Calculus I


1. Short
description:
Calculus
with the two branches of calculus: differential calculus and integral calculus. indefinite
or definite integrals. Calculus I includes Limits
and continuity, differentiation, chain rule, mean value theorems and applications,
integration, fundamental theorem of calculus, and applications of integration. 2. Course
objective: It is
a mistake to think of mathematics in general as primarily a tool for finding answers
(although it is also a mistake to think, as many graduate students do, that calculating is
an inferior, unworthy aspect of mathematics). The primary importance of calculus in the
hard sciences is that it provides a language, a conceptual framework for describing
relationships that would be difficult to discuss in any other language. Therefore, the
purpose of learning differential calculus is not to be able to compute derivatives. In
fact, computing derivatives is usually exactly the opposite of what one needs to do in
real life or science. In a calculus course, one starts with a formula for a function, and
then computes the rate of change of that function. But in the real world, you usually
don't have a formula. The formula, in fact, is what you would like to have: the formula is
the unknown. By the end of the course you will be
expected to 3.
Formal
requirement: Homework
is an important part of learning mathematics and will be assigned daily. Every assigned
problem should be tried and the answer checked. It is permissible to discuss problems with
other students or relatives. It is not permissible to copy another student's work. Do your
best to think through the problems and understand why things work the way they do.
Homework should take anywhere from 30 minutes to an hour, depending on the type of
assignment. Homework will be issued in class and submitted one week later. On test days
all homework associated with that test will be collected and graded. Homework should be
corrected and added, as the material is better understood. 4. Textbook: (1) J. Stewart,
Single Variable Calculus, 4^{th} ed, Brooks/Cole (1999). (2) P. O. Neill, Advanced Engineering Mathematics, 4^{th}
ed, Brooks/Cole (1999). (3) Courant, Richard and John, Fritz. Introduction to Calculus and
Analysis, New York: SpringerVerlag; 