61. Non-Newtonian Calculus Includes discussions of general theory and heuristic guides for application. http://www.geocities.com/nonnewtoniancalculus/

Non-Newtonian Calculus NON-NEWTONIAN CALCULUS A Brief Account: The non-Newtonian calculi were created in the period from 1967 to 1970 by Michael Grossman and Robert Katz. These calculi provide a wide variety of mathematical tools for use in science, engineering, and mathematics. They appear to have considerable potential for use as alternatives to the classical calculus of Newton and Leibniz. The first publication on non-Newtonian calculus was Grossman and Katz’s book "Non-Newtonian Calculus” (QA303.G88). It includes discussions of nine specific non-Newtonian calculi, the general theory of non-Newtonian calculus, and heuristic guides for application. The first non-Newtonian calculus is the topic of Grossman’s book "The First Nonlinear System of Differential and Integral Calculus" (QA303.G878). In that calculus the exponential functions play the role that the linear functions play in the classical calculus. A non-Newtonian calculus in which the power functions play that role is presented in Grossman’s book "Bigeometric Calculus: A System with a Scale-Free Derivative” (QA306.G84). Each non-Newtonian calculus, as well as the classical calculus, can be ‘weighted’ in a manner explained in the book "The First Systems of Weighted Differential and Integral Calculus” (QA303.G876) by Jane Grossman, Michael Grossman, and Robert Katz. Natural outgrowths of the systems of weighted calculus are the systems of meta-calculus, which are described in Jane Grossman's book "Meta-Calculus: Differential and Integral” (QA303.G877).

62. Toolkit The MathServ calculus Toolkit. During periods of heavy use, MathServ can be very slow to respond. Please do not resubmit jobs during http://mss.math.vanderbilt.edu/~pscrooke/toolkit.html

The MathServ Calculus Toolkit During periods of heavy use, MathServ can be very slow to respond. Please do not resubmit jobs during these periods because it only aggravates the situation. Simply give MathServ time to recover and try resubmitting the work in an hour or so. A short introduction to the MathServ system can be found here Several tools are available to perform specialized calculations e.g. find the equation of the tangent line to the graph of a function at a particular point. Listed below are catagories for the various tools. Algebra Functions Graphing Applications of the Derivative ... Integrals The page was last revised on March 7, 2002.

63. Oresme, Nicole Concise biography with a note on his mathematical contributions. http://occawlonline.pearsoned.com/bookbind/pubbooks/thomas_awl/chapter1/medialib

Oresme, Nicole (ca. 13201382) Frenchman Oresme went to the University of Paris in the 1340s, studying theology and liberal arts. Later he was a faculty member and administrator at the same university. Oresme served royalty as an educator and a scholar and, therefore, had support for his research. He translated Aristotle into French. Eventually he was made a bishop. He began to think about mathematics and in particular rates of change, like velocity and acceleration. His work entitled De configurationibus (1350s) contained results in geometry and was the first to present graphs of velocities. The argument we use to show the divergence of the harmonic series was devised by Oresme in this publication. Oresme was a popularizer of science and did not believe in Albert of Saxony’s generally accepted model of free fall. Oresme preferred Aristotle’s constant-acceleration model, which became popular among Oxford scholars in the 1330s and was eventually refined and tested by Galileo three hundred years later. In another publication

64. THE CALCULUS PAGE PROBLEMS LIST THE calculus PAGE PROBLEMS LIST. Problems and Solutions Developed by DA Kouba. And brought to you by ecalculus.org. Beginning Differential calculus http://www.math.ucdavis.edu/~kouba/ProblemsList.html

THE CALCULUS PAGE PROBLEMS LIST Problems and Solutions Developed by : D. A. Kouba And brought to you by : eCalculus.org Beginning Differential Calculus : Problems on the limit of a function as x approaches a fixed constant limit of a function as x approaches plus or minus infinity limit of a function using the precise epsilon/delta definition of limit limit of a function using L'Hopital's Rule Problems on the continuity of a function of one variable Problems on the "Squeeze Principle" Problems on the limit definition of the derivative Problems on the chain rule Problems on the product rule Problems on the quotient rule Problems on differentiation of trigonometric functions Problems on differentiation of inverse trigonometric functions Problems on detailed graphing using first and second derivatives Problems on applied maxima and minima Problems on implicit differentiation Problems on related rates Problems on logarithmic differentiation Problems on the differential Problems on the Intermediate-Value Theorem Problems on the Mean Value Theorem Beginning Integral Calculus : Problems using summation notation Problems on the limit definition of a definite integral Problems on u-substitution Problems on integrating exponential functions Problems on integrating trigonometric functions Problems on integration by parts Problems on integrating certain rational functions, resulting in

65. ESAIM Control, Optimisation And Calculus Of Variations Part of European Series in Applied and Industrial Mathematics. Full text from vol.1 (1995). http://www.edpsciences.com/cocv/

66. THE CALCULUS PAGE THE calculus PAGE HAS A NEW ADDRESS ! See http//ecalculus.Org. http://www.math.ucdavis.edu/~kouba/CalculusPage.html

THE CALCULUS PAGE HAS A NEW ADDRESS ! See http://eCalculus.Org

67. Focus On Calculus: Topics in calculus that are important in physics http://omega.albany.edu:8008/mat214dir/Baierlein.html

Focus on Calculus A Physicist's View of Teaching Calculus Ralph Baierlein, Wesleyan University What topics in calculus would physicists like to see their students learn? A lot of topics, of course, but the need to economize in this article forces me to economize in what I might ask of a calculus teacher, who is strapped for time, if not for space. Here are some highlights- some areas of especial concern to the study of physics. Exponentials and logarithms That the derivative of an exponential function is proportional to the function itself is the most important property of those functions. A physicist would like to start with that property, as displayed here: Numerical exploration with base (b=2) yields a coefficient of b X that is less than 1; trying (b = 10) yields a coefficient greater than 1. In between 2 and 10 there ought to be a number that yields 1, and thereby e enters the scene. Then it is a matter of small, relatively easy steps to develop the topic and to finish with ln y as the integral of one-over-x dx. That logarithmic relation always puzzles students, and so it is best to place it last, not at the start, where it might derail the entire development. Expansions and approximations Almost every ``exactly-solved'' problem in physics is based on some initial approximation. To be sure, solutions have become famous as exact solutions to nonlinear differential equations, but those equations themselves are merely approximations to more fundamental equations. Physics students need to become handy with the Taylor expansion and the binomial expansion. Their level of expertise should enable them to apply those expansions to functions like

68. Math Forum: Calculus The best Internet resources for calculus classroom materials, software, Internet projects, and public forums for discussion. calculus. Back to Math by Subject http://mathforum.org/calculus/calculus.html

Calculus Back to Math by Subject Math by Subject K12 Topics algebra arithmetic calculus discrete math geometry pre-calculus prob/stat Advanced Topics analysis calculus diff. equations game theory discrete math geometry (coll.) geometry (adv.) linear algebra modern algebra num. analysis Internet Calculus Resources See also Single-variable Calculus and Multi-variable Calculus in the Math Forum's Internet Mathematics Library. Classroom materials for teachers and students Selected calculus Internet resources for the classroom, including activities and interactive resources. Software for calculus Publicly available software and publishers online. Internet projects Activities for students and lovers of calculus. Public forums for discussing calculus Mailing lists and newsgroups sponsored by the Forum and others where mathematicians,teachers, and students trade ideas about calculus. Home The Math Library Quick Reference Search ... Contact Us http://mathforum.org/ webmaster@mathforum.org

69. Calculus History The main ideas of calculus developed over a very long period of time. Read about some of the mathematicians who contributed to this field of mathematics. http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/The_rise_of_calculus.html

A history of the calculus Analysis index History Topics Index The main ideas which underpin the calculus developed over a very long period of time indeed. The first steps were taken by Greek mathematicians. To the Greeks numbers were ratios of integers so the number line had "holes" in it. They got round this difficulty by using lengths, areas and volumes in addition to numbers for, to the Greeks, not all lengths were numbers. Zeno of Elea , about 450 BC, gave a number of problems which were based on the infinite. For example he argued that motion is impossible:- If a body moves from A to B then before it reaches B it passes through the mid-point, say B of AB. Now to move to B it must first reach the mid-point B of AB . Continue this argument to see that A must move through an infinite number of distances and so cannot move. Leucippus Democritus and Antiphon all made contributions to the Greek method of exhaustion which was put on a scientific basis by Eudoxus about 370 BC. The method of exhaustion is so called because one thinks of the areas measured expanding so that they account for more and more of the required area.

70. Calculus Bible "The calculus Bible" by GS Gill. http://www.math.byu.edu/Math/CalculusBible/

This document was designed for a frames-capable browser. You can still read the text here

71. Math Forum: Algebra & Calculus Sketches - Ruth Carver The Math Forum Corner for Interactive Geometry Software. Algebra and calculus Sketches. by Ruth Carver. calculus. Tangent Line Problem. http://mathforum.org/sum95/ruth/sketches/algcalc.sketches.html

The Math Forum - Corner for Interactive Geometry Software Algebra and Calculus Sketches by Ruth Carver Sketchpad Resources Main CIGS Page Teacher Exchange: Forum Web Units Viewing sketches on this page requires The Geometer's Sketchpad. For information about purchasing the software, downloading demo versions, and setting up Sketchpad as a helper application for your Web browser, see the Forum's Dynamic Geometry Software page. Algebra Line Sketch One line, Y=X, is fixed. You can manipulate the position of another line, Y=MX+B, by altering the values of M or B. There are also questions to go with this graph. Parabola Sketch 1 Similar to the first graph, here there's a fixed parabola Y=X^2, and one to experiment with, Y=AX^2+C. Parabola Sketch 2 Change even more variables by comparing Y=X^2 with Y=A(X-H)^2+K. Calculus Tangent Line Problem Given a function f and a point P on f, find an equation of the tangent to the graph at P. Why would you want to do this, and how would you go about solving this problem? These five sketches take you step-by-step through the solution of the tangent line problem: Sketch 1 Sketch 2 Sketch 3 Sketch 4 ... Contact Us http://mathforum.org/

72. Mathematics Reference Trigonometry identities and calculus rules for integration and differentiation. http://www.alcyone.com/max/reference/maths/index.html

Mathematics reference Ma MathRef A mathematics reference for students and teachers. Conventions. Mathematics reference: Notation A unified mathematical notation used throughout these pages. Ma Trigonometric identities and properties. Mathematics reference: Trigonometric identities Various identities and properties essential in trigonometry. Ma Mathematics reference: Hyperbolic trigonometry identities Various identities essential in hyperbolic trigonometry. Ma Differential and integral calculus. Mathematics reference: Limits Properties of limits. Ma Mathematics reference: Rules for differentiation Essential rules for differentiation. Ma Mathematics reference: Rules for integration Essential rules for integration. Ma Vectors and matrices. Mathematics reference: Rules for vectors Basic properties of vectors. Ma Mathematics reference: Rules for matrices Basic properties of matrices. Ma Navigation. Erik Max Francis TOP Welcome to my homepage. e Reference UP A technical reference. Re Mathematics reference: Notation START A unified mathematical notation used throughout these pages. Ma Quick links.

73. Lambda Calculus An online introduction to the lambda calculus by Lloyd Allison, complete with a web form that will evaluate lambda expressions. http://www.csse.monash.edu.au/~lloyd/tildeFP/Lambda/

Lambda Calculus (interpreters) LA home FP Lambda Introduction Examples There are lazy and strict versions of the toy lambda-calculus interpreter. They both share the same input syntax and can be used on the same example lambda-calculus programs, although some programs will not work (i.e. will loop) when using the strict interpreter of course. Introduction: Lambda-calculus and the lazy interpreter Syntax - quick guide Example lambda-calculus programs Lazy Interpreter Strict Interpreter main programs Lazy.p Strict.p declarations define values lazy.type.P interpreters proper lazy.exec.P strict.exec.P output lazy.show.P (evaluation is print driven) strict.show.P expressions lazy.eval.p (by-need evaluation) strict.eval.P (strict evaluation) apply functions lazy.apply.P strict.apply.P process declarations lazy.D.P strict.D.P binary operators lazy.O.P unary operators lazy.U.P strict.U.P manipulate environments lazy.env.P strict.env.P form basic values lazy.mkval.P It is a useful exercise to compare the strict and lazy versions of the above files, particularly *.eval.P General routines common to both interpreters: lexical syntax lex.type.P

74. Geometric Calculus R & D Home Page It advocates a universal scientific language grounded in an integrated Geometric and Inferential calculus. Geometric calculus is http://modelingnts.la.asu.edu/

Overview of GC Evolution of GC Intro to GA Found Math Phys ... Links Agenda. This web site is dedicated to perfecting a universal mathematical language for science, extending its applications and promoting it throughout the scientific community. It advocates a universal scientific language grounded in an integrated Geometric and Inferential Calculus. Geometric Calculus is a mathematical language for expressing and elaborating geometric concepts. Spacetime algebra is an application of this language to model physical space and time. It is the core of a universal language for physics, providing invariant formulations of basic equations and a powerful computational engine for deducing their consequences. Inferential Calculus integrates deductive and statistical inference into a coherent system for matching scientific models to empirical data. It provides a unified framework for data analysis, image/signaling processing and hypothesis testing from incomplete data. Thus, it supports the semantic bridge between theoretical constructs and empirical realities. Modeling.

75. Career Calculus Printable version. Career calculus. 19 Aug 2003. And You thought Math would Never be Useful. Remember your introductory calculus? Probably not. http://software.ericsink.com/Career_Calculus.html

Thoughts about software from yet another person who invented the Internet Home Feature Index Complete Archive Marketing for Geeks ... SourceGear Recent Items Features Printable version Career Calculus 19 Aug 2003 A couple weeks ago there was a flurry of blogging over the price of Microsoft's upcoming Professional Developers Conference ( PDC ). In the midst of this controversy, Doug Reilly chimed in with a post entitled " Who is responsible for your career? ". Doug's post got a lot of reads and links, including well-said "amen posts" from Sam Gentile and Robert Hurlbut While I don't care to debate the issue of PDC pricing, I do want to affirm the concept of taking responsibility for our own careers. Often we choose to focus on the things which are outside our control. But the truth is that our career path is largely determined by our own choices. I've known and worked with lots of developers, and I have noticed one thing which separates those with great careers from everybody else. Developers with outstanding careers understand a secret that seems to elude the majority: Focus on the first derivative.

76. Awesome Library - Mathematics Large resource for students of middle schools. Includes algebra, calculus, graphing, and data analysis by subject and standard. http://www.awesomelibrary.org/Classroom/Mathematics/Middle-High_School_Math/Midd

Awesome Talking Library Examples ... Spelling Here: Home Classroom Mathematics > Middle-High School Math Middle-High School Math Sub-Topics Algebra By Subject and Standard Calculus Data Analysis ... Trigonometry Also Try Assessment Information Math Lessons Problem Solving Standards Discussions Ask Dr. Math (Math Forum) Provides organized structure for gaining answers. Award-winning site. Questions for Discussion (Droujkov and Droujkova) Provides questions for students designed to turn a boring arthmetic exercise into an exciting research adventure. 5-00 Games Math Games (FunBrain.com) Provides almost two dozen games to help teens in junior high or high school learn basic math. 7-02 Math Puzzles (Bogomolny) Provides games and puzzles that require math to solve. 9-99 Lesson Plans By Grade Level (Learning Network - TeacherVision.com) Provides dozens of math lesson plans by grade level. 5-01 By Grade Level (PBS) 8-00 By Grade Level and Topic (8-10) (British Columbia Ministry of Education) Provides math outcomes and activities by topic and grade level (8-10). 5-00 By Topic (Thinkquest Team 20991) Provides math tutorials by topic. 5-00

77. I Finally Have My Own Domain! Which You Should Be Taken To Within I finally have my own domain! Which you should be taken to within the next 30 seconds. Otherwise click the below link http//www.IHatecalculus.com/. http://www.psyber.com/~jacob/math/calculus.html

78. Page Of Yves Lafont University of Marseille II Linear logic, lambda calculus, proof theory, term rewriting. Lafont invented the theory of interaction nets, an elegant theory of graph rewriting. http://iml.univ-mrs.fr/~lafont/welcome.html

photo by M. Arovas Yves LAFONT professor at Aix-Marseille 2 research at (team : Logique de la Programmation teaching at Maths adress: office: - phone: - fax: - e-mail: lafont@iml.univ-mrs.fr Discipline maths Specialities logic algebra theoretical computer science; Papers More information on my french home page

79. The MATHMAN Would you send us a sample copy of your calculus by and for Young People if Korean rights are still available? Get Ready for calculus. http://www.shout.net/~mathman/

The above is a copy of Don's watercolor painting of The Nautilus shell; it is Don's logo. The shell is beautiful, its shape a mathematical curve, and can be obtained from Shell World, at http://www.seashellworld.com/seashells/nautilus.htm . Also see the equation for the shell making a spiral IES java applet making a Nautilus, Xah Lee's work on spirals (and other curves) and student work on the growth of the Nautilus (chapter 6). WELCOME ! Refreshing insights into the learning and doing of some important mathematics, by young people (while doing lots of arithmetic, using many hands-on materials, science to math activities, and the non-trivial use of calculators and computers) for children, as well as adults. Don assumes only that a student can count. Don shows sample problems and solutions from his works, below. Exciting news- all the time! Don added something new to his website- he is giving you the ability to search his site with an Atomz search engine, if you want to. Like you can put in the word fractions and you will find all the pages that show how Don gets his students working on fractions and why he thinks this is important.

80. [math/9906155] Lectures On Pseudo-differential Operators These lecture notes cover a first year graduate course that was given on pseudodifferential operators. The calculus on manifolds is developed and applied to prove propagation of singularities and the Hodge decomposition theorem. http://arxiv.org/abs/math.AP/9906155

Mathematics, abstract math.AP/9906155 From: Mark S. Joshi [ view email ] Date: Wed, 23 Jun 1999 13:41:14 GMT (125kb,S) Lectures on Pseudo-differential Operators Authors: M. S. Joshi Subj-class: Analysis of PDEs MSC-class: This lecture notes cover a Part III (first year graduate) course that was given at Cambridge University over several years on pseudo-differential operators. The calculus on manifolds is developed and applied to prove propagation of singularities and the Hodge decomposition theorem. Problems are included. Full-text: PostScript PDF , or Other formats References and citations for this submission: CiteBase (autonomous citation navigation and analysis) Which authors of this paper are endorsers? Links to: arXiv math find abs

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