Instructor: Christian Rudnick
Office: C-113 Padelford Hall
E-mail:
rudnickc@math.washington.edu
Office Hours: Monday 1:30pm-2:30pm, Wednesday 8:20-9:20am, both in my office.
Announcements:
Announced 03/19/2012: The final as well as solutions are posted below.
Announced 03/06/2012: I shifted the due date of homework 8 to Friday, March 9, 9:30am.
Announced 03/02/2012: I corrected the typos on homework 8.
Announced 03/02/2012: Here are the notes on the Laplace transform. I did not correct that one mistake in the first row on page 12; it should be s^2 L(y) - s y(0) - y'(0). Since y(0)=y'(0)=0 in the example, the mistake has no consequences.
Announced 02/26/2012: Here is the eighth homework. It is due Wednesday, March 7, at 2pm.
Announced 02/22/2012: I took off the last problem of the sevnth homework. It will be a problem on homework 8.
Announced 02/21/2012: Here is the seventh homework. It it not as long as it might seem at first. Please make sure to review the material from problem 0 before Monday since I will start using the partial fractions decomposition. Also, I might not be able to cover the case n=1 from the last problem in which case I will move that problem to the next homework sheet.
Announced 02/20/2012: There is a typo in the second problem of the sixth homework (3.8.5 in Boyce & DiPrima): The external force is supposed to be 2cos(3t), and not 3cos(3t). I corrected it. You can hand the problem in with either one of those external force terms. Thanks for pointing that out.
Announced 02/17/2012: Since Monday, February 20 is a holiday, there will not be office hours. Instead, I will have office hours on Tuesday, February 21, 1:30-2:30. The notes on forces vibrations are available.
Announced 02/12/2012: Problem 1 on the fifth homework is actually 3.1.13 and 3.4.12, and not 3.1.13 and 3.4.11. I corrected that. Also, I randomized the order in problems 0 and 1 so that it is not clear in advance what sort of solution you will get.
Announced 02/12/2012: Here is the sixth homework. It is due Wednesday, February 22, at 2pm. Moreover, I fixed some mistakes in the solutions for the midterm.
Announced 02/11/2012: I reuploaded the fifth homework with some clarifications. Also, I fixed the tautology in the previous announcement.
Announced 02/10/2012: About the projected course grade: I computed it as 15% homework, 10% quizzes, and 75% midterm. If the midterm grade was better than that total score, I will make it the total score. I will base the final grade at the end of the quarter of whatever score is higher, the score you obtained in the final, or the total score. In spite of the fact that this is probably good news for those who did poorly on the midterm, note that I will design the final to be of the same difficulty as the midterm. Those people need to change something about how or how much they study. The last day to drop the course is February 20. If anyone has questions about that, feel free to drop by my office.
Announced 02/10/2012: If you have any complaints about the midterm please let me know about it soon. The mean and median are 13.77 and 13.75. I will take the score out of 21 points (not 24) since pretty much no one did the classification part of problem 4 with some sort of acceptable justification. I believe that if so few students do not do well on a problem that I judged to be of average difficulty, it is because I did not judge correctly.
Announced 02/10/2012: Here are the notes for the past two weeks. They include, among other things, how to solve second order constant coefficient differential equation; you need that for the second problem.
Announced 02/08/2012: I have posted the midterm and solutions below
Announced 02/06/2012: Here are the solutions of practice midterm.
Announced 02/05/2012: On the practice midterm, the points did not add up correctly for some problems. I fixed that.
Announced 02/04/2012: I fixed a mistake on the note sheet: The integral of e^x is e^x, not e^a. During the review session on Monday, I will go over the practice midterm. I am also happy to go over homework problems. Feel free to ask.
Announced 02/04/2012: Since the midterm is next week, there are the following changes: I will give a review session on Monday, 5:30pm at a to be determined location. I will let you know per class email list on Monday. Tuesday, I will give office hours from 10:00am-11:30am, 12:30pm-1:30pm, 2:30pm-9pm. Wednesday, my office hours will be a little earlier, 8-9am, since I have to oraganize the classroom before the test. Finally, you will get back the third homework on Monday at the end of class; the TA promised to drop them off during the class.
Announced 02/02/2012: Here is the practice midterm and the note sheet that you will be allowed to use during the exam.
Announced 02/01/2012: Here are my lecture notes that correspond to the second chapter. I did not cover everything that is included in the notes; you are only responsible for the material we have covered in class.
Announced 01/29/2012: I corrected a mistake on the forth homework, as mentioned in my email. Thanks to Sining for pointing it out. The fifth homework is posted. It is due February 15 at 2pm. There is no homework due on February 8 since you will write the midterm that day. I will post a practice midterm soon, and solutions to it somewhat later. My suggestion is that you study for the test, and then take the practice midterm as if it were an actual midterm. That will show you how well you are ctually prepared. The midterm will cover what we did in class until last Friday, January 27. The material corresponds to those parts of the second chapter that we have covered in class. In particular, you should be able to: Integrate (u-substitution, partial fractions, integration by parts), determine whether a differential equation is separable or linear, solve separable and linear differential equations, know how to approach applied problems (population dynamics, mixing problems, moving objects, heat transfer), and analyze autonomous equations (equilibrium solutions, their classification, determine properties of the solutions).
Announced 01/28/2012: The grades for the second grades are online (later than planned, sorry about that). It is graded out of 6 points. 46 out of 48 students wrote the quiz and the grades 6-5-4-3-2-1-0 were obtained 8-4-6-9-5-9-5 times. Note that both quizzes are weighted equally (each 5% of the total grade) in spite of the different total number of points that could be attained.
Announced 01/27/2012: I posted the second quiz and solutions to it. I will grade the quiz on Saturday morning. The grades should be online by noon.
Announced 01/25/2012: I updated the homework grades. I'll return the homework on Friday.
Announced 01/24/2012: Let me be more precise on what you should prepare for the quiz: First, you should be able to solve separable equations. Second, you should know how to analyze autonomous equations qualitatively in the way we did it for the logistic equation and the threshold model equation in class (i.e. find and classify equilibrium solutions, determine where the function is increasing, convex, etc.). I will hold office hours tomorrow from 1:30-2:30pm and Friday from 8:20-9:20am.
Announced 01/22/2012: We will write the second quiz this Friday, January 27, at the beginning of the lecture (from 9:30 to 9:40). It will cover what we did in class since January 16 and the second homework. That material corresponds to chapters 2.2 and 2.5, as well as the escape velocity example from 2.3. I will copy the same list of integrals as in the first quiz onto the back.
Announced 01/20/2012: I have updated the homework. What I called the the third homework is not really a homework: It contains only one problem which is an integration by parts review. I will start using this technique next Friday, so please make sure you are on top of it until then. There is nothing to turn in. The forth homework contains most of the problems from what has previously been the third homework. However, I substituted one easy problem from Boyce and DiPrima, 2.3.3, by one hard problem, a modification of 2.3.18, to reflect the fact that this homework is based on three, not two lectures. You should start working on that problem rather early. The problem is important because we will perform similar computations later when we talk about mechanical vibrations.
Announced 01/19/2012: The due date for homework 2 is now Monday, January 23, 2pm. My office hours this and the next week will be: Friday, January 20, 1:30-2:30pm; Monday, January 23, 8:20-9:20am. The due date and the content of homework 3 will be changed. The changes will be announced by this Saturday on the class webpage.
Announced 01/18/2012: Classes for Thursday are suspended, so there will, once again, be no office hours. I will move them to Friday, January 20, 8:30-9:20am. The homework is then due Friday, January 20, 2pm sharp.
Announced 01/18/2012: Starting next week, I will share office hours with Shuwen Lou, the instructor of Math 307J. Her office hours are Tuesday and Thursday, 2:40-4pm in her office, C-114 Padelford Hall, which is pretty much across from my office.
Announced 01/18/2012: Classes for today are suspended, so there will be no office hours either. Instead, there will be office hours tomorrow, January 19, from 2:30 to 3:30.
Announced 01/17/2012: Since we expect to get a lot of snow tonight and some of you might not be able to come to campus tomorrow, I shifted the homework due due date to Friday, during class.
Announced 01/15/2012: I fixed a typo on the third homework: I used a modification of problem 2.1.7, not 2.1.17 from Boyce & DiPrima.
Announced 01/14/2012: Homework 3 is posted and due January 25 at 2pm.
Announced 01/13/2012: The grades for quiz 1 are available on Catalyst. I graded the quiz out of seven points. 49 students wrote the quiz; the grade count for 7-6-5-4-3-2-1-0 was 21-7-3-4-1-6-4-4, e.g. three students received 5 out of 7 points.
Announced 01/13/2012: I have posted the quiz as well as solutions, see below. Since Monday is a holiday, there will be no class and no office hours. Instead, I will hold office hours on Tuesday, January 17, from 1:30-2:30 in my office.
Announced 01/12/2012: One last comment on the first homework problem: To find the times when the ball hits the ground, you will need to compute the zero of some function. This cannot be done by hand since the equation is transcendental. You can use, for example, WolframAlpha; just type in "zero of" followed by the equation. To compute the non-trivial integrals that come up, use the sheet that I distributed in class yesterday; you can also find those integrals (and many, many more) on Wikipedia and the links given in that article. Note that you may not use those on the midterm and final without justification; only those that are on that sheet that I handed out. The one last integral that you will have to compute is, up to several constants that I excluded, (1-e^t)/(1+e^t); split it up into two parts, 1/(1+e^t) and -e^t/(1+e^t). The right one is straightforward since the numerator is the derivative of the denominator. To integrate the left one, multiply numerator and denominator by e^-t; then, once again, the numerator is the derivative of the denominator. Thanks to Mr. Lewis for pointing that out.
Announced 01/10/2012: On Friday, we will have the first quiz during the first ten minutes of lecture, i.e. 9:30-9:40. The quiz will cover the material that we did during the first week and the first homework. Since there have been some issues with integrating functions: The only technique that I require you guys to know is substitution (the basic one, nothing fancy like inverse trig substitution). Moreover, you can use the list of integrals that you were allowed to use in Math125 (p. 484 in the sixth, and p. 495 in the seventh edition of Stewart's calculus book), I will provide you with a copy of that list of integrals---in spite of the fact that you will not need it for the first quiz. No aids are allowed for the quiz.
Announced 01/10/2012: In problem 1, I made a typo when copying the homework problem, it should have been |v|/30. You can hand it in with either |v|/20 or |v|/30, both is fine. Also, recall that the antiderivatice of tan(x) is -ln|cos(x)|. Finally, with the hint on how to set up the differential equation for the first problem: there is still some thinking to do on how to implement the drag term; my intention was not to suggest to merely add the function that is given in the problem.
Announced 01/09/2012: For problem 1, I suggest that you set up the equation as ma=-mg+f(v), where f(v) models the drag. Also, recall that the antiderivative of 1/(1+x^2) is arctan(x).
Announced 01/08/2012: I am sorry, but I had to make changes to the second homework. I had started to write the third homework a while ago, and when I continued today I realized that that one problem which I really wanted to assign for the second homework was in the third one.
Announced 01/07/2012: Homework 2 is posted. You can find the times of my office hours on the top of the page.
Announced 01/06/2012: The syllabus is definite. Moreover, I renumbered the problems from homework 1 because there was no problem 2. Please use the new numbers when you write up your homework.
Announced 01/03/2012: Here is the syllabus, and the first homework, due January 11 at 2pm.
Announced 12/19/2011: Hey there. This is the class webpage. I will upload some more information in the next couple of days, including a tentative syllabus.
Homework:
Homework 1, due January 11, 2pm January 13, 9:30am.
Homework 2, due January 18, 2pm January 20, 9:30am January 20, 2pm January 23, 2pm.
Homework 3, due January 25, 2pm January 27, 9:30am.
Homework 4, due February 1, 2pm.
Homework 5, due February 15, 2pm.
Homework 6, due February 22, 2pm.
Homework 7, due February 29, 2pm.
Homework 8, due March 7, 2pm March 9, 9:30 am.
Tests:
Quiz 1 and solutions.
Quiz 2 and solutions.
Midterm and solutions.
Final and solutions.
Ressources:
WolframAlpha, an online computing system. Can integrate and solve differential equations, and is therefore a valuable tool to check your work and look for mistakes.
Other than my office hours, you can get help at the
Center for Learning and Undergraduate Enrichment (CLUE) which provides help for a variety of math courses, including Math307.
When preparing for an exam, you can have a look at the webpages previously taught courses at the math department's class archive. Many instructors upload the exams they gave during the course.
About the course:
Syllabus
Math 307 Materials Website
Grades (Catalyst)