ÿþ<?xml version="1.0" encoding="utf-16"?> <!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.1//EN" "http://www.w3.org/TR/xhtml11/DTD/xhtml11.dtd"> <html xmlns="http://www.w3.org/1999/xhtml" xml:lang="en"> <head> <title> Edgar R. Chavez .. Calculus </title> <link rel="stylesheet" href="../erc01.css" type="text/css" /> </head> <body> <div id="top"> <img class="quill" src="../Images/myquill5.png" alt="myQuill"></img> <h2> Edgar R. Ch&aacute;vez</h2> <h3> Calculus </h3> </div> <div class="NavigationLinks"> <hr class="myLine" /> <ul> <li><a href="../home.html"> Home </a></li> <li><a href="./mathematics.html"> Mathematics </a></li> </ul> <hr class="myLine" /> <ul> <li><a href="./calculus.html"> Calculus </a></li> </ul> <ul class="NavMargin1"> <li><a href="#advancedcalculus"> Advanced Calculus </a></li> <li><a href="#calculus"> Calculus </a></li> <li><a href="#infinitesimals"> Infinitessimals </a></li> <li><a href="#textbooks"> Textbooks </a></li> </ul> <hr class="myLine" /> </div> <div class="InfoArea"> <div id="advancedcalculus"><span class="Subhead2"> Advabced Calculus </span> <div class="Tab5"> <p><a href="http://www.maths.abdn.ac.uk/~igc/tch/ma2001/notes/"> Advanced Calculus </a> &nbsp; <img src="../Images/stars4.gif" alt="Rank4" /> &nbsp; &nbsp; By Ian Craw. Teacher's notes from MA1002, University of Aberdeen, UK. </p> <p><a href="http://www.math.harvard.edu/~shlomo/docs/Advanced_Calculus.pdf"> Advanced Calculus </a> &nbsp; By Lynn H. Loomis and Shlomo Sternberg, Harvard University. Revised Edition, originally published by Jones and Bartlett Publishers, 1968 and 1989. </p> <p><a href="http://www.math.wisc.edu/~robbin/521dir/521.pdf"> Advanced Calculus course notes </a> &nbsp; Joel W. Robbin, University of Wisconsin. <br /> <a class="Tab5" href="http://www.math.wisc.edu/~robbin/521dir/cont.pdf"> Continuity and Uniform Countinuity </a> <img src="../Images/stars4.gif" alt="Rank4" /> </p> </div></div> <div id="calculus"><span class="Subhead2"> Calculus </span> <div class="Tab5"> <p> A <a href="http://www.worldscibooks.com/mathematics/4920_rev01.html"> review, </a> by Roy Smith, University of Georgia, of <a href="http://www.amazon.com/Calculus-Elements-Michael-Comenetz/dp/9810249047/ref=sr_1_1?ie=UTF8&amp;s=books&amp;qid=1228614960&amp;sr=1-1"> Calculus: The Elements </a> &nbsp; <img src="../Images/stars4.gif" alt="Rank4" /> &nbsp; &nbsp; by Michael Comenetz. "[A]n extremely scholarly work, by a pure mathematician with research credentials, as well as years of teaching experience, whose goal seems to be to explain the ideas behind the calculus, as well as its origins and applications, to the intelligent and curious but mathematically unsophisticated beginner, even lay persons." </p> <p><a href="http://homelink.cps-k12.org/teachers/canteys/CalculusMemoryBook.html"> Calculus Memory Book </a> &nbsp; By Susan Cantey. Good summary of Calculus core concepts; good to memorize.</p> <p><a href="http://www.math.temple.edu/~cow/"> Calculus on the Web </a> &nbsp; <img src="../Images/stars4.gif" alt="Rank4" /> &nbsp; &nbsp; An internet utility for learning and practicing calculus. Designed by two members of the Temple University Mathematics Department. </p> <p><a href="http://www.calculus.org/"> calculus.org </a> &nbsp; The Calculus Page. Resources for the student and the instructor. </p> <p><a href="http://www.math.ucdavis.edu/~kouba/ProblemsList.html"> The Calculus Page Problems List </a> &nbsp; <img src="../Images/stars4.gif" alt="Rank4" /> &nbsp; &nbsp; Calculus problems, from easy to challenging, solved in detail one step at a time. Still under development, but very well worth looking at. </p> <p><a href="http://archives.math.utk.edu/calculus/crol.html"> Calculus resources online </a> &nbsp; From the <a href="http://archives.math.utk.edu/"> Math Archives </a></p> <p><a href="http://mathforum.org/library/drmath/view/61537.html"> Delta-Epsilon Proofs and Arbitrary Epsilon Choice </a> &nbsp; at Math Forum. </p> <p><a href="http://en.wikipedia.org/wiki/E_%28mathematical_constant%29"> e </a> &nbsp; <img src="../Images/stars4.gif" alt="Rank4" /> &nbsp; &nbsp; Wikipedia. A series of articles about the mathematical constant e. </p> <p><a href="http://www.ocf.berkeley.edu/~yosenl/math/epsilon-delta.pdf"> Further Examples of Epsilon-Delta Proof </a> &nbsp; Yosen Lin, University of California at Berkeley. </p> <p><a href="http://www.math.hmc.edu/calculus/"> HMC Mathematics Online Tutorial </a> &nbsp; <img src="../Images/stars4.gif" alt="Rank4" /> &nbsp; &nbsp; Harvey Mudd College </p> <p><a href="http://mathforum.org/calculus/calculus.html"> Internet Calculus Resources </a> &nbsp; The Math Forum, Drexel University. </p> <p><a href="http://www.karlscalculus.org/index.shtml"> Karl's Calculus Tutor </a> &nbsp; &nbsp; <img src="../Images/stars4.gif" alt="Rank4" /> &nbsp; &nbsp; </p> <p><a href="http://www.kent.wednet.edu/staff/dwright/calculus/book/index.html"> Kentridge AP Calculus </a> &nbsp; Course outline, with problems and answers. </p> <p><a href="http://people.usd.edu/~ylio/Calcul/Limit_and_Continuity.html"> Limit and Continuity </a> &nbsp; Yuhlong Lio, University of South Dakota. Good delta-epsilon examples. </p> <p><a href="http://archives.math.utk.edu/visual.calculus/index.html"> Visual Calculus </a> &nbsp; A collection of modules that can be used in the studying or teaching of Calculus. </p> <p><a href="http://www4.ncsu.edu/unity/lockers/users/f/felder/public/kenny/papers/dx.html"> What dx Actually Means </a> &nbsp; by Kenny Felder, North Carolina State University. </p> </div></div> <div id="infinitesimals"><span class="Subhead2"> Infinitesimals </span> <div class="Tab5"> <p><a href="http://www.lightandmatter.com/calc/calc.pdf"> Calculus </a> &nbsp; by Benjamin Crowell. A short introductory text that focuses mainly on integration and differentiation of functions of a single variable. Infinitesimals are used when appropriate, and are treated more rigorously than in Thompson&apos;s <span class="InlineTitle">Calculus Made Easy</span>, but in less detail than in Keisler&apos;s <span class="InlineTitle"> Elementary Calculus: An Approach Using Infinitesimals</span>. </p> <p><a href="http://www.cds.caltech.edu/~marsden/books/Calculus_Unlimited.html"> Calculus Unlimited </a> &nbsp; by Jerrold E. Marsden and Alan Weinstein </p> <p><a href="http://www.math.hawaii.edu/~heiner/calculus.pdf"> Calculus Without Limits </a> &nbsp; Karl Heinz Dovermann, University of Hawaii. See also his <a href="http://www.math.hawaii.edu/~heiner/"> website </a> for other resources. </p> <p><a href="http://plato.stanford.edu/entries/continuity/"> Continuity and Infinitesimals </a> &nbsp; John L. Bell, Stanford Encyclopedia of Philosophy </p> <p><a href="http://www.math.wisc.edu/~keisler/calc.html"> Elementary Calculus: An Approach Using Infinitesimals </a> &nbsp; <img src="../Images/stars4.gif" alt="Rank4" /> &nbsp; &nbsp; Second Edition, by H. Jerome Keisler, University of Wisconsin. A freshman-level online textbook based on Abraham Robinson's infinitesimals, a modern approach that puts the intuitive ideas of the calculus on a mathematically sound footing and is easier to understand than limits.<br /> <a class="Tab5" href="http://www.math.wisc.edu/~keisler/foundations.html"> Foundations of Infinitesimal Calculus</a> &nbsp; A companion to <span class="InlineTitle">Elementary Calculus</span>; it can be used as an introduction to the infinitesimal approach to calculus for mathematicians, as background material for instructors, or as an undergraduate textbook. This monograph presents the subject from a more advanced viewpoint and includes proofs of almost all of the theorems stated in <span class="InlineTitle">Elementary Calculus</span></p> <p><a href="http://www.cs.uiowa.edu/~stroyan/InfsmlCalculus/FoundInfsmlCalc.pdf"> Foundations of Infinitesimal Calculus </a> &nbsp; by K. D. Stroyan, University of Iowa. You can download this text as a PDF file, or you can preview the <a href="http://www.math.uiowa.edu/~stroyan/InfsmlCalculus/FoundationsTOC.htm"> Table of Contents</a>. <br /> <a class="Tab5" href="http://www.math.uiowa.edu/~stroyan/InfsmlCalculus/InfsmlCalc.htm"> A Brief Introduction to Infinitesimal Calculus</a>. </p> <p><a href="http://www.lightandmatter.com/calc/inf/"> Inf </a> &nbsp; A calculator that can handle infinite and infinitesimal numbers. Inf is open source software by Ben Crowell and Mustafa Khafateh. </p> <p><a href="http://mathforum.org/dr.math/faq/analysis_hyperreals.html"> Nonstandard Analysis and the Hyperreals </a> &nbsp; By Jordi Gutierrez Hermoso. </p> <p><a href="http://www.physics.orst.edu/~tevian/bridge/papers/differentials.pdf"> Putting Differentials Back into Calculus </a> &nbsp; Tevian Dray and Corinne A. Manogue, Oregon State University. </p> <p><a href="http://synechism.org/drupal/yact/"> Yet Another Calculus Text </a> &nbsp; by Dan Sloughter, Furman University. An introduction to calculus based on the hyperreal number system. Aimed primarily at readers who already have some familiarity with calculus, the book does not explicitly assume any prerequisites beyond basic algebra and trigonometry, but in practice the pace is too fast for most of those without some acquaintance with the basic notions of calculus. </p> </div></div> <div id="textbooks"><span class="Subhead2"> Textbooks </span> <div class="Tab5"> <p><a href="http://www.lightandmatter.com/calc/calc.pdf"> Calculus </a> &nbsp; Benjamin Crowell. </p> <p><a href="http://www.whitman.edu/mathematics/multivariable/"> Calculus </a> &nbsp; David Guichard, Whitman College. Licensed under the Creative Commons Attribution-NonCommercial-ShareAlike License. </p> <p><a href="http://www.math.byu.edu/~smithw/Calculus/"> The Calculus </a> &nbsp; By William V. Smith. A free online calculus course. Essentially an ordinary text, but you can read it online. Lots of exercises and examples. Unusual features: (1) The text is rigorous; proofs are done for nearly everything - eventually. (2) Calculus is done in both one and two variables at the same time.</p> <p><a href="http://ocw.mit.edu/ans7870/resources/Strang/strangtext.htm"> Calculus </a> &nbsp; <img src="../Images/stars4.gif" alt="Rank4" /> &nbsp; &nbsp; By Gilbert Strang. Online copy, available in PDF format, of the book published in 1991 by Wellesley-Cambridge Press. Light on theory but great explanations and exercises. Excellent for self-study. Instrutor's manual and student study guide at MIT Open Courseware. <br /> <a class="Tab5" href="http://math.mit.edu/calculus/Article_Exponential.pdf"> Introducing e<sup>x</sup></a> &nbsp; <img src="../Images/stars4.gif" alt="Rank4" /></p> <p><a href="http://en.wikibooks.org/wiki/Calculus"> Calculus </a> &nbsp; Wikibooks </p> <p><a href="http://www.math.umn.edu/~garrett/calculus/first_year/notes.pdf"> Calculus Refresher </a> &nbsp; Paul Garrett, University of Minnesota </p> <p>Differential and Integral Calculus, by Richard Courant &nbsp; <img src="../Images/stars4.gif" alt="Rank4" /></p> <ul class="noLineBreak"> <li><a href="http://kr.cs.ait.ac.th/~radok/math/mat6/startdiall.htm"> Volume 1 </a></li> <li><a href="http://kr.cs.ait.ac.th/~radok/math/mat9/startall.htm#Differential%20and%20Integral%20Calculus"> Volume 2 </a></li> </ul> <p><a href="http://clem.mscd.edu/~talmanl/TeachCalculus/"> The Teacher's Guide to Calculus </a> &nbsp; <img src="../Images/stars4.gif" alt="Rank4" /> &nbsp; &nbsp; Louis A. Talman, Metropolitan State College of Denver. Certain questions concerning the theoretical underpinnings of single-variable calculus arise frequently among those who teach the first two or three calculus courses. The purpose of this book is to answer those questions, and others as well. </p> <p><a href="http://www.understandingcalculus.com/"> Understanding Calculus </a> &nbsp; By Faraz Hussain. A complete online introductory book that focuses on concepts. Many engineering applications aimed at developing the student's scientific approach towards problem solving. </p> </div></div> <!-- div class="Quote1"> <hr class="myLine" /> Any idiot can learn anything in mathematics. It requires only patience. <br /> Now, to create something - that is another matter. <br /> Alonzo Church <hr class="myLine" /> </div--> </div> <div class="MyCopyright"> <hr class="myLine" /> Copyright &copy; 2003-2011 by Edgar R. Ch&aacute;vez. All rights reserved. <hr class="myLine" /> </div> </body> </html>