Calculus III---Multivariable and Vector Calculus

Math 2210

Class location and Schedule:

LCB 215
T Th 6:00-7:30 PM


Instructor:

David George
LCB 318
tel: 801-581-8340
fax: 801-581-4148
george@math.utah.edu
office hours: T Th 5:00-5:50 PM

Syllabus

Textbook

Course Topics

This course covers introductory multivariable calculus---vectors in the plane and in 3-space, differential calculus in several variables, integration and its applications in several variables, vector fields and line, surface, and volume integrals. Green's and Stokes' theorems. In the text we will cover most sections in chapters 11-14.

Reading Schedule

Below is an approximate reading schedule. You should also consult the lecture and the homework assignments to gauge your reading. The following schedule might change (or appear) as the course proceeds.

Week

Dates

Textbook Sections

Topics

1 Jan. 9,11 11.1-11.3 (8th ed: 13.3,14.1-14.2) Coordinates in three-space, vectors, and the dot product
2 Jan. 16,18 11.4-11.5 (8th ed: 14.3-14.4) The cross-product, vector-valued functions, curvilinear motion (position, velocity and acceleration of a point).
3 Jan. 23,25 11.5-11.7 (8th ed: 14.4-14.5) Curvilinear motion continued, lines and tangent lines in 3-space, Curvature, principal normal and binormal vectors.
4 Jan. 30, Feb. 1 11.8-11.9 (8th ed: 14.6-14.7) Equations for surfaces in 3-D, cylindrical and spherical coordinates.
5 Feb. 5, 7 12.1-12.3 (8th ed: 15.1-15.3) Functions of two or more variables, Partial Derivatives, Limits and Continuity
6 Feb. 13, 15 12.3 (8th ed: 15.3) Midterm #1 and Limits and Continuity continued.
7 Feb. 20, 22 12.5-12.7 (8th ed: 15.5-15.7) Gradients, Directional Derivatives, Tangent Planes.
8 Feb. 27, March 1 12.4, 12.8 (8th ed: 15.4, 15.8) Differentiability, Maxima and Minima
9 March 6, March 8 13.1-13.2 (8th ed: 16.1-16.2) Multiple Integrals: Double Integrals over rectangles
10 March 13, March 15 13.3-13.5 (8th ed: 16.3-16.5) Double Integrals over general regions, integrals in polar coordinates and applications.
11 March 20, March 22 Spring Break!
12 March 27, March 29 13.7-13.8 (8th ed: 16.7-16.8) Triple Integrals in Cartesian, Cylindrical and Spherical Coordinates.
13 April 3, April 5 Review and Midterm #2
14 April 10, April 12 13.9-14.2 (8th ed: 16.9-17.2) General change of variables for multiple integrals, Vector Fields, Line Integrals
15 April 17, April 19 14.3-14.4 (8th ed: 17.3-17.4) Independence of Path, Integral Theorems in the Plane
16 April 24 14.4 (8th ed: 17.3-17.5) Review

Homework Assignments

Homework assignments will typically be assigned weekly, usually on Thursdays and collected the following Thursday before class. Late homework will not be accepted. Homework accounts for 30% of your final grade.

Homework Assignment

Due Date

Solution Set

Average/Total Score

Homework #1 (.pdf) Thurs. Jan 18th. Solution Set # 1 (.pdf) 86/100
Homework #2 (.pdf) Thurs. Jan 25th. Solution Set # 2 (.pdf) 83/100
Homework #3 (.pdf) Thurs. Feb. 1st. Solution Set # 3 (.pdf) 69/100
Homework #4 (.pdf) Thurs. Feb. 8th. Solution Set # 4 (.pdf) 83/100
Homework #5 (.pdf) Tues. Feb. 27th. Solution Set # 5 (.pdf) 84/100
Homework #6 (.pdf) Thurs. March 8. Solution Set # 6 (.pdf) 84/100
Homework #7 (.pdf) Thurs. March 29. Solution Set # 7 (.pdf) 76/100
Homework #8 (.pdf) Thurs. April 19. Solution Set # 8 (.pdf) 79/100
Homework #9 (.pdf) Thurs. April 26. Solution Set # 9 (.pdf) 59/100

Exams

There will be 2 midterms and one comprehensive final. Each midterm is worth 15% of your grade. Together the midterms constitute 30% of your grade. The final accounts for 40% of your grade. The final is on May 1st, Tuesday of finals week, from 6:00-8:00 PM in the regular class location---LCB 215. The tentative dates for the midterms are below.

Exam

Tentative Date

Solution Set

Practice Problems

Average/Total Score

Midterm #1 (.pdf) Tues. Feb. 13 Midterm #1 Solutions(.pdf) Midterm #1 Practice (.pdf). Some Practice Solutions (.pdf) 80/100
Midterm #2 (.pdf) Thurs. April 5 Midterm #2 Solutions (.pdf) Midterm #2 Practice(.pdf) . Practice Solutions (.pdf) 76/100
Final (.pdf) Tues. May 1st. Final Solutions (.pdf) Supplemental Material(.pdf) 73/100

Supplemental Material