Facebook Group Essay

2666 WordsFeb 21, 201311 Pages
MOOCULUS massive open online calculus CALCULUS THIS DOCUMENT WAS TYPESET ON JANUARY 6, 2013. 2 Copyright © 2013 Jim Fowler and Bart Snapp This work is licensed under the Creative Commons Attribution-NonCommercial-ShareAlike License. To view a copy of this license, visit http://creativecommons.org/licenses/by-nc-sa/3.0/ or send a letter to Creative Commons, 543 Howard Street, 5th Floor, San Francisco, California, 94105, USA. If you distribute this work or a derivative, include the history of the document. This text is based on David Guichard’s open-source calculus text which in turn is a modification and expansion of notes written by Neal Koblitz at the University of Washington. New material has been added, and old material has been modified, so some portions now bear little resemblance to the original. The book includes some exercises and examples from Elementary Calculus: An Approach Using Infinitesimals, by H. Jerome Keisler, available at http://www.math.wisc.edu/~keisler/calc.html under a Creative Commons license. In addition, the chapter on differential equations and the section on numerical integration are largely derived from the corresponding portions of Keisler’s book. Albert Schueller, Barry Balof, and Mike Wills have contributed additional material. This book is typeset in the Kerkis font, Kerkis © Department of Mathematics, University of the Aegean. We will be glad to receive corrections and suggestions for improvement at fowler@math.osu.edu or snapp@math.osu.edu. Contents 1 Limits 6 Index 36 List of Main Theorems 1.3.1 Theorem (Limit Laws) ......................... 17 1.3.5 Theorem (Squeeze Theorem) . . . . . . . . . . . . . . . . . . . . . . 19 1.6.3 Theorem (Intermediate Value Theorem) . . . . . . . . . . . . . . . . 31 How to Read Mathematics Reading mathematics is not the same as

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