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.

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.

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).

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 |

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

- [9.1-9.5]: Cartesian coordinates and vectors
- [9.5, 9.6, 11.1]: More vectors and functions of x,y and z
- [10.1-10.5]: Vector-valued functions and topics related.
- [11.2, 11.3, 11.5]: Partial derivatives.
- [11.4, 11.6]: Tangent planes and linearizations.
- [11.7, 11.8]: Min/Max and Lagrange multipliers.
- [12.2, 12.3, 12.7]: Double and Triple Cartesian Integrals.
- [10.5, 9.7, 12.9, 12.4, 12.8]: Jacobians and Integration in other coordinates.
- [13.1, 13.5]: Curl, divergence, and vector fields.
- [13.2, 13.3]: Line integrals, FTC, conservative vector fields.
- [12.6, 13.6]: Surface area and surface integrals.
- [13.4, 13.7, 13.8]: Green's, Stokes', and Gauss' Theorems.

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...

- [Due Sep. 5] Project I: vectors, calculus of vector-valued functions, partial derivatives
- [Due Oct. 17] Project II: applications of partial derivatives, parametrized surfaces, higher dimensional integration
- [Due Nov. 14] Project III: differential and integral vector calculus

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Last Updated: 8-14-08