Calculus for Liberal Arts: a Humanistic Approach

Abstract:

Calculus has played an enormous role in the development of modern science and technology. It still constitutes the primary college mathematics course for those continuing in mathematics and other technical fields. Liberal arts students should be exposed to this important branch of mathematics in a positive way, one which they will find relevant and interesting. Although it has had an enormous impact on their lives and is the cornerstone of modern mathematics and science, Calculus is often ignored in general education courses. Some argue that it is impossible to do calculus without sufficient algebra skills and many or most liberal arts students are lacking those skills. It has been deemed unproductive to force these students into yet another attempt to learn algebra; and therefore calculus is not available to them. This argument, while it once had some merit, is really not compelling today. With computer algebra systems readily available there is no reason liberal arts students with weak algebra backgrounds must be denied an opportunity to understand calculus concepts or to use calculus concepts to solve problems. There still, however, remains the question of interest and a conceptual framework. Why should students who do not plan to use calculus in their fields have any interest in it? Algebra and calculus are rarely presented in a social or historical context. This makes it difficult for liberal arts students to find them relevant. This paper will outline an approach to calculus for the liberal arts student that puts it in a cultural and historical context. Calculus can be presented in terms of its role in the Enlightenment and its historical and cultural significance. Then students from all disciplines would have a framework of interest in which to work. They should see the calculus as one of the most profound intellectual achievements of the modern world. They can and will appreciate its significance. They should no longer have to ask "what is calculus?"

Outline:

Introduction
Four Problems:
1. Zeno's Paradox(es)
2. The Area Problem
3. The Tangent or Velocity Problem
4. Optimization Problems
Preliminaries to Solution
1. A Number System
2. Limits Infinite Sums and an Answer for Zeno
3. Real Numbers
4. Functions and Continuity
Calculus
1. The Derivative
2. The Fundamental Theorem of Calculus and Integrals
Conclusion

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