Calculus (by Michael Spivak)

 

Spivak's celebrated textbook is widely held as one of the finest introductions to mathematical analysis. His aim is to present calculus as the first real encounter with mathematics: it is the place to learn how logical reasoning combined with fundamental concepts can be developed into a rigorous mathematical theory rather than a bunch of tools and techniques learned by rote. Since analysis is a subject students traditionally find difficult to grasp, Spivak provides leisurely explanations, a profusion of examples, a wide range of exercises and plenty of illustrations in an easy-going approach that enlightens difficult concepts and rewards effort. Calculus will continue to be regarded as a modern classic, ideal for honors students and mathematics majors, who seek an alternative to doorstop textbooks on calculus, and the more formidable introductions to real analysis. One of the most celebrated texts of its type combines the rigor of more formidable books with the leisurely explanations, profusion of examples, exercises and illustrations associated with 'doorstops' Ideal for students; clear, crisp explanations of what analysis and mathematics are really about Full range of exercises, from the straightforward to the challenging that deepen understanding.

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