81. BRIEF HISTORY OF VECTOR CALCULUS A (Very) Short Note on the history of Vector calculus. Two traditionshave been associated with the development of the concepts of http://www.math.mcmaster.ca/lovric/history.html

A (Very) Short Note on the History of Vector Calculus Two traditions have been associated with the development of the concepts of a vector and vector operations. Since the time of Babylonians and Egyptians, there have been attempts to extend the notion of a (natural) number. (Natural numbers are numbers like 1, 2, 3, 4, etc.) Successive generalizations have added negative numbers, zero, fractions and irrational numbers, forming what is now known as the set of real numbers. An attempt to solve the equation x ^2 + 1 = led to the discovery of complex numbers, and their geometric interpretation in a two-dimensional coordinate system to the discovery of a vector. The second tradition relates to an eternal search for (mathematical) entities that could best describe physical phenomena. It suffices to use a single number (and a unit of measurement) to describe the distance between two cities, the area of a lake or the temperature on the surface of the Earth. However, to convey information on the velocity of a wind or on the attractive force of a planet, one needs to specify not only a number, but also a direction. Although, for instance, temperature is a scalar (scalar, in our context, is a synonym for a real number), the way it changes cannot be described using a number only if we fly south from Toronto we will experience an increase in the air temperature; but the temperature will decrease if we fly north. The need to describe a

82. Basic Calculus 5. The calculus of Leibniz. 6. The calculus of Newton Basic calculus Differential and Integral calculus and Science, 2002. http://www.nd.edu/~hahn

83. Calculus Features introduction to function limits, derivatives, and integration. Includes finding maxima and minima, area approximations, resource tables and related links. http://www.bloom-enterprises.com/Math/calculus.html

Understanding Calculus Differential Calculus Symbols and Notation Graphing Calculator Integral Calculus ... Tamie's Art Gallery Original artwork by Tamie Bloom ©Bloom-Enterprises 2004 All images are the sole property of the author and may be used for not for profit educational purposes only.

84. Newton an impartial committee to decide whether he or Leibniz was the inventor of thecalculus. The URL of this page is http//wwwhistory.mcs.st-andrews.ac.uk http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Newton.html

Sir Isaac Newton Born: 4 Jan 1643 in Woolsthorpe, Lincolnshire, England Died: 31 March 1727 in London, England Click the picture above to see twenty-five larger pictures Show birthplace location Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index Isaac Newton 's life can be divided into three quite distinct periods. The first is his boyhood days from 1643 up to his appointment to a chair in 1669. The second period from 1669 to 1687 was the highly productive period in which he was Lucasian professor at Cambridge. The third period (nearly as long as the other two combined) saw Newton as a highly paid government official in London with little further interest in mathematical research. Isaac Newton was born in the manor house of Woolsthorpe, near Grantham in Lincolnshire. Although by the calendar in use at the time of his birth he was born on Christmas Day 1642, we give the date of 4 January 1643 in this biography which is the "corrected" Gregorian calendar date bringing it into line with our present calendar. (The Gregorian calendar was not adopted in England until 1752.) Isaac Newton came from a family of farmers but never knew his father, also named Isaac Newton, who died in October 1642, three months before his son was born. Although Isaac's father owned property and animals which made him quite a wealthy man, he was completely uneducated and could not sign his own name. You can see a picture of Woolsthorpe Manor as it is now Isaac's mother Hannah Ayscough remarried Barnabas Smith the minister of the church at North Witham, a nearby village, when Isaac was two years old. The young child was then left in the care of his grandmother Margery Ayscough at Woolsthorpe. Basically treated as an orphan, Isaac did not have a happy childhood. His grandfather James Ayscough was never mentioned by Isaac in later life and the fact that James left nothing to Isaac in his will, made when the boy was ten years old, suggests that there was no love lost between the two. There is no doubt that Isaac felt very bitter towards his mother and his step-father Barnabas Smith. When examining his sins at age nineteen, Isaac listed:-

85. Coolmath.com - An Amusement Park Of Math And More! Designed For FUN! An amusement park of mathematics. Puzzles and number problems, fractals, geometry, calculus, algebra, online games, online calculators, and links. http://www.coolmath.com/

Coolmath.com: An amusement park of math designed for fun! Coolmath Sponsors (Ad Links): Find out how to get a link here! Insurance And Loans Bad Credit Loans Home Equity Loans ... Please help us serve you better by completing a demographic survey. Results will only be used internally for new lessons, etc. and for our sponsors HELP SUPPORT COOLMATH link to us make a donation sponsorships text link advertising ... ScienceMonster.com Thanks for visiting Coolmath.com

86. Math.com - World Of Math Online Offers free math lessons and homework help, with an emphasis on geometry, algebra, statistics, and calculus. http://www.math.com/

Home Teacher Parents Glossary ... Email this page to a friend Select Subject Basic Math Everyday Math Pre-Algebra Algebra ... Others Search New Game FREE! Math Super Fighters Play Now! ... Square Roots Free Email @ Math.com Email Login Password New users sign up Contact us Partnership Link to us ... Legal Notices . Please read our Privacy Policy

87. Contents Home. This calculus resource is keyed to Thomas calculus (10th Edition). FundamentalTheorem of calculus. Differential Equations. Multivariable calculus. http://occawlonline.pearsoned.com/bookbind/pubbooks/thomas_awl/chapter1/medialib

This calculus resource is keyed to Thomas' Calculus (10th Edition). It contains a chronology of the development of the subject, essays on major topics, biographies of more than 100 important people in the development of the subject, and over 100 questions to consider (keyed by chapter). Timelines B.C A.D. Topics ... Biographies (over 100 people of calculus) Problems (over 100 questions to consider) Further Reading

88. Calculus@Internet Tutorials on calculus subjects ranging from precalculus to differential equations. Math tools and resource links. http://www.calculus.net/

89. Welcome To The UMR BrainTrax System! Offers assistance in algebra, geometry, trigonomety and calculus. Contains realworld examples, detailed example problems, and interactive features. Internet Explorer 5.0+ on a Windows PC is required. http://braintrax.umr.edu/

90. 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

91. Exterior Differential Calculus And Symbolic Matrix Algebra @ Mathematica Freeware enables Mathematica to carry out calculations with differential forms. http://www.inp.demokritos.gr/~sbonano/EDC/ExteriorDifferentialCalculus.html

Exterior Differential Calculus and Symbolic Matrix Algebra @ Mathematica Overview This package enables Mathematica to carry out calculations with differential forms. It defines the two basic operations - Exterior Product (Wedge) and Exterior Derivative (d) - in such a way that: (1) they can act on any valid Mathematica expression (2) they allow the use of any symbols to denote differential forms (3) input - output notation is as close as possible to standard usage There are two versions of this package: scalarEDC and matrixEDC . The first can handle scalar differential-form expressions only, while the second can also handle matrix-valued differential forms, i.e., matrices whose components are (scalar) differential forms. Both versions are included in the compressed files below. The matrix package, offering user-controlled application of trace identities and the Cayley-Hamilton theorem, can also be used for symbolic matrix calculations. Version 3.3.5 allows Wedge and d to act on expressions that are series expansions ( SeriesData objects).

92. Free Textbook Tensor Calculus And Continuum Mechanics Textbook by John H. Heinbockel. Whole book or chapters in PostScript and PDF. http://www.math.odu.edu/~jhh/counter2.html

OLD DOMINION UNIVERSITY COLLEGE OF SCIENCES DEPARTMENT OF MATHEMATICS AND STATISTICS John H. Heinbockel Professor Emeritus Department of Mathematics and Statistics Old Dominion University Norfolk, Virginia 23529 E-Mail: jhh@math.odu.edu I have completed writing what I consider to be an introductory text for applied mathematicians, physicists and engineers. The finished work is titled INTRODUCTION TO TENSOR CALCULUS and CONTINUUM MECHANICS In Part One I have included introductory topics in tensors, differential geometry and relativity. In Part Two is presented basics from the areas of continuum mechanics (dynamics, elasticity, fluids, electricity, magnetism). The final section covers an introduction to quaternions, multvectors and Clifford algebra. You can purchase the final version of this project by Clicking Here Catalogue number is 01-0535. The free version below represents about 80% of the final version. From this free version you can see what you are getting. What the final version has that the free version does not have: 1. Additional worked examples.

93. Lambda Calculus Introduction to the lambda calculus for computer scientists. Shows how the calculus can be formalised in Scheme. http://www.mactech.com/articles/mactech/Vol.07/07.05/LambdaCalculus/

About MacTech Home Page Subscribe to MacTech! ... Webmaster Feedback Volume Number: Issue Number: Column Tag: Lisp Listener Lambda Calculus Abe Lincoln Introduction Intro to l-calculus LISP 101 What follows will be a crash course in LISP. or even because a list in any position can have a function position and argument positions of its own, and so on, to arbitrary depth. The next thing we need is a way to abstract out common process patterns into descriptions. This is done via lambda, the anonymous function. For instance, (lambda(x)(+x1)) is a function that takes in an evaluated argument, binds it with x, and then computes the body of the lambda form with the understanding that any occurrence of parameter x in the body will refer to the value of x bound by the lambda form. In this case, the returned result will be the argument plus one, and the argument will not be side effected. To invoke an anonymous function, we simply invoke it like any other function. We invoked sine like this: (sin3). Invoking (lambda(x)(+x1)) on the argument 3 would look like this: To define something we do this: (definefoo3). Thereafter, typing foo at the MacScheme prompt, we find it evaluates to 3.

94. Frank Potter Apos;s Science Gems - Mathematics Frank Potter apos;s Science Gems Mathematics This site has numerous mathematics resources. Included are sites on pre algebra, algebra, geometry, trigonometry, pre calculus, calculus, probability http://rdre1.inktomi.com/click?u=http://www.sciencegems.com/math.html&y=02B0

95. Calculus And Probability Online course by Stefan Waner and Steven R. Costenoble http://people.hofstra.edu/faculty/Stefan_Waner/cprob/cprobintro.html

Calculus Applied to Probability and Statistics for Liberal Arts and Business Majors A Complete Text Resource on the World Wide Web by Stefan Waner and Steven R. Costenoble Table of Contents 1. Continuous Random Variables and Histograms Exercises 2. Probability Density Functions: Uniform, Exponential, Normal, and Beta Exercises 3. Mean, Median, Variance and Standard Deviation Exercises 4. You're the Expert Creating a Family Trust Back to Main Page Introduction Y ou are a financial planning consultant at a neighborhood bank. A 22-year-old client asks you the following question: "I would like to set up my own insurance policy by opening a trust account into which I can make monthly payments starting now, so that upon my death or my ninety-fifth birthday - whichever comes sooner - the trust can be expected to be worth $500,000. How much should I invest each month?" Assuming a 5% rate of return on investments, how should you respond? To answer the question on the previous page, we must know something about the probability of the client's dying at various ages. There are so many possible ages to consider (particularly since we should consider the possibilities month by month) that it would be easier to treat his age at death as a continuous variable, one that can take on any real value (between 22 and 95 in this case). The mathematics needed to do probability and statistics with continuous variables is calculus. The material on statistics in this resource will be readily accessible to you if you are familar with derivatives and integrals (through Chapter 6 of

96. Homepage Henk Barendregt University of Nijmegen Lambda calculus, type theory and formalising mathematical vernacular. http://www.cs.kun.nl/~henk/

Henk Barendregt Chair Foundations of Mathematics and Computer Science Nijmegen University The Netherlands Henk Barendregt (1947) holds the chair of Foundations of Mathematics and Computer Science at Nijmegen University, The Netherlands, and is adjunkt professor at Carnegie Mellon University, Pittsburgh Pennsylvania, USA. He studied at Utrecht University mathematical logic, obtaining under his Masters in 1968 and his Ph.D. in 1971, both cum laude and Since 1986 he is professor at Nijmegen University, where he and his group work on Constructive Interactive Mathematics Awards Barendregt was elected member of the Academia Europaea Koninklijke Hollandsche Maatschappij der Wetenschappen (1995) and the Royal Dutch Academy of Sciences (1997). In 1998 he obtained a generous seven year grant of the Board of Directors of Nijmegen university. In 2002 he was knighted in the Orde van de Nederlandse Leeuw . Barendregt obtained on February 6, 2003 the NWO Spinoza Award 2002, the highest scientific award in the Netherlands. Papers Foundations Other papers Lectures Talks Courses Other interests Links Address:Nijmegen Institute for Computing and Information Science (NIII) Nijmegen University Box 9010 6500 GL Nijmegen The Netherlands Contact: henk loc AT ed cs.kun.nl

97. MathPages: Calculus And Differential Equations Kevin Brown's compilation of postings including many topics in differential equations. http://www.mathpages.com/home/icalculu.htm

Calculus and Differential Equations The Laplace Equation and Harmonic Functions Curvature, Intrinsic and Extrinsic Radial Paths in Schwarzschild Spacetime Analytic Functions, The Magnus Effect, and Wings ... Math Pages Main Menu

98. Bondi K-Calculus A simple derivation of Einstein's theory of relativity which is widely taught to undergraduate physics students. The mathematics required though make this easy for anyone to understand. http://www.geocities.com/ResearchTriangle/System/8956/Bondi/intro.htm

Bondi K-Calculus In simple terms, Bondi k-calculus is a method of deriving the effects of Einstein's theory of special relativity which requires only basic mathematics, and yet gives all the appropriate results. Now before all of the 'scientists' click to the next page and dismiss this as a derivation without substance, let me present a few details. The method was created by Sir Hermann Bondi, who not only wrote numerous papers on the theory of relativity, but was also given a professorship at Cambridge University. The derivation presented here is taught in undergraduate and graduate level physics courses around the world. Unfortunately it is rarely taught in High Schools, where its simplicity would benefit all students struggling with the traditional lorentz transformation derivation of relativity. Lesson 1 As is done in most derivations, let us limit space to a single dimension to spare having to draw four-dimensional figures on a two dimensional screen. In the diagram below, let the vertical axis represent time and the horizontal axis represent space. Then a curve in the diagram represents a point in space which is 'moving'.(As time progresses, the point changes its position). If the curve is a straight line, the point moves at a constant velocity. Let A and B be two such lines, (representing observers or spaceships, or whatever seems appropriate) which cross at some point. Each observer carries a clock and at the instant they meet, both reset their clocks to 0. As soon as they cross, A begins shining a flashlight at B for a period of time T.

99. The Epsilon Calculus Discussion of David Hilbert's development of this type of logical formalism with emphasis on prooftheoretic methods. http://plato.stanford.edu/entries/epsilon-calculus/

version history HOW TO CITE THIS ENTRY Stanford Encyclopedia of Philosophy A B C D ... Z This document uses XHTML-1/Unicode to format the display. Older browsers and/or operating systems may not display the formatting correctly. last substantive content change MAY The Epsilon Calculus The epsilon calculus is a logical formalism developed by David Hilbert in the service of his program in the foundations of mathematics. The epsilon operator is a term-forming operator which replaces quantifiers in ordinary predicate logic. Specifically, in the calculus, a term x A denotes some x satisfying A x ), if there is one. In Hilbert's Program, the epsilon terms play the role of ideal elements; the aim of Hilbert's finitistic consistency proofs is to give a procedure which removes such terms from a formal proof. The procedures by which this is to be carried out are based on Hilbert's epsilon substitution method. The epsilon calculus, however, has applications in other contexts as well. The first general application of the epsilon calculus was in Hilbert's epsilon theorems, which in turn provide the basis for the first correct proof of Herbrand's theorem. More recently, variants of the epsilon operator have been applied in linguistics and linguistic philosophy to deal with anaphoric pronouns. Overview The Epsilon Calculus The Epsilon Theorems Herbrand's Theorem ... Epsilon Operators in Linguistics, Philosophy, and Non-classical Logics

100. Financial Calculus By Martin Baxter and Andrew Rennie (CUP, 1996). Contents, preface, errata, supplementary text, reviews. http://www.financialcalculus.co.uk/

Web Site Selection Financial Calculus The website of Financial Calculus: an introduction to derivative pricing . This book has been written by Martin Baxter and Andrew Rennie, and is published by Cambridge University Press. The site contains features, errata, additional bonus text plus information about the authors and the book, which is now also available in Japanese and Hungarian. General Election Prediction The next British General Election result is predicted using scientific analysis of opinion polls and electoral geography. There are also detailed predictions of every seat, including a list of target vulnerable seats, and a complete nationwide list of seat predictions. Martin Baxter Home Page Personal website, containing contact information, past academic publications and assorted trivia.

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