## Math 20a, Fall 2009, Brandeis University

This is the website for the class Math 20a, Calculus of Several Variables, taught in the fall of 2009 at Brandeis University.

### Vital statistics

Lecturer: Thomas Barnet-Lamb
Office: Goldsmith 205
Email: consists of the identifier 'tbl', followed by an at sign, followed by the word brandeis, a dot, and the suffix 'edu'.
Schedule: Tues, Fri 10.30am-12 noon
Office hours: Tues 2-3.30pm, Fri 3-4.30pm

Further information can be gleaned by perusal of the syllabus.

On the final, you will be allowed to bring one formula sheet, of length not more than two sides of letter paper. You can either choose to make your own, which must then either be handwritten or word-processed using a font no smaller than 12 point; or choose to use the one I have prepared for you. (In the latter case there is some space on the second side which you can fill in with further handwritten notes as you wish.)

The final will contain a mixture of more straightforward problems, which will be like the homework, and a few harder problems. Some final practice problems are available, to give you an idea of what the latter problems might be like.

And here are some hints and solutions to the practice problems.

### Homework

Homework one (vectors and coordinates).
Homework two (dot products, cross products, and visualizing paths).
Homework three (differentiation of vector valued functions; velocity, acceleration, arc length, and curvature).
Homework four (parametric surfaces, functions of several variables, lines and planes).
Homework five (the chain rule, partial derivatives, tangent planes).
Homework six (Directional derivatives, graph sketching, maxima and minima.).
Homework seven (Maximizing functions.).
Homework eight (Integration.).
Homework nine (Vector fields and line integrals.).
Homework ten (Fundamental theorem of line integrals, flux integrals, and div and curl.).
Homework eleven (Green's theorem, surface integrals.).
Homework twelve (Gauss and Stokes.).