Welcome to Math S-1ab

This course meets Monday-Friday, 10am-noon in SC 309. The discussion section meets Monday-Friday, 2-3pm in SC 310.

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 π, the area of the unit circle, is roughly 22/7 (in fact, Archimedes showed that π 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 π 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 explore models of the world around us...

Goals/Objectives

Our goal is to obtain a sound, working knowledge of basic, single variable Calculus.  This means not only being able to solve exemplary problems, but understanding the major concepts problem-solving techniques. Students who complete this course with high grades 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.
     

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Copyright ©2004 The President and Fellows of Harvard College
Last updated July 19, 2004 .