Welcome to Math 253, Calculus III. The syllabus is here. It contains information on class times, exam times, office hours, contact info, etcetera.
This website will be used to make announcements, post homework assignments, post practice exams and solutions, etcetera.
Here is an answer to a commonly asked question about the textbook.
1) The Midterm Exam is POSTPONED until week 9, most likely Wednesday. It will still cover the same material.
2) On friday of week 8, my colleague Prof. He (who is teaching one of the other sections of MAT253 now) will fill in for me. He'll be doing more on the Taylor Remainder Theorem.
3) I'll be doing midterm review at the start of week 9. Then on Friday of week 9 (and possibly a bit before) we'll start the final topic, solving differential equations with power series. We won't go as deep as we otherwise would.
4) The last two homeworks will be due on Friday (of weeks 9 and 10) rather than wednesday. I've posted the next one, its short. I may change the details after I hear from Prof. He about what is covered in class.
5) You can hand in the week 8 homework on Friday. I do not know whether Prof. He can get you your previous homeworks back that day, or whether it will wait until Monday.
6) Stay warm and get well!
The notes I'm lecturing off can be found here and here and here and here. My notes are probably full of errors and I didn't end up doing them in the same order, but here they are. (The lecture numbering is really about topics, not about how it fits into a 50 minute class.) That table of series convergence tests is at the start of Lecture 7.
HW is due at the BEGINNING OF CLASS each Wednesday. (You may also put it in my mailbox in Fenton hall if you don't come to class, but then you'll miss the quiz.)
Use complete sentences in your homework. Justify your answers by stating what tools you use. Abbreviations are acceptable. For more on acceptable homework practice, see the syllabus.
Reading: Section 8.1 and Appendix D pages A32-33
Section 8.1: 6, 8, 10, 12, 14, 16, 18, 20, 22, 23, 26, 28, 29, 31, 32, 34, 41.
Reading: Section 8.1 (squeeze and monotone), 8.2 (no telescoping sums)
Section 8.1: 25, 30, 46, 48, 50, 51, 54, 56, 59
Section 8.2: 12, 14, 16, 18, 19, 22, 23, 24.
Reading: Section 8.3 (integral test only), Section 8.4 (ratio test only), Appendix D (pages A32-33 only)
Section 8.3: 2, 12, 14, 15, 21, 23, 25, 28, 34, 36
Section 8.4: 22, 23
Appendix D: 21 (use Wolfram alpha, you don't need to hand in the graph).
Hints: You can use the ratio test in chapter 8.3, of course! Also, for 8.3.36, what is the derivative of (ln n)-1?
Here is the first practice midterm. Solutions are here.
Reading: Appendix D (page A33, just for limit being infinity), the rest of Sections 8.3 and 8.4 (we probably won't get to absolute convergence but it is good to read ahead)
Appendix D: 24
Section 8.3: 16, 19, 24, 25, 27, 28, 37, 38
Section 8.4: 4, 6, 8, 10, 14, 16, 20.
Reading: Section 8.4 for absolute convergence, Section 8.5, Section 8.6 pages 598-599.
Section 8.4: 30, 32
Section 8.5: 4, 5, 6, 8, 10, 12, 14, 15, 20, 23, 26, 33
Section 8.6: 4, 5, 6.
Reading: Section 8.6, 8.7 examples 5 and 6, and from the table on p613 until the end.
Section 8.6: 7, 9, 15, 18, 24, 26, 27, 28, 32
Section 8.7: 25, 27, 28, 30, 39, 43, 44, 50, 55, 58.
Extra credit: confirm this.
I've had several questions about this in class... I'm referring to the statement made in the last panel, that a certain series is surprisingly convergent. But be warned, this is quite a hard problem!
Reading: Section 8.7. We're not doing the binomial theorem. Section 8.8 ignoring the applications to physics.
Section 8.7: 2, 3, 4, 8, 9, 11, 16, 18
Section 8.8: 4, 6, 8, 11, 12, 14, 17.
Here is the second practice midterm. Note that I have included waaaay too many problems on purpose, and the first page tells you how to get about two practice midterms from this file. Solutions are here.
Reading: Same as last time, we're filling in the holes. Note: the material covered by this homework was not sufficiently covered in class due to the snowstorm, and will not be on the final exam.
Section 8.7: 7, 19, 20
Section 8.8: 21, 22, 23, 25.
For the final week of the course we will be studying power series methods for approximating solutions to differential equations, which is not covered in your textbook. Here is a link to a free online ODE textbook which I think is pretty reasonable. I will be assigning chapters 0.2 and 7.2. Chapter 0.3 may be a helpful read to get one's bearings, and Chapter 7.1 may be a helpful review of power series. I will post my own lecture notes as well.
This online textbook is not perfect for our use, but I have found no better. Here are some comments on notation:
For an additional reference, here is a scan of some chapters from the MAT256 textbook, covering similar material. This textbook is also in the library. It covers essentially the same material from the online source, but is not as well written.
Reading: Chapters 0.2 and 7.2 from here and perhaps my lecture notes here.
The homework assignment is here. I have included an example problem with detailed solution. As of Friday you should be able to do part (a) of each problem based on what we did in class. After Monday you should be able to do parts (b) and (c).
Note: there was a typo on number 3b) in the previous version of the homework, which is fixed in the current version.
Solutions are posted here.
Also inlcuded on the assignment are some extra problems for practice, that I don't want anyone to turn in. Also, the online textbook has some exercises with solutions.
Here is a practice final. Solutions are posted here, but you should really try the problems before you look at solutions. Not every problem type is accounted for, so one should also look at the previous midterms and practice midterms.
I have not carefully checked this practice final for length. My guess is that it is slightly too long. My intention is for the final to be a little more than twice as long as the second midterm. There will be at least two problems on differential equations, as in this practice final.