In Math 10, you learned the differential calculus of functions of one
variable. In this course, you will learn the integral calculus of
functions of one variable. The process we will use to develop the concept
of the integral is very similar to the process we used in developing the
derivative in Math 10. It will begin by approximating a quantity and
proceed an exact answer by taking a limit. As with derivatives, computing
integrals from this definition is very hard and not very practical, so (as
with derivatives) we will develop better tools for computing integrals.
These will center around the Fundamental Theorem of Calculus, which
provides a remarkable connection between integrals and derivatives.
Notice that the goal is not to provide the student with a set of
computational techniques and procedures for solving a set of predefined
problems. Rather, the emphasis is on the fundamental concepts and how
they relate to each other. Computation is an important part of this
process, but it is not the only one, nor is it the primary one. Students
who approach this course assuming that "the answer" is the only thing that
counts will find it frustrating and are not likely to do well.
The material to be covered includes: the definite integral,
antiderivatives and the indefinite integral, the Fundamental Theorem of
Calculus, integration techniques, applications of integrals, logarithms and
exponential functions, inverse trigonometric functions, and improper
integrals. See the the course
outline for more details.
||Math 12 - 1 (Winter 2000) web pages|
Created: 24 Mar 1998
Last modified: 28 Dec 1999 16:14:56