Math 2280 - Introduction to Differential Equations
University of Utah
Summer, 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 - 1:00 PM - 2:00 PM; Mondays and Wednesdays
Class Location - Frederick Albert Sutton Building (FASB) Room 250.
Class Time - 10:00 AM - 11:00 AM Monday, Tuesday, Wednesday, and Thursday
All grades for the class are posted on canvas
Headline Announcements
- Review Sessions This Week - There will be a review session for the final on the evening of Tuesday, July 30th from 7:00 PM until 8:30 PM. The review will be in LCB 219, the room in which we've had the other two evening review sessions. This is in addition to the in-class review session on Wednesday, July 31st.
- Textbook On Reserve in Marriott Library - The Marriott library does not have a copy of the fourth edition of our textbook to place on reserve. However, I've had them order a copy, and when it arrives I'll let you know. In the mean time, a copy of the third edition of our textbook is available from the reserve desk at the Marriott library. It should cover pretty much the same material.
Announcements
- August 7th - The final exams have been graded, and the grades are now posted on canvas. The average score on the final was 181.2, the median was 186, and the standard deviation was 21.2. All in all, good job everybody! Grades are also posted for assignments 10, 11, and 12. Assignments 11 and 12 were graded on the basis of completion. So, if you handed in the assignment, you received full credit. Final grades have also been calculated, and are available on canvas. I'll be out of town this weekend, but will be around next week, so you can come by and pick up your final exam, and any old assignments or exams, during that time. If you'd like to discuss your final grade with me, you may do so next week as well. I won't be posting grades to the university system until Friday, August 16th.
- August 1st - The final exam and its solutions are now posted below. The final exam, along with assignments 11 and 12, will be graded, and final grades will be calculated, by the end of next week. I'll of course send out an email to let you know when the grades are up. I won't post grades to the university system until Friday, August 16th. This will give you a week to come by, pick up your exams and old homework assignments, and ask me any questions you have about your final grades.
- July 30th - The lecture notes with examples for lecture 35 are now posted below. Please remember that our final exam is on Thursday!
- July 29th - The lecture notes with examples for lecture 34 are now posted below, as are the lecture notes for tomorrow's lecture, lecture 35. The solutions to assignment 10 are also posted below.
- July 26th - The lecture notes with examples for lecture 33 are now posted below, as are the lecture notes for next Monday's lecture, lecture 34. Assignment 9 has been graded, and the grades are posted on canvas. I'll hand back the assignment in class on Monday. Also, please note that there will be a review session for the final on the evening of Tuesday, July 30th from 7:00 PM until 8:30 PM in LCB 219, the room in which we've had the other two evening review sessions. The is in addition to in-class review session on Wednesday, July 31st. Hope you all have a good weekend. Happy studying!
- July 24th - The lecture notes with examples for lecture 32 are now posted below, along with the lecture notes for tomorrow's lecture, lecture 33. Assignment 12, the extra credit assignment, has now been posted below as well. Hope everybody is having a fun Pioneer day. I'll see you in class tomorrow.
- July 22nd - The lecture notes with examples for lecture 31 is now posted below. Exam 3 has been graded, and the grades are posted on canvas. The average score on the exam was 73.55, the median was 75, and the standard deviation was 15.53. I'll hand back the exams in class tomorrow.
- July 19th - The lecture notes for with examples for lectures 29 and 30 are now posted below, along with the lecture notes for lectures 31 and 32. Also posted below are the solutions to assignment 9, and exam 3 with solutions. I'm grading exam 3 now, and will try to have it graded by the end of the weekend. Have a nice weekend!
- July 16th - The lecture notes with examples for today's lecture, lecture 29, are now posted below. Also posted below are the solutions to assignment 8.
- July 15th - The lecture notes with examples for lectures 27 and 28 are now posted below, along with the lecture notes for lectures 29 and 30. Please note that, like today, tomorrow we'll be in our original classroom, WBB 207. From this Wednesday, July 17th until the end of the class we'll be back in our usual classroom, FASB 250. Please note that our third exam will be this Thursday, July 18th. The exam will cover sections 5.1 through 5.6, along with sections 7.1, 7.2, and 7.3. Finally, as we will not have a review session in class this Wednesday, there will be a review session tomorrow night in LCB 219 from 7:00 PM until 8:30 PM. Please come if you can, and bring any questions you've got.
- July 8th - The lecture notes for lecture 28 are posted below, along with the lecture notes with examples for today's lecture, lecture 27. There was a request in class today that I announce the assigned problems for section 7.3 in class tomorrow. You can find these at the start of lecture 28 below, but I just went ahead and posted assignment 10 below as well. Don't worry, it's not due for a while. Also posted below are the solutions to assignment 7. Finally, assignment 6 has been graded, and the grades are posted on canvas. I'll be returning the assignment in class tomorrow. See you there!
- July 7th - The lecture notes for lectures 26 and 27 are now posted below, along with the lecture notes with examples for lecture 25. Assignment 9 is now posted below as well. It is due on Thursday, July 18th. Our classmate Kurt Fisher has made some very detailed Maple files that explore how we can plot the slopefields and solutions for Exercises 5.2.1, 5.2.9, and 5.2.15. You can find these below. Also, there's a link below to a video lecture by Prof. Arthur Mattuck at MIT that goes into much greater detail than we had time for in class on how to graph solutions to 2x2 first-order systems. Finally, please be aware that on Monday, July 15th and Tuesday, July 16th we'll be back in our original classroom, WBB 207, for those dates. See you tomorrow!
- July 2nd - The second exam has been graded, and the grades are now posted on canvas. The class average was 72.48 our of 100, and the median was 76. The standard deviation was 16.56, and there were two perfect scores. Assignment 5 has also been graded, and the grades are posted on canvas. I'll be handing both back in class tomorrow. Also, exam 2 and its solutions are now posted below. Also posted below are the solutions to assignment 6. The lecture notes with examples for lectures 23 and 24 are posted below, as is assignment 8. Please note that Problem 5.4.33 from the textbook has a typo. The vector v2 should be [0 0 1 i]^T and NOT [9 0 1 i]^T. Wow, that's a lot of stuff posted below. I'll see you tomorrow!
- June 25th - Assignment 4 has been graded, and the grades are now posted on canvas. I'll hand back the assignment in class tomorrow. The lecture notes with examples for today's lecture, lecture 22, are now posted below, as are the lecture notes for next Tuesday's lecture, lecture 24. Please note that on Problem 3.7.5 of assignment 6 there was a typo in the problem that has now been corrected. The version posted below is now correct. Finally, please remember that our second exam is this Thursday. The exam will cover sections 2.4, 3.1 through 3.8, 4.1, and 4.2. You will be alllowed two pages of notes, front and back, and you can use a calculator. Tomorrow's class will be a review session for the exam, so please bring your questions. See you then.
- June 24th - The lecture notes with examples for today's lecture, lecture 21, are now posted below, as are the lecture notes for next Monday's lecture, lecture 23. The solutions to assignment 5 are now posted below as well, along with assignment 7, which is due on Wednesday, July 3rd. Finally, there have been some questions about which sections will be covered on the exam. The second exam, which is this Thursday, will cover section 2.4 (Euler's method), all of chapter 3, and sections 4.1 and 4.2 from the textbook. In particular, sections 5.1 and 5.2, upon which I'll be lecturing this week, will not be on this Thursday's exam.
- June 20th - Much to announce today. First, the lecture notes for next Tuesday's lecture, lecture 22, are now posted below. Also posted below are the lecture notes with examples for today's lecture, lecture 20. Please be aware that originally there was a typo in these lecture notes and it said problem 4.2.30 is assigned. It is not, so you don't have to do it. Kurt Fisher has written some Matlab and Maple code for some of the problems from section 2.4 and 3.1. This code can be found below, and might be interesting/useful to you as you study for the second exam. Speaking of the second exam, it will be one week from today on Thursday, June 27th. It will cover section 2.4, 3.1 through 3.8, 4.1, and 4.2. You'll be allowed two pages of notes, front and back, and can use a calculator. We'll be having a review session during class the day before on Wednesday, June 26th. Also, the mid-semester class reviews are available. There's a link to these in the headline announcements with an explanation. Please fill one out ASAP! Finally, on Monday there will be somebody from the Center for Teaching and Learning Excellence in class to film my lecture. This is for my learning and improvement, but I just wanted to you know why the camera will be there, and there will be somebody watching the lecture who's never been to our class before. I think that's it! Hope you all have a great weekend. I'll see you on Monday.
- June 19th - The lecture notes for lecture 21 are now posted below, along with the lecture notes with examples for today's lecture, lecture 19. Also, the solutions to assignment 4 are now posted below.
- June 18th - The lecture notes for lecture 20 are now posted below, along with the lecture notes with examples for lectures 17 and 18. Also posted below is assignment 6, which will be due on Thursday, June 27th, the day of the second exam.
- June 17th - The lecture notes for lectures 18 and 19 are now posted below. Also, the assignments 2 and 3 have been graded, and the grades are available on canvas. The solutions to assignments 2 and 3 are posted below.
- June 11th - The lecture notes with examples for lectures 15 and 16 are now posted below, along with the lecture notes for next Monday's lecture, lecture 17. Also, the solutions for assignment 2 are now posted below. Have a nice break! See you next Monday.
- June 9th - The lectures notes for this week's lectures, lectures 15 and 16, are now posted below, as is assignment 5. Assignment 5 is due on Thursday, June 20th. See you tomorrow!
- June 6th - The lecture notes with examples for today's lecture, lecture 14, are now posted below, as is assignment 4. Assignment 4 is due on Monday, June 17th. Have a nice weekend!
- June 5th - The lecture notes with examples for today's lecture, lecture 13, are now posted below, as are the lecture notes for tomorrow's lecture, lecture 14.
- June 4th - Exam 1 has been graded, and the grades are posted on canvas. Also, assignemnt 1 has been graded, and the grades are also posted on canvas. I'll bring both to class tomorrow. The average grade on exam 1 was 84.23, with a median of 92, and a standard deviation of 13.73. There were 8 perfect scores! So, all in all, well done! The lecture notes with examples for lectures 11 and 12 are posted below, along with the lecture notes for tomorrow's lecture, lecture 13. Exam 1 and its solutions are also posted below.
- May 30th - Today, as you all hopefully know, was our first exam. The exam and its solutions will be posted here tomorrow. I'll grade the exam this weekend, and will send out an email when the grades are posted on canvas. Also, assignment 2 was due today. I'll post the solutions to assignment 2 here on Monday. Assignment 3 is now posted below. It's much shorter than assignment 2. Also, the lecture notes with examples for yesterday's lecture, lecture 10, are posted below, as our the lecture notes for lectures 11 and 12. Finally, a cellphone was left behind in class today. It's in the main office of the JCB math building. Please come by the office and pick up the cellphone if it's yours. Have a nice weekend!
- May 29th - Exam 1 is tomorrow during class. So, I'll see you all there. Also, Kurt Fisher from our class has found an awesome website with a java applet for generating slope fields and plotting solution curves based on these slope fields. Check out the cool website here
- May 28th - The lecture notes with solutions for lectures 8 and 9 are now posted below. We have our first exam this Thursday, and it will cover everything up through section 2.3 of the textbook. So, everything covered in the first 9 lectures. As mentioned in class today, I will let you have a sheet of paper for formulas, although you probably won't need them. Finally, there was not outcry against moving around the week off. So, our schedule has now been changed. Instead of having no class the entire week of June 10th, we will have class on June 10th and June 11th, and we won't have class on July 10th or 11th. The schedule on this website and on the syllabus have been updated to reflect these changes.
- May 22nd - The lecture notes for today's lecture, lecture 7, are posted below. Sorry things got a little confused in the middle of lecture today. I'll go over the issue at the start of class tomorrow. Also, I've scheduled a review for exam 1 on the evening Tuesday, May 28th. The review will be at 7:00 PM in LCB 219.
- May 21st - The lecture notes for lecture 10 are now posted below, as are the lecture notes with examples for today's lecture, lecture 6. I've also posted assignment 2, which will be due on Thursday of next week. See you tomorrow!
- May 20th - The lecture notes for lectures 8 and 9 are now posted below, as are the lecture notes with examples for today's lecture, lecture 5. I won't be able to do a Maple demonstration in class tomorrow, but I have posted some example code below on how you can use Maple to plot slopefields, using the example function from lecture 3 we did in class.
- May 16th - The big announcement is that we have a new classroom! Please see the headline announcement above for specifics. Also, lecture notes for lectures 6 and 7 are now posted below, along with the lecture notes with examples for today's lecture, lecture 4. Have a good weekend! I'll see you on Monday.
- May 15th - The lecture notes with examples for the first three lectures are now posted below, along with the lecture notes for tomorrow's lecture (lecture 4) and next Monday's lecture (lecture 5).
- May 12th - The class webpage is (obviously) up and running. If you'd like to check out the syllabus, schedule, or the lecture notes for the first two days, all are posted below. Our first class is tomorrow morning. See you then!
Administrative
Syllabus
Schedule
Note: The final exam for the class will be on Thursday, August 1st from 10:00 AM to 12:00 Noon.
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
Other
Slopefield Example in Maple
Our classmate Kurt Fisher has made some nice Matlab programs for solving exercises 2.4.26 and 2.4.30 from homework assignment 3. I've linked to the appropriate files in case anybody else wants to check them out. To do so, download the linked directory to a directory on your computer, then type the name of the file "nnnnMain" of the "nnnnMain.m" file. Or you can open the file nnnnMain.m from Matlab and run it from there. Of course, you need Matlab on your computer in order to run these programs.
Exercise 2.4.26
Exercise 2.4.30
Kurt has also created a lovely Maple file that illustrates the technique of plotting multiple particular solutions for a second order homogeneous solutions. Such graphs are shown in Fig. 3.1.5 and 3.1.8 in the course text book, and these approaches are based on the Edwards, Application Manual, Sec. 3.1. The maple file is available here. To use the file just download it to your computer and open it with Maple.
Kurt Fisher has made some very detailed Maple files that explore how we go about plotting the slopefields and solutions for Exercises 5.2.1, 5.2.9, and 5.2.15. You can check these out here:
Plotting Exercise 5.2.01
Plotting Exercise 5.2.09
Plotting Exercise 5.2.15
To use these files just download them to your computer and open them with Maple.
Also, if you'd like a MUCH more detailed discussion on how to graph and plot solutions to 2x2 first-order systems of equations with constant coefficients you can find such a discussion on Prof. Arthur Mattuck's MIT video lecture no. 27. This lecture is available online here.
A professor a Lamar University named Paul has a useful set of notes for calculating inverse Laplace transforms. They should supplement the material from sections 7.2 and 7.3 of the textbook (lectures 27 and 28) nicely. The notes can be found here. Hope you find them useful.
Kurt Fisher has kindly made some Laplace transform flashcards that might be useful to you in your studying. You can download a .pdf for these flashcards here. You should print them out using both sides of the paper, and then you can cut them out and the flashcards will align.
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 Thursday, May 23rd
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 Thursday, May 30th
Assignment 3
Section 2.3 - 1, 2, 4, 10, 24
Section 2.4 - 1, 5, 9, 26, 30
Assignment 3
Due Thursday, June 6th
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 Monday, June 17th
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 Thursday, June 20th
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 Thursday, June 27th
Assignment 7
Section 5.1 - 1, 7, 15, 21, 27
Section 5.2 - 1, 9, 15, 21, 39
Assignment 7
Due Wednesday, July 3rd
Assignment 8
Section 5.4 - 1, 8, 15, 25, 33
Section 5.5 - 1, 7, 9, 18, 24
Section 5.6 - 1, 6, 10, 17, 19
Assignment 8
Note - There is a typo on Problem 5.4.33 in the textbook. The vector v2 should be [0 0 1 i]^T, and NOT [9 0 1 i]^T.
Due Monday, July 15th
Assignment 9
Section 7.1 - 1, 6, 20, 30, 36
Section 7.2 - 1, 4, 15, 20, 29
Assignment 9
Due Thursday, July 18th
Assignment 10
Section 7.3 - 3, 8, 19, 24, 30, 33
Section 7.4 - 1, 5, 10, 19, 31
Section 7.5 - 1, 6, 15, 21, 26
Assignment 10
Due Thursday, July 25th
Assignment 11
Section 7.6 - 1, 6, 11, 14, 15
Section 9.1 - 1, 8, 11, 13, 21
Section 9.2 - 1, 9, 15, 17, 20
Assignment 11
Due Thursday, August 1st
Assignment 12
Section 9.3 - 1, 5, 8, 13, 20
Section 9.5 - 1, 3, 5, 7, 9
Assignment 12
Due Thursday, August 1st
Note - This assignment is for extra credit, and it will not count against your grade if you don't have it in.
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.
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 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