Math 13, Calculus of vector-valued functions
Last updated November 20, 2002

## Covered topics

Text-book: Basic Multivariable Calculus, by J. Marsden, A. Tromba, A. Weinstein, corrected 3rd printing, 2000, Springer, W.H.Freeman and Company.

Lectures Sections in Text Brief Description
Day 1:  9/25 1.1, 1.2 Vectors and inner product, equations of a line
Day 2:  9/27 1.4 Cross product, equation of a plane
Day 3:  9/30 1.5, 1.6 n-dimensional Euclidean space; curves in space
Day 4:  10/1
x-hour
2.1 Graphs and level surfaces
Day 5:  10/2 2.1, 2.2 Graphs and level surfaces; Partial derivatives
Day 6:  10/4 2.3 Tangent planes; Jacobian matrix
Day 7:  10/7 2.4 Chain rule
Day 8:  10/9 2.5 Gradients: fundamental properties
Day 9:  10/11 2.5 Gradients and tangent planes
Day 10:  10/14 4.1, 4.2 Acceleration; Arc length
Day 11:  10/15
x-hour
4.2, 4.3 Arc length; Vector fields
Day 12:  10/16 4.3, 4.4 Vector fields; Curl and divergence
Day 13:  10/18 4.4, 5.1 Curl and divergence; Integrals; Cavalieri's principle
Day 14:  10/21 5.2 The double integral over a rectangle
Day 15:  10/23 5.3 The double integral over general regions
Day 16:  10/25 5.3, 5.4 The double integral over general regions; Triple integrals
Day 17:  10/28 5.4 Triple integrals
Day 18:  10/29
5.4 Triple integrals
Day 19:  10/30 5.5 Change of variables: cylindrical coordinates
Day 20:  11/4 5.5 Change of variables: spherical coordinates
Day 21:  11/5
x-hour
5.6 Applications of multiple integrals
Day 22:  11/6 6.1 Line integrals
Day 23:  11/8 6.1 Line integrals
Day 24:  11/11 6.2 Parametrized surfaces
Day 25:  11/13 6.3 Surface area
Day 26:  11/15 6.3, 6.4 Surface area; Surface integrals
Day 27:  11/18 6.4 Surface integrals
Day 28:  11/20 6.4, 7.1 Surface integrals; Green's theorem
Day 29:  11/22 7.1, 7.2 Green's theorem; Stokes' theorem
Day 30:  11/25 7.2 Stokes' theorem
Day 31:  11/26
x-hour
7.3 Gauss' theorem
Day 32:  12/2 7.4 Path independence; FTC
Day 33:  12/4 -- Review