# Calculus of Several Variables (Math 22) Spring 1999, UCSC

Lecture Sections
Thim Lecture 1 M W F, 8-9:10pm 11P: T TH 10-11:50am Applied Sci 268.
12P: M W 2-3:50pm Applied Sci 268.
13p: M W 4-5:50pm Applied Sci 295.

Instructor
Check instructor's web site periodically for revised versions of this syllabus, and to obtain copies of old tests and quizzes.

Teaching Assistants
Don Kim, and Kirk Lackey
The section assignments for each TA are as follows: Don, Section 12p; Kirk, Sections 11P and 13P.

Course Description
Continuation of Calculus 19B. Study of derivatives and integrals of functions of several variables. For a list of topics see the Lecture and reading schedule below.

Prerequisites
Calculus 19B--a sound understanding of derivatives and integrals of functions of one variable.

Textbook
Calculus Early Transcendentals, by J. Stewart, Third Edition.

Homework and Quizzes
There will be weekly homework assignments to be turned in to the teaching assistants. Students in M-W sections will turn in their homework on Wednesdays, and students in T-Th sections will turn in their homework on Thursdays. Late homeworks will not be accepted. Also, there will be weekly quizzes. Students in M-W sections will take their quizzes on Mondays, and students in T-Th sections will take their quizzes on Tuesdays.

We will cover chapters 11, 12, and 13 of the textbook. The lecture schedule appears below. You should try to read the sections, or at least glance at them, before coming to class.
 Dates Lectures MarchApril 312 WF 11.111.2 Three dimensional coordinatesVectors April 579 MWF 11.311.411.5 Dot productCross productLines and planes 121416 MWF 11.611.711.8 Quadric surfacesVector Functions and Space curvesArc length and Curvature 192123 MWF 11.911.1012.1 Motion in Space: Velocity and AccelerationCylindrical and Spherical coordinatesFunctions of several Variables 262730 MWF 12.212.3. Limits and ContinuityPartial DerivativesReview May 3 57 MWF .12.412.5 Midterm (covers up to 12.2)Tangent planes and DifferentialsThe chain rule 101214 MWF 12.612.712.8 Directional derivatives and GradientMax and MinLagrange Multipliers 171921 MWF 13.113.2 13.3 Double integrals over rectanglesIterated integralsDouble integrals over general regions 242628 MWF 13.413.513.6 Double integrals in polar coordinatesAppications of double integrals Surface area June 124 T*WF 13.713.8. Triple integralsTriple integrals in cylindrical and spherical coordinates Review 7 M . Final (Comprehensive)

* Exchange day (Monday classes will meet on Tuesday).

Assignments
The following are the homework assignments for the first two weeks. The rest will be announced later, and will be posted on this website. You should plan to work on these problems over a period of several days. Getting a head start on each assignment is perhaps the most critical factor determining your success in this class.
 Homework # Due Date Problems 1 Apr 7/8 11.1) 2, 8, 12, 18, 24, 36, 40, 46; 11.2) 4, 12, 16, 20, 28, 36; 11.3) 8, 9, 14, 22. 2 Apr 14/15 11.3) 38, 43, 52, 54, 62; 11.4) 4, 8, 12, 15, 20, 22, 26, 30; 11.5) 2, 6, 20, 24, 28, 36, 44, 55; 11.6) 2, 6. 3 Apr 21/22 11.6)18, 22, 26, 44; 11.7)2, 6, 8, 10, 24, 36, 38, 49; 11.8)4, 12, 18, 24, 32, 34. 4 Apr 28/29 11.9)4, 6, 10, 14, 18, 20; 11.10)4, 10, 16, 22, 26, 30, 36, 40, 54, 63; 12.1)4, 6, 12, 16, 34, 40, 44, 54. 5 May 5/6 12.2)6, 8, 12, 16, 30, 36, 44, 49; 12.3)2, 6, 10, 20, 49, 50, 57, 91. 6 May 12/13 12.4)2, 4, 12, 16, 20, 22, 24, 26, 30, 32; 12.5)2, 6, 8, 14, 20, 26, 30, 34, 38. 7 May 19/20 12.6)2, 6, 10, 18, 24, 26, 36, 48; 12.7)2, 8, 20, 26, 30, 36, 48, 50; 12.8)4, 8, 16, 20, 23. 8 May 26/27 13.1)1, 4, 8, 14, 16; 13.2)4, 10, 20, 26, 28, 36; 13.3)4, 10, 18, 20, 24, 36, 42. 9 June 2/3 13.4)2, 4, 16, 32, 22; 13.5)2, 4, 8, 14, 16; 13.6)2, 6, 8, 17. 10 Not to be turned in 13.7)3, 9, 17, 29, 35, 37; 13.8)3, 5, 9, 13, 17, 23, 33, 35, 37.

Tests and exams
There will be a midterm on Monday May 3. The final exam will be on Monday, Jun 7, 12-3pm.