Math 12 Course Goals:

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 integral is very similar to the process we used in developing the derivative in Math 10. It will begin by approximating a quantity and taking a limit (this will be the definition of the integral). As with derivatives, computing integrals from the 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 techiques, applications of integrals, logarithms and exponential functions, inverse trigonometric functions, and improper integrals. See the the course outline for more details.