MATH 121-01/02, Calculus I, Fall 2011

Abstract

Calculus is a powerful tool in modeling real world problems. This course provides an overview of a portion of calculus with some emphasis placed on applications. The style of this course may be different from your experience in previous math courses – even if you have studied some calculus in the past. Calculus is more than just rules for turning algebraic formulas into other algebraic formulas. Indeed, with the advances in current technology, much of the algebraic side of the subject can be done automatically by computers. Real understanding comes in knowing what the formulas tell you, and how to apply them in real and diverse situations. We will develop both a theoretical and conceptual understanding of the mathematics of calculus as well as the ability to “manipulate symbols.” Additionally, we will work on skills of mathematical justification and communication, that is, showing (with mathematical rigor) how a solution is arrived upon and follows from previously established mathematical truths. Every topic is presented algebraically, numerically, in graphs, and in words. You will be asked to engage the course material from all of these points of view. Lastly, much of the content of this course will be discovered through active learning in which you, with your classmates (and some guidance from your instructor) will “discover” some of the fundamental properties and theorems of calculus. To this end, you will be encouraged daily, in class, to explore and discuss the mathematics of calculus with your classmates.