# Spring 2012: Elementary Differential Equations

 Section 01, meets Tues/Thurs, 10:30 - 11:50 Week 15 Thu. May 3: Final exam in class. Tue. May 1: We'll go over the final exam review (linked in the previous week) in class. Solutions can be downloaded here: [PDF] Week 14 Thu. Apr. 26: Finish Chapter 5.2; hand out the final exam review, to be completed in class on Tuesday, May 1. You can download the exam review here: [PDF] Update: Quiz 7 solutions are now available. [PDF] Homework, due Thursday, May 3: Chapter 5.2, #2, 5 (just the solutions, not the Wronskians) Tue. Apr. 24: Spent much of the class period going over material from section 6.3, including several homework problems that had caused trouble. Concluded with an intro to Chapter 5.2. Quiz 7 has been given as a take-home assignment, due in class on Thursday, April 26, which you can download here [PDF] Week 13 Thu. Apr. 19: Chapter 5.1. Reminder: Quiz 7 has been postponed and will be in class on Tuesday, April 24. Homework, due Thursday, April 26: Chapter 5.1, #2, 5, 8, 9. 13. 20, 22, 25 Tue. Apr. 17: Review Chapters 6.3 and 6.4. Quiz 6 solutions now available [PDF] Week 12 Thu. Apr. 12: Begin Chapter 6.4. Quiz 6, in class, on 6.1 and 6.2. Homework, due Tuesday, April 24: Chapter 6.3, #2, 4, 8, 15, 20; 6.4, #2, 6, 10, 14. Tue. Apr. 10: Chapter 6.3. Week 11 Thu. Apr. 5: Chapter 6.2. Homework, due Thursday, April 12: Chapter 6.1, #5, 7, 10, 13, 15, 21; Chapter 6.2, #2, 7, 8, 12, 15, 18, 20. Tue. Apr. 3: Hand back quiz 5 (solutions now available), cover Chapter 6.1, and begin Chapter 6.2. Remember to review improper integrals and partial fraction decomposition before this class, because this chapter will use a great many techniques of integration that you may not have seen in a while. [Quiz 5 solutions] Week 10 Thu. Mar. 22: Quiz 5 in class, at the beginning, in order to give us time to go into 6.1 afterward. Homework, due Tuesday, April 3: Chapter 7.6, # 2, 3, 7, 10; Chapter 6.1 TBA. Tue. Mar. 20: Note: Quiz 5 has been rescheduled to Thursday, March 22. Covered another example from 7.5, and began 7.6 on linear systems with complex eigenvalues. Week 9 Thu. Mar. 15: Will hand back midterm part B, and cover the remainder of 7.2, and (finally!), and then get into systems of linear equations, in chapters 7.3 (briefly) and 7.4. Midterm solutions are also now available here. [PDF] Homework "due" March 22 in class: Chapter 7.5, # 7, 9, 12, 15, 17, 24. It is only "due" then, and not truly due, because I said that I will automatically extend it to the following Tuesday if anyone needs a little extra time. Tue. Mar. 13: Handed back and went through a couple of questions from midterm part A, and then covered most of chapter 7.2 (up to the definition of an eigenvalue). Week 8 Thu. Mar. 8: Midterm (Part A is in-class, and there is a Part B that will be take-home, due on Tuesday, March 13.) Tue. Mar. 6: Midterm review (See the previous week for a copy of the review sheet). Midterm review solutions are now available. Note that there was an error in problem 1 which made the integrals very difficult. You should not expect such an error on your midterm this Thursday. [PDF] Week 7 Thu. Mar. 1: We spent a large portion of class on understanding the variation of parameters techniques, and solved one of the homework problems together. Afterward, we continued working on essential concepts from linear algebra (Chapter 7.2 - 7.3). Reminder: The midterm is in class next week. In Tuesday's class, we will go over as many as possible of the problems from the review linked here. [PDF] Homework due Thu. Mar. 8: Chapter 7.2, #1c, 1d, 2a, 3d, 4, 8, 10, 15, 21, 22, 25 Tue. Feb. 28: Discuss essential concepts from linear algebra that will be used later in the course (Chapter 7.2). Note that because this week's homework is relatively light in terms of technical difficulty, if you have extra time I recommend peeking ahead to Chapter 7.4 to see how these techniques will be used. Week 6 Thu. Feb. 23: Chapter 3.7, Mechanical and Electrical Vibrations. Note that next week we will begin to talk about matrices and linear algebra, as covered starting in Chapter 7.2. Especially if you have not taken a linear algebra course, but even if you have, I recommend you review the basics of matrix algebra before we begin to discuss it in class. Chapter 7.2 is a good place to start, and as a supplement I can recommend a set of notes used at Carnegie Mellon for this course as well, which I link here: [PDF] Homework due Thu. Mar. 1: Chapter 3.6, #1, 5, 6, 13; Chapter 3.7: #2, 3, 6, 7, 11 Tue. Feb. 21: Finish Chapter 3.6. Quiz on Chapters 3.1 - 3.4. [Quiz 4 solutions] Week 5 Thu. Feb. 16: Covered the remainder of Chapter 3.5 and began 3.6. Homework due Thu. Feb. 23: Chapter 3.4, #1, 2, 5, 11, 12; Chapter 3.5, #3, 4, 8, 13, 14 Tue. Feb. 14: Cover Chapter 3.4 and begin 3.5. (No quiz this week.) Week 4 Thu. Feb. 9: We'll cover Chapters 3.3 and 3.4 in class. Homework due Thu. Feb. 16: Chapter 3.1, #1, 2, 6, 10, 12, 16; Chapter 3.3: #7, 8, 18 [Link to the 3.1 problems] [Link to the 3.3 problems] Tue. Feb. 7: Collect and briefly discuss HW from 2.2-2.3; review an exact equation from 2.6; cover Chapter 3.1. Note on Quiz 3: Quiz 3 has become a take-home assignment, due in class on Thursday of this week. No late submissions allowed, and you may not collaborate with other students or tutors on the quiz itself. [PDF] [Quiz 3 solutions] Week 3 Thu. Feb. 2: Will review partial derivatives and antiderivatives, and cover Chapter 2.6 on exact equations. This section will involve some work using partial derivatives, and taking iterated integrals in several variables. While the techniques are not difficult, and I won't ask you to prove anything with them, it is still a good idea for you to get some practice outside of class to get comfortable. Toward that end, I recommend studying any text used for Calculus III (if you're using Thomas, the text used by Columbia, take a look at chapter 14.3). Another good resource is "Paul's Online Notes", specifically here. Note on Homework originally due this week: In class, I promised to extend the homework (2.2 and 2.3) due date until Tue. Feb. 7; I also promised a hint on 2.3 problem 1, which follows. [PDF] Homework due Thu. Feb. 9: Chapter 2.5 #2, 12, 15, 16* (#16 is optional, for two bonus points); Chapter 2.6 #1, 2, 8, 14, 16 [Link to the 2.5 problems] [Link to the 2.6 problems] Tue. Jan. 31: Covered the remainder of Chapter 2.5 on autonomous and logistic equations, as well as taking Quiz 2. [Quiz 2 solutions] Week 2 Thu. Jan. 26: Will cover Chapters 2.3 and 2.5 on modeling and autonomous equations. Homework due Thu. Feb. 2: Chapter 2.2, #1, 2, 6, 10, 11, 21 (you may use WolframAlpha to sketch the solutions). Chapter 2.3, #1, 8, 9, 13; [Link to the 2.2 problems] [Link to the 2.3 problems] Tue. Jan. 24: Covered separable differential equations (Chapter 2.2), and looked at a few examples of sketching solutions, as well as taking Quiz 1. [Quiz 1 solutions] Week 1 Update: I made a brief set of notes to help you clarify the difference between linear and non-linear differential equations. [PDF] Thu. Jan. 19: Will cover chapter 2.1 on First-order linear differential equations. Also, please note there was an error on the review homework problem sheet due on Tuesday. The version attached below has been corrected. Homework due Thu. Jan. 26: Chapter 1.3, #2, 8, 9, 13, 18. Chapter 2.1: #1, 2, 14, 15, 16. [Link to the 1.3 problems  Link to the 2.1 problems] Tue. Jan. 17: Will go over the syllabus, introduce major topic points, and go over chapter 1.3 on the classification of differential equations. Supplementary handout: Raw mathematica printout with some other slope fields and solutions which I didn't get a chance to put on the board. [PDF] Homework due Tues. Jan. 24: These review problems: [PDF] 