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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 reading a novel. To read mathematics you
need:

(a) A pen.
(b) Plenty of blank paper.
(c) A...

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Facebook Group. Anti Essays. Retrieved December 15, 2018, from the World Wide Web: http://teachingsail.com/free-essays/Facebook-Group-409872.html


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