SYLLABUS

Calculus for Science and Engineering (Math 19A)
Winter 2000, UCSC

Lecture Sections
M W F 12:30-1:40 pm Earth&Marine B206. 11P: M W 2-3:50 pm Applied Sci 268;
12P: M W 4-5:50 pm Applied Sci 268;
13P: T TH 4-5:50 pm Applied Sci 295;
14P: T TH 12-1:50 pm Applied Sci 295;
15P: T TH 6-7:50 pm Crown Clrm 208;
16P: M W 5-6:50 pm Earth&Marine B214.
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
Ralph Gomez, Atichart Kettapun, and Sara Solberg
Each TA will conduct two sections where their students take quizzes and turn in their homeworks. Here are the section assignments for each TA: Ralph, Sections 15P and 16P; Atichart, Sections 12P and 14P; and Sara, Sections 11P, and 13P.

Course Description
This is the first half of a course on Calculus of single variables. We will study limits and derivatives of functions within the context of applications to Physics, Geometry, Biology, Economics, and Engineering. The main goal of the class is to develop a sound intuitive understanding of derivatives, as well as the formal skills required to evaluate and apply them to a wide range of problems.

Prerequisites
A precalculus course such as Math2B or Math3A--familiarity with functions and their graphs; specifically, an understanding of exponential, logarithmic, and trignometric functions, and basics of analytic geometry.

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
January 5
7		 W
F		 1.1
1.2, 1.3		 Preview of Calculus
Review of basics of functions and their graphs
10
12
14		 M
W
F		 1.5,1.6
2.1
2.2		 Exponential and logarithmic functions
Tangent and velocity problems
Limit of a function
17
19
21		 M
W
F		 .
2.3, 2.4
2.5		 MLK Jr. day, no class
Limit laws; Precise definition of limit
Continuity
24
26
28		 M
W
F		 2.6
2.7, 2.8
2.9		 Limits at infinity, asymptotes
Rates of change; Derivatives
Derivative as a function
31  M 3.1 Derivatives of polynomials and exponential functions
February 2
4		 W
F		 3.2
3.3		 The product and quotient rules
Rates of change in natural and social sciences
7
9
11		 M
W
F		 .
3.4, 3.5
3.6		 Midterm(covers up to and including 2.9)
Derivatives of trig. functions; The chain rule
Implicit differentiation
14
16
18		 M
W
F		 3.7
3.8
3.9		 Higher derivatives
Derivatives of logarithmic functions
Hyperbolic functions
21
23
25		 M
W
F		 .
3.10, 3.11
4.1		 President's day, no class
Related rates; Linear approximations
Maximum and minimum values
28 M 4.2 The mean value theorem
March 1
3		 W
F		 4.3
4.4, 4.5		 Derivatives and graphs
L'Hopital's rule; Summary of curve sketching
6 
8
10		 M
W
F		 4.7
4.8
4.9		 Optimization problems
Applications to economics
Newton's method
13
16		 M
TH		 .
.		 Review
Final (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 Jan 12-13 1.1) 2, 4, 10, 14, 19, 22, 28, 41, 44, 48, 52; 
1.2) 2, 4, 8, 11, 20; 
1.3) 2, 4, 6, 27, 36, 46.
2 Jan 19-20 1.5) 8, 10, 16; 
1.6) 10, 12, 24, 26, 36; 
2.1) 1, 4, 6; 
2.2) 2, 4, 14, 16.
3 Jan 26-27 2.3) 2, 8, 10, 12, 35, 47; 
2.4) 2, 6, 13, 16, 26, 28; 
2.5) 2, 6, 8, 10, 16, 43, 61.
4 Feb 2-3 2.5) 44, 59; 
2.6) 2, 4, 8, 16, 18, 22, 49, 51, 52; 
2.7) 2, 6 a b, 12 a b; 
2.8) 1, 4, 7, 16, 18, 20; 
2.9) 4, 8. 
5 Feb 9-10 2.9) 43; 
Pg.179) 8; 
3.1) 6, 12, 20, 40, 44, 47, 51; 
3.2) 2, 4, 6, 16, 24, 41; 
3.3) 8, 11, 12, 14, 18. 
6 Feb 16-17 3.4) 8, 13, 18, 30, 33, 35, 36, 39, 46, 47;
3.5) 2, 6, 12, 39, 45, 53, 54, 73, 78;
3.6) 4, 8, 16, 26, 40, 42, 69.
7 Feb 23-24 3.7) 4, 8, 12, 20, 24, 32, 35, 39, 44, 51, 53;
3.8) 4, 8, 22, 32, 36, 40;
3.9) 8, 12, 16, 19, 32, 38, 49, 53.
8 March 1-2 3.10) 6, 9, 12, 14, 21;
3.11) 14, 18, 26, 28, 34, 39, 42;
4.1) 4, 8, 14, 16, 32, 50, 60, 63.
9 March 8-9 4.2) 2, 6, 18, 27, 34, 35;
4.3) 12, 14, 23, 35, 38, 44, 72;
4.4) 2, 6, 10, 16, 57, 77;
4.5) 4, 8, 14, 44.
10 March 15 4.7) 4, 10, 15, 28, 33, 35;
4.8) 14, 21, 23;
4.9) 4, 6, 16.

Tests and Exams
There will be one midterm, on Monday, February 7. The final exam will be on Thursday, March 16, 4-7 pm. No calculators, or notes will be allowed during 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.