The student of calculus is entitled to ask what calculus is and what it can be used for. This short book provides an answer. The author starts by demonstrating that calculus provides a mathematical tool for the quantitative analysis of a wide range of dynamical phenomena and systems with variable quantities. The text then looks at the origins and intuitive sources of calculus, its fundamental methodology, and its general framework and basic structure, before examining a few typical applications. The author's style is direct and pedagogical. The new student should find that the book provides a clear and strong grounding in this important technique
Nonstandard analysis represents a fundamental change of perspective in mathematics (and sciences), comparable to the introduction of Cantor's set theory in the nineteenth century. This book is a short, readable introduction to the subject, based on the axiomatic or IST approach. The first part gives a clear, rigorous exposition of the theory; the second part consists of a number of self-contained chapters dealing with applications. As an aid to self-study, the author has included exercises at the end of each chapter, with hints as well as full solutions.
We are all classicists--we come into touch with the classics on a daily basis: in our culture, politics, medicine, architecture, language, and literature. What are the true roots of these influences, however, and how do our interpretations of these aspects of the classics differ from their original reality? This introduction to the classics begins with a visit to the British Museum to view the frieze which once decorated the Apollo Temple a Bassae.
From Zeus and Europa, to Diana, Pan, and Prometheus, the myths of ancient Greece and Rome seem to exert a timeless power over us. But what do those myths represent, and why are they so enduringly fascinating? Why do they seem to be such a potent way of talking about our selves, our origins, and our desires? This imaginative and stimulating Very Short Introduction goes beyond a simple retelling of the stories to explore the rich history and diverse interpretations of classical mythology.
