Welcome, please note that the schedule and syllabus are linked just below.

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: (Click here for Solution)
- [Due Oct. 17] Project II: applications of partial derivatives, parametrized surfaces, higher dimensional integration: (Click here for Solution)
- [Due Nov. 14-21] Project III: differential and integral vector calculus : (Click here for Solution)

The tests for our course will have a different focus, but perhaps these will give you some idea of the length of the tests.

What is the name of the scientist pictured below ? It's worth a point on any test if you can tell me. It is also possible to earn bonus points by asking particularly good questions or suggesting corrections to errors in notes and materials on the course website. This does not include spelling or grammatical errors, those are provided for your amusement. Once I notify the class of the error you may no longer ask for that point. To start with check our page of known errors (errata page)

These are not required. It is entirely possible to earn an A without completing these. You may achieve a maximum of 10pts bonus (put towards a test I don't drop).

These are my course notes from Calculus I and II, somtimes I reference them in the calculus III notes, so there here if you need them.

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Last Modified: 9-1-08