Math S-1ab - Calculus I and II

Instructors: John Mackey (June 26 - July 20) and Robert Winters (July 21 - Aug 14)
Course Assistant: Nick Ramsey

Some useful links: Syllabus Homework

Overview

In this course, we'll cover the fundamental notions of Calculus. First, we'll review the notion of function.  Next, we'll explore infinity and the notion of limit.  These ideas will be illustrated with sequences and series.

The concepts of function and limit are basic, and when we're comfortable with those ideas, we'll be ready to embark upon one of the greatest journey's of human history: a journey through the world of Calculus!

We'll begin our journey with the the derivative. With this new notion, countless problems which once perplexed and stymied the human mind become solvable!  Many problems, which previously required laborious techniques to solve, now can be dismissed in a few well thought lines. You will solve many such problems yourselves.

Next, we encounter the integral.  Archimedes showed that Pi, the area of the unit circle, is roughly 22/7 (in fact, Archimedes showed that Pi lies between 3 10/71 and 22/7). For the next two millenia, obtaining more accurate estimates required stupendous efforts from skilled mathematicians. Suddenly, armed with the concept of the integral, Sir Isaac Newton effortlessly approximates Pi to sixteen decimal places! (Found as a ``By the way'' comment amidst weightier computations!)

So powerful are these newfound techniques that our entire conception of the Universe is changed.  Our last journey together will involve getting a first hand look at this glorious new conception: we shall understand how planets move...

Goals/Objectives

Our goal is to obtain a sound, working knowledge of basic, single variable Calculus.  This means understanding the major concepts and being able to solve exemplary problems. Upon completion of this course, you should be in a good position to move on to multivariable calculus or linear algebra. For those in high school, successful completion of this course will put you way ahead of the game should you be planning to take AP Calculus or first year College Calculus.

Grading

Homework counts 25% toward the course grade.
The three hour exams each count 15% for a total of 45% toward the course grade.
The final exam counts 30% toward the course grade.

Course syllabus

Page maintained by Robert Winters.
Last updated: June 25, 2001