1. Tokens from the Gods.- Variables, Functions, and Limits.- 2. The Spirit of Greece.- Pre-calculus Mathematics.- 3. Sherlock Holmes Meets Pierre de Fermat.- Derivatives.- 4. Optimistic Steps.- Techniques of Optimization.- 5. Chains and Change.- Instantaneous rates.- 6. The Integrity of Ancient and Modern Mathematics.- Integrals and Antiderivaties.- 7. A Circle of Ideas.- Calculus of Trigonometric Functions.- 8. House of Integrals.- Fundamental Principles Revisited.- 9. The Central Height.- Logarithmic and Exponential Functions.- 10. Romance in Reason.- Seventeenth-century Mathematics.- Review Problems for Chapters 1-10.- Appendices and Tables.

This book is for students being introduced to calculus, and it covers the usual topics, but its spirit is different from wh at might be expected. Though the approach is basically historical in nature, emphasis is put upon ideas and their place-not upon events and their dates. Its purpose is to have students to learn calculus first, and to learn incidentally something about the nature of mathematics. Somewhat to the surprise of its author, the book soon became animated by a spirit of opposition to the darkness that separates the sciences from the humanities. To fight the speil of that darkness anything at hand is used, even a few low tricks or bad jokes that seemed to offer a slight promise of success. To lighten the darkness, to illuminate some of the common ground shared by the two cultures, is a goal that justifies almost any means. It is possible that this approach may make calculus more fun as weil. Whereas the close ties of mathematics to the sciences are weil known, the ties binding mathematics to the humanities are rarely noticed. The result is a distorted view of mathematics, placing it outside the mainstream of liberal arts studies. This book tries to suggest gently, from time to time, where a kinship between mathematics and the humanities may be found.