SYLLABUS

Calculus I (Math 141, Sections 11 & 12)
Fall 2000, USC

Lecture Recitations
M W F 12:20-1:10 am PSC 002. 11: T TH 11-11:50 am LC 115;
12: T TH 12:30-1:20 am LC 115;
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
Joseph Patterson

Course Description
This is an introduction to Calculus. We will study derivatives and integrals together with a range of their applications in geometry, physics, and engineering.

Prerequisites
Math 112 or Math 115--familiarity with basic functions and their graphs.

Textbook
Calculus, by J. Varberg, Pursell, and Rigdon, Eighth Edition.

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

Also, there will be weekly quizzes every Thursday. 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 may 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 keep up with your reading assignments; otherwise, you may significantly compromise your ability to benefit from the lectures.
Dates Lectures
Aug 25 F 2.1, 2.2 Functions and their Graphs
28
30		 M
W		 2.2, 2.3
2.4		 Trig functions
Intro to Limits
Sep 1 F 2.5 Rigorous Definition of Limits
4
6
8		 M
W
F		 .
2.6
2.7, 2.8		 Labor Day-no classes
Limit Theorems
Limits of Trig. Functions, Asymptotes
11
13
15		 M
W
F		 2.9
3.1
3.2		 Continuity
Intro to Derivatives
Definition of Derivative
18
20
22		 M
W
F		 3.3
3.4
3.5		 Rules for Derivatives
Derivatives of Trig Functions
The Chain Rule
25
27
29		 M
W
F		 3.6, 3.7
.
.		 Leibniz Notation
Review
Midterm 1(covers up to and including 3.4)
Oct 2
4
6		 M
W
F		 3.8
3.9
3.10		 Implicit Differentiation
Related Rates
Differentials and Approximations
9
11
13		 M
W
F		 4.1
4.2
4.3		 Maxima and Minima
Monotonicity and Concavity
Local Maxima and Minima
16
18
20		 M
W
F		 .
4.4
4.6		 Fall Break-no classes
More Max-Min Problems
Sophisticated Graphing
23
25
27		 M
W
F		 4.7
5.1
5.2		 The Mean Value Theorem
Indefinite Integrals
Intro to Diff Equations
30 M 5.3 Sums and Sigma Notation
Nov 1
4		 W
F		 5.4
5.5		 Intro to Area
Definite Integrals
6
8
10		 M
W
F		 5.6
.
.		 The First Fundamental Theorem of Calc
Review
Midterm 2(covers up to and including 5.4)
13
15
17		 M
W
F		 5.7
5.8
6.1		 The Second Fundamental Theorem of Calc
Evaluating Definite Integrals
The Area of a Plane Region
20
22
24		 M
W
F		 6.2
.
.		 Volumes of Solids
Thanksgiving Recess-no classes
Thanksgiving Recess-no classes
27
29		 M
W		 6.4
6.5		 Length of a Plane Curve
Work
Dec 1 F 6.6 Center of Mass
4
6
8		 M
W
F		 6.7
.
.		 Chapter Review
Review
Review
14 Th . 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 Aug 29 1.5) 2, 7, 14;
1.6) 2, 10, 18, 37, 38, 42 ;
1.7) 4, 10;
1.8) 25.
2 Sep 5 2.1) 4, 7, 8, 10, 14 a b, 15, 16, 34;
2.2) 2, 12, 24;
2.3) 11 a b, 26 a b, 42, 45;
2.4) 4, 8, 12, 30, 32.
3 Sep 12 2.5) 2, 8, 11;
2.6) 6, 10, 14, 16, 36.
4 Sep 19 2.7) 1, 5, 6, 17;
2.8) 2, 6, 16, 22, 34, 36;
2.9) 2, 15, 40, 43, 47.
5 Sep 26 3.1) 9, 13;
3.2) 14, 20, 32;
3.3) 8, 14, 18, 38, 50, 52;
3.4) 7, 11, 12, 16, 28.
6 Oct 3 3.5)4, 8,14, 30, 46, 52;
3.6)2, 5, 10, 22, 39;
3.7)4, 30, 34.
7 Oct 10 3.8) 2, 14, 26, 28;
3.9) 2, 4, 13, 15.
8 Oct 17 3.10)10, 18, 23, 24;
4.1) 2, 8, 20, 22, 23, 30;
4.2) 2, 14, 24, 30, 35, 52.
9 Oct 24 4.3)2, 12, 18;
4.4)4, 6, 8, 23.
10 Oct 31 4.6) 2, 14, 28, 30, 40;
4.7) 2, 6, 8, 22, 33, 34, 46;
5.1)16, 21, 29, 34, 39.
11 Nov 9 5.2)3, 10, 16, 22, 25;
5.3) 2, 10, 18, 22, 36;
5.4) 2, 8, 12, 20, 24.
12 Nov 14 5.5)4, 8, 16, 24;
5.6)2, 8, 13, 46.
13 Nov 21 5.7)4, 10, 16, 37;
5.8)2, 6, 10, 31, 34.
14 Nov 28 6.1)2, 6, 12, 16, 20, 31, 36;
6.2)2, 6, 17, 18, 20, 23.
15 Dec 5 6.3)2, 10, 17, 19;
6.4)2, 10, 15, 18, 19;
6.5)3, 5, 13, 19.

Tests and Exams
There will be two midterms, on Friday Sep 29 and on Friday Oct 10. The final exam will be on Thursday, Dec 14, 2 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%, midterms, 20% each, and the final exam, 40%.

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 10 hours each week. Also, it is very important that you faithfully attend all lectures.

A good deal of class time shall be devoted to working through problems. Do not get into the habit of sitting passively and expecting the professor to make you understand. Rather, you should 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 privilege, 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.