Mathematics Maths21A Summer 2007

Multivariable Calculus

Supplements

by Oliver Knill

Office: SciCtr 434

Email: knill@math.harvard.edu

We post here some summaries and some complements to the lecture topics. These notes have been evolved since a few years. They are quite densely written and do not replace the book of course. If you find typos, please email them or talk to me about it. Errata found after the notes being distributed are acknowledged to the right. The files found here are already corrected. |

- 1. Coordinates, Homework 1 (with solutions)
- 2. Vectors, Homework 2 (with solutions)
- 3. Distance, Lines Planes
- 3. Cross product, Homework 3 (with solutions)

- Contours, Functions and Homework 4 (with solutions)
- Other coordinates, Implicit surfaces, >Parametric surfaces and Homework 5 (with solutions)

- 2D Integrals and Homework 6
- Arc length and Homework 7

- Partial derivatives Linearization Tangent spaces and Homework 8
- Extrema and Homework 9
- Constrained extrema Homework 10

- 3D integrals, Integration in cylindrical coordinates and Homework 13
- Integration in spherical coordinates
- Vector fields and Homework 14
- Line integrals
- Fundamental theorem of line integrals and Homework 15

Please send questions and comments to maths21a@fas.harvard.edu

Maths21A | Oliver Knill | Summer 2007 |
Summer school |
Department of Mathematics |
Faculty of Art and Sciences |
Harvard University