Math 13

Calculus of Vector-Valued Functions

General Information Schedule Homework Assignments Links Exams


Schedule

The following schedule is subject to change throughout the quarter.

Lecture Number Date Readings
(unqualified numbers refer to sections in text)
Brief Description
1 9/23 13.1, 13.2, 13.3, 13.4 Sections 13.1 and 13.2 are to be considered as a review. Please go through them on your own. In class we will focus on projections from Section 13.3 and on determinants, volumes and cross products from 13.4.
2 9/25 13.4 (cont.), 13.5 cross product, lines and planes
3 9/28 13.5(cont), 13.6 (we will just touch lightly)
Matrix Add./Sub || Matrix Multiplication
Quadric Surfaces (briefly), Matrix operations
4 9/30 14.1, 14.2 vector-valued functions
5 10/2 14.3 (through page 867), 14.4 arclength, motion
6 10/5 15.1, 15.2, 15.3, 15.4 Functions of several variables
7 10/7 15.6 directional derivative and gradients
8 10/9 'Derivative as a matrix' posted on here, also Section 15.5 Derivative as a matrix/Chain rule
9 10/12 Chain rule Section 15.5 and document posted on webwork Derivative as a matrix/Chain rule (cont.)
10 10/14 16.1, 16.2 Double integrals over rectangles
11 10/16 16.3 Double integrals over general regions
12 10/19 11.3 Polar Coordinates (We will also discuss cylindrical coordinates.)
x-hour 10/20 Review Review
13 10/21 16.4 Double Integrals over polar coordinates
14 10/23 16.4 (cont.), 16.5 Double integrals over polar coordinates. Double integral applications.
15 10/26 16.6 Triple integrals
16 10/28 16.9 Change of variable theorem.
17 10/30 16.7, 16.8 Integration in cylindrical coordinates. Integration in spherical coordinates.
18 11/2 TBA TBA
19 11/4 17.1, 17.2 Vector fields, line integrals
20 11/6 17.2 (cont.) Line Integrals
21 11/9 17.3 Fundamental Theorem for line integrals.
x-hour 11/10 Review Review
22 11/11 17.4 Greenís Theorem
23 11/13 17.5 Divergence and Curl
24 11/16 17.6 through Example 9 Parametrized surfaces and their tangent planes
25 11/18 Finish 17.6, possibly begin 17.7 Surface area and surface integrals of real-valued function
26 11/20 17.7 Surface integrals of Vector fields
27 11/23 17. 9 Also read page 1103 Divergence Theorem
28 11/30 17.8 Stokes Theorem
x-hour 12/1 17.8, 17.9. more examples from 17.8 and 17.9.
29 12/2 Review Review