Math21a, Spring 2004, Section Knill Multivariable Calculus

Physics Section Handouts, Math21a, Spring 2004

All in one PDF (8Megs)

Week 1:	Syllabus Section Vectors Cross product Lines and Planes Distances	Week 2:	Curves Knots Arc Length Keplers Laws	Week 3:	Functions, level curves Partial derivatives PDE (practice partial derivatives)

Week 4:	Chain Rule Directional derivative Surfaces	Week 5:	Linearization Review Critical points	Week 6:	Lagrange Multipliers More on Maxima-Minima Double integrals The Gauss problem

Week 7:	Applications of 2D integrals Integration in Polar coordinates 3D integration Integration in Cylindrical coordinates	Week 8:	Spherical coordinates Volume of sphere and torus Vector Fields Scalar Line integrals Line integrals Line integrals II	Week 9:	Fundamental theorem of lineintegrals Perpetuum motion machines Greens theorem

Week 10:	Flux integrals Surface area Stokes	Week 11:	Conservative fields Nash problem Divergence theorem Gravity inside earth Divergence theorem II	Week 12:	Overview integral theorems Problems Beyond Calculus

Creative Commons License

This work is licensed under a Creative Commons License.

Please send comments to knill@math.harvard.edu

Math21a, Multivariable Calculus, Spring 2004, Department of Mathematics, Faculty of Art and Sciences, Harvard University