Schedule for MATH 231 section 1, Fall 2008

You will find a tentative schedule of lectures below. Homework Quizzes make up 13% of your course grade and they will be selected from the homework detailed in the table. You should notice that the solved problems (posted by topic below the table) contain many problems like the homework.

The "Homework Projects" comprise 30% of your grade. If you go to the base of this page you will find that the actual problems linked in pdf-file format. The Homework Projects will also be distributed in lecture long before their due date.

Homework and Lecture Schedule:

It is important to both complete and understand the homework. I encourage you to form study groups, however, it is very important that in the end you come to an understanding of the material for yourself. You will most likely find the homework in this course challenging at times, so it is important to begin early and give yourself a chance to talk to others (for example me) before the due date. You may also email me reasonable questions.

It is not enough to find the answer - you must be able to justify each step. Imagine that you are writing the solution for a person who doesn't know calculus. On our tests I will expect you to explain your work since presentation and proper notation are arguably as important as the answer itself. In my lectures I strive to present calculations in a coherent and logical manner and I will expect you to do the same. So, take some time to notice what the notation means and don't just scribble the bare amount to get the answer. It's a bad habit and it will most likely knock a letter grade or two off of your tests.

I am always happy to look over your derivations of homework during office hours. Additionally, most days (time permitting), I'll answer a question about the homework. I try to give you all the tools you need to do the homework, but it is you who must put those tools to work. Think.

The homework is posted below. Notice I have indicated which portion of my lecture notes as well as which part of the textbook is most relevant to the assigment. Beware, sometimes the homework is not exactly matched up with the lecture notes link, sometimes you need to look at the next few pages. The pdf's of my lecture notes are chopped up chapter by chapter, usually you can find what you need somewhere in that chapter. If you are lost send me an email, I'll try to point you in the right direction. It would be wise to print out a copy of the lecture notes - you will find them helpful for certain homework problems. It is your responsibility to finish the homework assigned by the due date (before class).

  • On the due date, or anytime after, any problem assigned in the table below is fair game for a "Homework Quiz"

    • I have placed * next to a number of homework exercises. This is a reminder to myself and you that I have something to say about that given problem. In some cases just a hint, in other cases I mean to work the problem in class. It would be good to remind me of these before the due date when I ask "are there any questions ?". That is your cue to get me to do some of your homework, or at least to help. So, take advantage of my offer please.

    I will give you enough time to copy a solution of the problem neatly onto a seperate sheet of paper. I do not collect all of the homework which is due when we have a "homework quiz". I choose a few problems and have you rewrite your solution.

    The Homework Quizzes will be based on one of the problems below, unless I explicitly say otherwise (I would warn you in advance if I was to stray from these problems for a particular Homework Quiz).

    Section # My Notes Due Date Assignment Description / Hints / Mathematica helps
    Sec. 13.1 236-239 Aug. 21 7, 11, 13, 15, 20, 23-31(odds), 39, 40 3d-Cartesian Coordinates
    Sec. 13.2 240-250 Aug. 26 4, 5, 7, 13, 17, 21, 24, 26, 29, 31, 35 vectors
    Sec. 13.3 240-250 Aug. 26 3, 5, 7, 9, 11, 13*, 17, 19, 21, 23, 29, 31, 35-40, 45, 57* dot product
    Sec. 13.4 240-250 Aug. 26 1, 3, 5, 7, 10, 20, 33, 39, 43 cross product
    Sec. 13.5 251-256 Aug. 26 3, 5, 7, 10, 11, 14, 16, 17, 18, 25, 26, 30, 31, 35, 40, 49, 55 lines and planes
    Sec. 13.6 257-262 Aug. 28 21, 23, 25, 27, 49* functions of several variables
    Sec. 14.1 263-268 Sep. 4 7, 9, 11, 13, 19, 23, 25*, 41, 42* vector-valued functions
    Sec. 14.2 263-268 Sep. 4 5, 9, 11, 13, 15, 16, 27-33, 35, 43, 45 calculus of vector-valued functions
    Sec. 14.3 269-279 Sep. 4 1, 13 arclength and moving TNB-frame
    Sec. 14.4 280-283 Sep. 4 9, 11, 13, 15, 19, 21*, 33, motion in space
    . . Sep. 5 Homework Project I .
    Sec. 15.2 290-291 Sep. 9 5, 7, 9 limits and continuity
    Sec. 15.3 292-295 Sep. 9 5, 15-38, 41, 43*, 45, 47, 49, 50, 51, 53, 55, 56, 61, 65, 70, 71 basic partial derivatives
    Sec. 15.5 296-299 Sep. 9 1, 2, 7, 8, 10, 11, 21, 22, 25, 38, 39, 40, 45, 53 chain rule for several variables
    N/A 300-305 Sep. 9 will give in lecture, see my notes for examples* constrained partial differentiation
    Test I . Sep. 11 Test I .
    Sec. 15.4 311-313, 317-319 Sep. 23 1, 3, 11, 17, 19, 25, 27, 29, 39, 42 tangent plane and linearization
    Sec. 15.6 311-319 Sep 23 5, 8-15, 20-22, 25, 29, 31, 38, 39, 43, 53 directional derivative
    Sec. 15.7 320-324 Sep 23 5, 7, 9, 14, 29, 33, 35, 45*, 49 extrema in functions of several variables
    Sec. 17.6a 402-406 Sep. 30 1, 3, 4, 5, 6, 13, 19-26, 33-36(graph optional), parametrized surfaces and surface area
    Sec. 16.2 330-342 Oct. 7 3, 6, 7, 10, 12, 13, 15, 21, 25, 31 basic double integrals
    Sec. 16.3 330-342 Oct. 7 1, 3, 5, 7, 9, 11, 13, 16, 18, 19, 21, 33, 40, 41, 43 double integrals over general regions
    Sec. 16.6 339-343 Oct. 7 3, 5, 6, 7, 9, 10, 13, 19, 32 basic triple integrals
    Sec. 16.9 343-359 Oct. 14 1, 3, 4, 5, 6, 7, 10, 13*, 17a, 21 the Jacobian
    Sec. 16.4 343-359 Oct. 16 9, 10, 11, 13, 15, 16, 17, 19, 23, 25, 28, 31 double integrals in polar coordinates
    . . Oct. 17 Homework Project II .
    Sec. 16.7 343-359 Oct. 21 1, 3, 5, 7, 9, 11, 15, 17-20, 26*, 27 triple integrals in cylindrical coordinates
    Sec. 16.8 343-359 Oct. 21 1-27(odd), 36* triple integrals in spherical coordinates
    Test II . Oct. 23 Test II .
    Sec. 13.1 360-365 Nov. 4 1, 3, 5, 7, 15, 17, 21, 23, 24, 25, 29, 35 vector fields
    Sec. 13.5 366-368, 369-372, 373-374 Nov. 4 1, 3, 4, 5, 11, 12, 13, 15, 19-22, 30, 31, 32, 39(wildcard) curl and divergence
    Sec. 13.2 385-394 Nov. 11 1-5, 8, 11, 12, 15, 17, 18, 19-22, 39, 41, 42 line integrals
    Sec. 13.3 395-401, 400-401 Nov. 13 3, 5, 7, 11, 13, 17, 19, 21, 27, 28, 29-33, 34a FTC for line integrals, conservative forces
    Sec. 17.6b 402-406 Nov. 13 37, 41, 43 surface area
    Sec. 13.6 407-411 Nov. 13 5, 7, 11, 14, 18, 21, 23, 29, 40*, 41, 43, 44, 47* surface integrals
    . . Nov. 14 Homework Project III .
    Sec. 13.4 412-419 Nov 18 1, 3, 5, 7, 9, 11, 29(wildcard) Greene's Theorem
    Sec. 13.7 412-419 Nov. 20 2, 3, 4, 5, 6, 7, 9, 10*, 16*, 17* Stoke's Theorem
    Sec. 13.8 421-423 Nov. 20 5, 7, 9, 10, 13, 17*, 23 Divergence Theorem
    N/A . Nov. 20 See handout "Added Vector Calculus" additional problems in vector calculus
    Event . Nov. 24-28 . Thanksgiving Break
    Test III . Dec. 2 Test III .
    Final . Dec. 10 10:30am-12:30pm comprehensive

  • "wildcard" exercises can be turned in anytime before the last test. If they are nearly correct then I allow you to substitute your wildcard grade for some unsatisfactory Homework Quiz grade, or if you missed one it can substitute for the missed Homework Quiz. (Recall that if you miss a Homework Quiz then you are supposed to contact me and explain why so we can arrange to increase the weight of the final. Finals are risky so this is a good option if you have time)



    • Select Homework Solutions:

    These are my solutions to some of your homework. I have tried to select at least one of each type of problem you will encounter. These serve as additional examples to those given in lecture. You are of course free to ask me for further clarification if you find my solution to terse. Some of these problems are more advanced than the typical level of this course, I include those problems for your edification and my amusement (wait, maybe switch that). I have tried to include little remarks to alert you to the fact my solution is optional (meaning I don't expect you to do it the way I do it, for example anywhere I use the repeated index notation or "Einstein" notation you may ignore it if you like, but you should think about how to do it in your own brute-force way). Generally speaking you may choose the notation that you find most natural, sometimes I will use a notation that all of you find obtuse and obscure. I have my reasons, perhaps some of you will appreciate them. Those things which are "optional" are likely to show up as bonus questions on test ( just a point or two)

    note: problem numbers probably do not match your text. These solutions were written originally for Calculus and Concepts which is a different, somehow, version of your text. You can look at the other version during office hours if you so desire. Additionally, I should mention that these solutions may in places use notation which I am avoiding in lecture. The main distinction is that I have made an effort to adorn every vector with the vector symbol. Strictly speaking this is just notation so leaving the vector off is no big deal so long as you say somewhere "HEY THIS IS A VECTOR". Of course, students are not always so careful and I will admit that my omission of the vector symbol has likely confused a few students. Some professors are not as open minded as I am on this point. For example, my Junior-level Mechanics professor started his whole class with an proclaimation that failure to write the vector over vectors would be graded as incorrect. Strict adherence to the vector notation can in principle help avoid making silly mistakes like dividing by a vector (almost never makes sense).

    Homework Projects:

    It would be foolish to not look over these well before the due date. These can be tricky in places. If you ask nicely I might help you when you are stuck...
  • These problems should appear soon, still selecting problems at the present time



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    Last Updated: 8-14-08