Syllabus

Multivariable Calculus (Math23B)
Fall 1999, UCSC

Lecture Sections
T TH 10-11:45 am Stevenson Acad 175 11P: M W 2-3:50 pm Applied Sci 295.
12P: M W 4-5:50 pm Applied Sci 295.

Instructor
Professor Mohammad Ghomi Check the course web site periodically for revised versions of this syllabus, and to obtain homework assignments and copies of old tests and quizzes.

Teaching Assistant
Kirk Lackey

Course Description
Continuation of Calculus 23A. We will study integrals of scalar and vector valued functions of several variables, and their applications to a range of problems in geometry, physics, and engineering.

Our goal is to develop an intuitive understanding of the integrals, as well as the formal skills required to set up and evaluate them, within the context of a variety of applications. The main learning objectives of the course are as follows:

Prerequisites
Calculus 23A--familiarity with basics of vector geometry (inner product and cross product), vector valued functions (divergence and curl), and basic rules for computing single integrals.

Textbook
The required text is Vector Calculus, by Marsden and Tromba, Fourth Edition. There is also an accompanying manual, Study Guide For Vector Calculus, by Pao and Soon, which you might find helpful.

Homework and Quizzes
There will be weekly homework assignments to be turned in every Wednesday to the teaching assistant. Late homeworks will not be accepted.

Also, there will be weekly quizzes every Monday. No calculators, textbooks, or notes will be allowed during quizzes. You should save copies of these quizzes as they are a very good source for preparing for the final and midterms.

Doing the homework problems is the most important part of this class. You may work with a group of your classmates if you are all at about the same level; however, you should definitely try to do many problems on your own. Further, try to practice doing at least some of the problems in settings which resemble that of the test and quizzes, i.e., without using your calculator or constantly referring to the textbook.

Lecture and Reading Schedule
You should try to read the sections, or at least glance at them, before coming to class.
Dates Lectures
Sep 23 TH 5.1, 5.2 Intro to double integrals: Cavalieri's Principle, and Fubini's theorem
28
30		 T
TH		 5.3
5.4		 Double integrals over general regions
Changing the order of integration, The mean value theorem
Oct 5
7		 T
TH		 5.6
6.1		 Triple integrals
Geometry of mappings from plane to plane
12
14		 T
TH		 6.2
6.3		 Change of variables theorem, the Jacobian
Applications: average values, and center of mass
19
21		 T
TH		 7.1
7.2		 Path integrals
Line integrals, total work
25
28		 T
TH		 7.3
7.4		 Parametrized surfaces
Area of Surfaces, Review
Nov 2
4		 T
TH		 .
7.5		 Midterm(covers up to 7.2)
Surface integrals of scalar functions
9
11		 T
TH		 7.6
8.1		 Surface integrals of vector functions
Green's theorem
16
18		 T
TH		 8.2
8.3		 Stokes theorem
Conservative vector fields
23
25		 T
TH		 8.4
.		 Gauss's theorem
Thanksgiving (No Class)
30 T 8.5 Some more applications
Dec 2 TH . Review
7 T . Final Exam(Comprehensive)

Assignments
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 Sep 29 5.1) 1 a c, 2 a c, 4, 5, 6, 9;
5.2) 1 c, 2 c, 3, 5, 6.
2 Oct 6 5.3) 1 c, 2 a, 3, 5, 8, 11, 12;
5.4) 1 c, 2 b, 5, 7, 9.
3 Oct 13 5.6) 4, 5, 10, 12, 19, 25;
6.1) 1, 3, 7, 8.
4 Oct 20 6.2) 1, 3, 9, 13, 21, 29;
6.3) 2, 4, 9, 10, 17.
5 Oct 27 7.1) 2c, 4, 9, 12;
7.2) 1b, 2a, 3, 4, 17, 18.
6 Nov 3 7.3) 2, 5, 11, 12;
7.4) 3, 4, 6, 7, 11.
7 Nov 10 7.4 14, 16;
7.5) 2, 4, 9, 10, 11, 15.
8 Nov 17 7.6)2, 3, 4, 15, 16;
8.1) 2, 4, 12, 13, 20.
9 Nov 24 8.2) 2, 3, 8, 17, 19;
8.3) 4, 5, 7, 10, 15a.
10 Dec 1 8.4) 1, 3, 7, 8, 9, 13, 14, 18.

Tests and Exams
There will be one midterm, on Tuesday, November 2. The final exam will be on Tuesday, Dec 7, 8-11 am. No calculators, or textbooks will be allowed during the exams; however, for the midterm and the final, you may bring a single sheet of paper bearing formulas. .

Grading
The final grade is based on homeworks and quizzes, 20%, midterm, 35%, and the final exam, 45%.

A Few More Study Hints and Guidelines
Learning Mathematics is a demanding affair. It requires a good deal of self discipline and hard work to appreciate the power and beauty of the subject. Further, solving Calculus problems, much like playing a musical instrument, is a skill, which can be developed only through persistent practice. You should plan to work on your exercises everyday, and for a total of at least 12 hours each week.

A good deal of class time shall be devoted to working through problems. Do not sit back and dare the professor to make you understand. Take out your paper and pencil and try to do the problems at the same time with your instructor. If something is unclear to you, feel free to ask questions, and if you need more help, go see your instructor and/or the TA during the office hours. If you cannot come during the office hours, you are welcome to knock on the professor's door at another time, or send an email for an appointment.