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AuthorPriestley, William McGowen. author
TitleCalculus: A Liberal Art [electronic resource] / by William McGowen Priestley
ImprintNew York, NY : Springer New York : Imprint: Springer, 1998
Edition Second Edition
Connect tohttp://dx.doi.org/10.1007/978-1-4612-1658-2
Descript XVII, 404 p. online resource

SUMMARY

reason for delaying its study has to do with the question of mathematical maturity. * No use is made here of trigonometric, logarithmic, or expoยญ 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


CONTENT

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


Mathematics Algebra Mathematical analysis Analysis (Mathematics) Mathematics Analysis Algebra



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