SYLLABUS

Calculus for Science and Engineering (Math 19B)
Spring 2000, UCSC

Lecture Sections
M W F 3:30-4:40 pm Thimann 3. 11P: M W 12-1:50 pm Applied Sci 268;
12P: T TH 6-7:50 pm Applied Sci 295;
13P: T TH 12-1:50 pm Applied Sci 295;
14P: M W 10-11:50 am Applied Sci 295;
15P: T TH 4-5:50 pm Applied Sci 268.
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 Assistants

Course Description
This is the second half of a course on Calculus of single variables. We will study integrals, infinite series, and their applications in geometry, physics, and engineering.

Prerequisites
Math 19A--a sound understanding of derivatives.

Textbook
Calculus, by J. Stewart, Fourth 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 homewrok on Wednesdays, and those in T-Th sections will turn in their homework on Thursdays. Late homeworks will not be accepted.

Also, there will be weekly quizzes every Monday or Tuesday (depending on which section you attend). 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. There will be a number of practice quizzes during the lectures as well.

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 make a sincere effort to read the sections, before coming to class. If you do not keep up with your reading schedule, you may significantly compromise your ability to benefit from the lectures.
Dates Lectures
March 29
31		 W
F		 4.10
5.1, 5.2		 Antiderivatives
Areas and Definite Integrals
April 3
5
7		 M
W
F		 5.3
5.4, 5.5
5.6		 Fundamental theorem of Calculus
Indefinite Integrals and The Substitution Rule
The logarithm as an Integral
10
12
14		 M
W
F		 6.1
6.2, 6.3
6.4		 Areas Between Curves
Volumes
Work
17
19
21		 M
W
F		 6.5
7.1
7.2, 7.3		 Average Values
Integration by parts
Trig. Integrals
24
26
28		 M
W
F		 7.4
7.5
7.8		 Partial Fractions
Review of Integration Techniques
Improper Integration
May 1
3
5		 M
W
F		 8.1
8.2
.		 Arc Length
Surfaces of Revolution, Review
Midterm (Covers up to and including 7.8)
8
10
12		 M
W
F		 8.3
11.1, 11.2
11.3 		Applications to Physics and Engineering
Sequences and Series
The Integral Test
15
17
19		 M
W
F		 11.4
11.5, 11.6
11.7		 The Comparison Test
Alternating Series, Ratio Test
More on Convergence
22
24
26		 M
W
F		 11.8
11.9, 11.10
11.11		 Power Series
Taylor Series
The Binomial Series
29
31		 M
W		 .
11.12		 Holiday
Application of Taylor Series
June 2
6		 F
T		 .
.		 Review
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 Apr 5-6 4.10) 2, 12, 20, 22, 60, 62, 66, 68, 74;
5.1) 2, 4, 11, 16, 20, 24;
5.2) 2, 6, 16, 32, 34, 37, 44, 52.
2 Apr 12-13 5.3) 2, 4, 6, 20, 22, 32, 57;
5.4) 2, 8, 12, 22, 50, 54, 58;
5.5) 4, 10, 14, 20, 28, 50, 56, 78;
5.6) 3, 4, 5, 6.
3 Apr 19-20 6.1) 6, 8, 16, 28, 32, 40;
6.2) 2, 6, 31, 45, 46, 47, 59, 61;
6.3) 4, 16, 27, 41, 42, 44;
6.4) 3, 6, 12, 16, 24.
4 Apr 26-27 6.5) 3, 8, 10, 13, 17, 21, 22;
7.1) 4, 9, 10, 30, 38, 41, 55, 57;
7.2) 5, 10, 51, 61;
7.3) 2, 11, 22, 35, 39.
5 May 3-4 7.4) 3, 6, 16, 20, 26, 43, 45, 57;
7.5) 1, 4, 12, 29, 37;
7.8) 2, 8, 14, 17, 27, 41, 50, 65.
6 May 10-11 8.1)2, 8, 22, 36;
8.2)7, 9, 17, 27, 31, 36.
7 May 17-18 8.3) 20, 22, 25, 32, 35, 38, 39;
11.1) 4, 8, 10, 12, 16, 47;
11.2) 12, 14, 22, 23, 36, 49, 52;
11.3) 4, 6, 12, 20, 28, 32.
8 May 24-25 11.4) 2, 4, 10, 14, 20, 24, 37;
11.5) 3, 7, 8, 24;
11.6) 2, 8, 13, 19, 20, 42;
11.7) 2, 8, 12, 18, 30.
9 May 31-June 1 11.8) 4, 8, 14, 30;
11.9) 6, 10, 14, 28, 37;
11.10) 4, 10, 14, 17, 26, 36, 41, 46;
11.11) 4, 8, 11, 14, 15.
10 Not to be turned in TBA

Tests and Exams
There will be one midterm, on Friday, May 5. The final exam will be on Tuesday, June 6, 12-3 pm. No calculators, or notes will be allowed during the exams. Note: bring a bluebook to the exams..

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 passively and expect 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.

Calculus is one of the greatest accomplishments of the human mind. Having the opportunity to study it is a true privelege, and an excellent chance to practice the art of thinking in a clear and organized way. I hope that this class will be a rewarding experience for you.