19, are now posted below. Sorry to be late in posting! Also posted below are the lecture notes with examples for lecture 18, and the lecture notes for lectures 20 and 21. Assignment 6 is also posted below. It is due a week from today on Friday, October 11th. Also, thank you to everybody who took the time to offer mid-semester course feedback. I appreciate it! Have a nice weekend.
- October 1st - The lecture notes with examples for today's lecture, lecture 17, are now posted below. Don't forget to fill out the mid-semester evaluation form! See you tomorrow.
- September 30th - The lecture notes with examples for lecture 16 are now posted below, along with the lecture notes for lectures 17 and 18. Also posted below are the solutions to assignment 4. Don't forget to fill out the mid-semester course feedback! Also, assignment 3 has been graded, and your grades are now posted on canvas. I'll hand back the assignment in class tomorrow. See you then in the behavioral sciences building.
- September 24th - The lecture notes with examples for lectures 13 and 14 are now posted below, along with the lecture notes for lectures 15 and 16. Also posted below are assignment 5, which is due on Friday, October 4th, and the solutions to assignment 3. I'll be having office hours tomorrow at the usual time, so if you've got questions please stop by.
- September 23rd - The lecture notes with examples for lectures 11 and 12 are now posted below. Assignment 2 has been graded, and the grades are posted on canvas. I'll hand back assignment 2 in class tomorrow. See you then!
- September 22nd - Exam 1 and its solutions are now posted below. The exam has been graded, and the grades are posted on canvas. I'll hand back the exam in class tomorrow. Most people did very well, so, good job! The maximum possible score was 100, the average score was 88.19, the median was 90, and the standard deviation was 9.4. See you tomorrow!
- September 19th - The lecture notes for lecture 14 are posted below. I've decided to shorten assignment 3, so now assignment 3 only covers sections 2.3 and 2.4. It is still due in class on Monday, September 23rd. Assignment 4 is now posted below. Assignment 4 covers sections 3.1, 3.2, and 3.3, and will be due in class on Friday, September 27th. Please remember that our first exam is in class tomorrow! See you then.
- September 17th - The lecture notes for lectures 12 and 13 are now posted below, along with the solutions to assignment 2. Assignment 1 has been graded, and the grades are posted on canvas. I'll hand back the assignment in class tomorrow. Please remember that tomorrow is a review session, so I won't be lecturing, I'll just be answering questions. Your job is to bring questions! The review session is, of course, a review for our first exam, which will be this Friday during class. Also, please note that I've moved the due date for assignment 3 back from this Friday, September 20th to Monday, September 23rd. See you in class tomorrow morning!
- September 16th - The lecture notes with examples for lecture 10 are posted below, along with the lecture notes for tomorrow's lecture, lecture 11.
- September 15th - The lecture notes with examples for lecture 9 are posted below. Please remember that assignment 2 is due in class tomorrow. See you then!
- September 11th - The lecture notes with examples for lectures 7 and 8 are posted below, along with the lecture notes for lectures 9 and 10. Also, I've updated the lecture notes for lectures 6 and 7 so they've got some notes about the assigned homework problems. Also, assignment 3 is now posted below, and is due on Friday, September 20th. Finally, please note that the due date for assignment 2 has bee pushed back, and the assignment is now due on Monday, September 16th.
- September 9th - The lecture notes with examples for lecture 6, and the lecture notes for lecture 7, are now posted below. Also, the solutions to the first assignment are posted below as well.
- September 8th - The lecture notes with examples for lectures 4 and 5 are now posted below, along with the lecture notes for lecture 6. See you tomorrow morning!
- September 3rd - I'm back! Class has now resumed on its usual schedule. Posted below are the lecture notes with examples for lectures 2 and 3, along with the lecture notes for Friday's lecture, lecture 5. I've also posted assignment 2 below, but don't worry, It's not due until Friday, September 13th. See you in AEB 350 tomorrow morning!
- August 26th - Our first day of class was today, so, welcome everybody! Lectures 3 and 4 for next week are now posted below, as are the lecture notes with examples for today's lecture, lecture 1. Please note that assignment 1 is also posted below, and is due on Friday of next week. I'll see you all tomorrow morning in room 106 of the Behavioral Sciences Building!
- August 24th - The website for the class is, obviously, now up. Posted below you will find the syllabus, the class schedule, the first four days of lecture notes, and the first two assignments. Enjoy!
Administrative
Syllabus
Schedule
Note: The final exam for the class will be on Tuesday, December 17th from 8:00 AM to 10:00 AM.
MIT offers a similar course (Math 18.03) and the course is available on their open courseware system. There are lecture notes, assignments with solutions, and video lectures available from the website. It's pretty nice! You can check it out here. The video lectures are available here
Lecture Notes
Lecture 1 Lecture 1 with Examples
Lecture 2 Lecture 2 with Examples
Lecture 3 Lecture 3 with Examples
Lecture 4 Lecture 4 with Examples
Lecture 5 Lecture 5 with Examples
Lecture 6 Lecture 6 with Examples
Lecture 7 Lecture 7 with Examples
Lecture 8 Lecture 8 with Examples
Lecture 9 Lecture 9 with Examples
Lecture 10 Lecture 10 with Examples
Lecture 11 Lecture 11 with Examples
Lecture 12 Lecture 12 with Examples
Lecture 13 Lecture 13 with Examples
Lecture 14 Lecture 14 with Examples
Lecture 15 Lecture 15 with Examples
Lecture 16 Lecture 16 with Examples
Lecture 17 Lecture 17 with Examples
Lecture 18 Lecture 18 with Examples
Lecture 19 Lecture 19 with Examples
Lecture 20 Lecture 20 with Examples
Lecture 21 Lecture 21 with Examples
Lecture 22 Lecture 22 with Examples
Lecture 23 Lecture 23 with Examples
Lecture 24 Lecture 24 with Examples
Lecture 25 Lecture 25 with Examples
Lecture 26 Lecture 26 with Examples
Lecture 27 Lecture 27 with Examples
Lecture 28 Lecture 28 with Examples
Lecture 29 Lecture 29 with Examples
Lecture 30 Lecture 30 with Examples
Lecture 31 Lecture 31 with Examples
Lecture 32 Lecture 32 with Examples
Lecture 33 Lecture 33 with Examples
Lecture 34 Lecture 34 with Examples
Lecture 35 Lecture 35 with Examples
Lecture 36 Lecture 36 with Examples
Lecture 37 Lecture 37 with Examples
Lecture 38 lecture 38 with Examples
Lecture 39 Lecture 39 with Examples
Lecture 40 Lecture 40 with Examples
Lecture 41 Lecture 41 with Examples
Lecture 42 Lecture 42 with Examples
Lecture 43 Lecture 43 with Examples
Lecture 44 Lecture 44 with Examples
Lecture 45 Lecture 45 with Examples
Lecture 46 Lecture 46 with Examples
Lecture 47 Lecture 47 with Examples
Other
Assignments
Assignment 1
Section 1.1 - 1, 12, 15, 20, 45
Section 1.2 - 1, 6, 11, 15, 27, 35, 43
Section 1.3 - 1, 6, 9, 11, 15, 21, 29
Section 1.4 - 1, 3, 17, 19, 31, 35, 53, 68
Assignment 1
Due Friday, September 6th
Assignment 2
Section 1.5 - 1, 15, 21, 29, 38, 42
Section 1.6 - 1, 3, 13, 16, 22, 26, 31, 36, 56
Section 2.1 - 1, 8, 11, 16, 29
Section 2.2 - 1, 10, 21, 23, 24
Assignment 2
Due Monday, September 16th
Assignment 3
Section 2.3 - 1, 2, 4, 10, 24
Section 2.4 - 1, 5, 9, 26, 30
Assignment 3
Due Monday, September 23rd
Assignment 4
Section 3.1 - 1, 16, 18, 24, 30
Section 3.2 - 1, 10, 16, 24, 31
Section 3.3 - 1, 10, 25, 30, 43
Assignment 4
Due Friday, September 27th
Assignment 5
Section 3.4 - 1, 5, 18, 21
Section 3.5 - 1, 11, 23, 28, 35, 47, 56
Section 3.6 - 1, 2, 9, 17, 24
Assignment 5
Due Friday, October 4th
Assignment 6
Section 3.7 - 1, 5, 10, 17, 19
Section 3.8 - 1, 3, 5, 8, 13
Section 4.1 - 1, 2, 13, 15, 22
Section 4.2 - 1, 10, 19, 28
Assignment 6
Due Friday, October 11th
Assignment 7
Section 5.1 - 1, 7, 15, 21, 27
Section 5.2 - 1, 9, 15, 21, 39
Section 5.4 - 1, 8, 15, 25, 33
Assignment 7
Due Friday, October 25th
Assignment 8
Section 5.5 - 1, 7, 9, 18, 24
Section 5.6 - 1, 6, 10, 17, 19
Assignment 8
Due Friday, November 1st
Assignment 9
Section 7.1 - 1, 6, 20, 30, 36
Section 7.2 - 1, 4, 15, 20, 29
Section 7.3 - 3, 8, 19, 24, 30, 33
Assignment 9
Due Friday, November 8th
Assignment 10
Section 7.4 - 1, 5, 10, 19, 31
Section 7.5 - 1, 6, 15, 21, 26
Section 7.6 - 1, 6, 11, 14, 15
Assignment 10
Due Friday, November 15th
Assignment 11
Section 8.1 - 2, 8, 13, 21, 25
Section 8.2 - 1, 7, 14, 17, 32
Section 8.3 - 1, 8, 15, 18, 24
Assignment 11
Due Friday, November 22nd
Please note there is an error in the textbook (but not in the .pdf file for this assignment) on problem 8.1.25. The initial conditions should be y(0) = 0 and y'(0) = 1, not y(0) = 0 and y(1) = 1.
Assignment 12
Section 8.4 - 1, 6, 8, 9, 14
Section 8.5 - 1, 5, 6, 13, 16
Assignment 12
Due Monday, December 2nd
Assignment 13
Section 9.1 - 1, 8, 11, 13, 21
Section 9.2 - 1, 9, 15, 17, 20
Section 9.3 - 1, 5, 8, 13, 20
Assignment 13
Due Monday, December 9th
Assignment 14
Section 9.5 - 1, 3, 5, 7, 9
Section 9.6 - 1, 3, 5, 7, 14
Section 9.7 - 1, 2, 3, 4
Assignment 14
Due Tuesday, December 17th
I've decided to make this an extra credit assignment. However, you will still be expected to know this material for the final exam, so I'd highly recommend doing the assignment!
Assignment 15
Section 6.1 - 1, 5, 10, 18, 30
Section 6.2 - 1, 5, 8, 15, 31
Section 6.3 - 3, 4, 5, 6, 7
Assignment 15
Due Tuesday, December 17th
This assignment is also extra credit. You don't need to know the material for the final exam, but there may be an extra credit problem on the final exam relating to the material.
Exams
Exam 1 Exam 1 Solutions
Exam 2 Exam 2 Solutions
Exam 3 Exam 3 Solutions
Final Final Solutions
Exams from Previous Years
These are the exams, along with solutions, from previous times I've taught this class. The exams do not necessarily correspond with the current class schedule, and there may be some sections covered in previous semesters that we will not cover this semester, and vice-versa. With those disclaimers, they might be a helpful study resource, so they're provided below.
Summer 2013
Exam 1 Exam 1 Solutions
Exam 2 Exam 2 Solutions
Exam 3 Exam 3 Solutions
Final Final Solutions
Spring 2013
Practice Exam 1 Practice Exam 1 Solutions
Practice Exam 2 Practice Exam 2 Solutions
Practice Exam 3 Practice Exam 3 Solutions
Practice Exam 4 Practice Exam 4 Solutions
Practice Final Exam Practice Final Exam Solutions
Exam 1 Exam 1 Solutions
Exam 2 Exam 2 Solutions
Exam 3 Exam 3 Solutions
Exam 4 Exam 4 Solutions
Final Final Solutions
Spring 2009
Exam 1 Exam 1 Solutions
Exam 2 Exam 2 Solutions
Exam 3 Exam 3 Solutions
Final Exam Final Exam Solutions
Spring 2008
Exam 1 Exam 1 Solutions
Exam 2 Exam 2 Solutions
Exam 3 Exam 3 Solutions
Final Exam Part 1 Final Exam Part 1 Solutions
Final Exam Part 2 Final Exam Part 2 Solutions
Old Classes
Math 10 Fall, 2013
Math 2280 Summer, 2013
Math 2280 Spring, 2013
Math 15 Spring, 2013
Math 2270 Fall, 2012
Math 2210 Summer, 2012
Math 2210 Summer, 2010
Math 1010 Fall, 2009
Math 1210 Summer, 2009
Math 2280 Spring, 2009
Math 2210 Fall, 2008
Evolutionary Biology and Game Theory Fall, 2008
Math 2210 Summer, 2008
REU on Computational Algebraic Geometry Summer, 2008
Knot Theory Spring, 2008
Math 2280 Spring, 2008
Math 1030 Fall, 2007
Math 2210 Summer, 2007
Talks
Notes for Math Department Talks