Calculus A Liberal Art [Paperback]

Presenting mathematics as forming a natural bridge between the humanities and the sciences, this book makes calculus accessible to those in the liberal arts. Much of the necessary geometry and algebra are exposed through historical development, and a section on the development of calculus offers insights into the place of mathematics in the history of thought.reason for delaying its study has to do with the question of mathematical maturity. * No use is made here of trigonometric, logarithmic, or expo? nential functions except in occasional optional material indicating how such functions can be handled. A perceptive remark made by George P6lya suggests how we can simultaneously learn mathematics and learn about mathematics-i.e., about the nature of mathematics and how it is developed: If the learning of mathematics reflects to any degree the invention of mathematics, it must have a place for guessing, for plausible inference. The reader will find plenty of opportunity here for guessing. The early chapters go at a gentle pace and invite the reader to enter into the spirit of the investigation. Exercises asking the reader to make a guess should be taken in this spirit-as simply an invitation to speculate about what is the likely truth in a given situation without feeling any pressure to guess correctly . Readers will soon realize that a matter about which they are asked to guess will likely be a topic of serious discussion later on.1. Tokens from the Gods Variables, Functions, and Limits.- 2. Rational Thoughts The Rise of Mathematics and the Liberal Arts.- 3. To Measure Is to Know More Pre-calculus Mathematics.- 4. Sherlock Holmes Meets Pierre de Fermat Derivatives.- 5. Optimistic Steps Techniques of Optimization.- 6. Chains and Change Instantaneous Rates.- 7. The Integrity of Ancient and Modern Mathematics Integrals and Antiderivatives.- 8. Romance in Reason Seventeenth-century Mathematics.- Appendices.- Answers to Selected Problems.With only a modest amount of l3…