21. Fractional Calculus -- From Wolfram MathWorld Defines the fractional integral in terms of the gamma function and contains links to information on fractional derivatives. http://mathworld.wolfram.com/FractionalCalculus.html

Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics ... Fractional Calculus Fractional Calculus The study of an extension of derivatives and integrals to noninteger orders. Fractional calculus is based on the definition of the fractional integral as where is the gamma function . From this equation, fractional derivatives can also be defined. SEE ALSO: Derivative Fractional Derivative Fractional Differential Equation Fractional Integral ... Riemann-Liouville Operator REFERENCES: Butzer, P. L. and Westphal, U. "An Introduction to Fractional Calculus." Ch. 1 in Applications of Fractional Calculus in Physics (Ed. R. Hilfer). Singapore: World Scientific, pp. 1-85, 2000. Kilbas, A. A.; Srivastava, H. M.; and Trujiilo, J. J. Theory and Applications of Fractional Differential Equations. Amsterdam, Netherlands: Elsevier, 2006. McBride, A. C. Fractional Calculus. New York: Halsted Press, 1986. Nishimoto, K. Fractional Calculus. New Haven, CT: University of New Haven Press, 1989. Samko, S. G.; Kilbas, A. A.; and Marichev, O. I. Fractional Integrals and Derivatives.

22. Calculus - Simple English Wikipedia, The Free Encyclopedia calculus is a branch of mathematics which looks at things that change over time. It tries to say what type of change it is and how big it is using functions at the exact moment http://simple.wikipedia.org/wiki/Calculus

Calculus From Wikipedia, the free encyclopedia Jump to: navigation search This page or section does not have any sources . You can help Wikipedia by finding sources, and adding them. Tagged since September 2009 Calculus is a branch of mathematics which looks at things that change over time. It tries to say what type of change it is and how big it is using functions at the exact moment at which the change is taking place. There are two different types of calculus. Differential calculus divides things into small ( different ) pieces and tells us how they change from one moment to the next, while integral calculus joins ( integrates ) the small pieces together and tells us how much of something is made by a change. It is used in many different fields such as physics astronomy biology engineering ... medicine and sociology The word Calculus is derived from the Latin for "small stone". Contents History Differential calculus Main idea of calculus Demonstration of main idea of calculus ... change History In the 1670s and 1680s, Sir Isaac Newton in England and Gottfried Leibniz in Germany figured out calculus at the same time, working separately from each other. Newton wanted to make new math to predict where to see

23. Multivariable Calculus Textbook by George Cain and James Herod. Chapters in PDF. http://www.math.gatech.edu/~cain/notes/calculus.html

Multivariable Calculus George Cain James Herod This is a textbook for a course in multivariable calculus. It has been used for the past few years here at Georgia Tech. The notes are available as Adobe Acrobat documents. If you do not have an Adobe Acrobat Reader, you may down-load a copy, free of charge, from Adobe Title page and Table of Contents Table of Contents Chapter One - Euclidean Three Space 1.1 Introduction 1.2 Coordinates in Three-Space 1.3 Some Geometry 1.4 Some More GeometryLevel Sets Chapter Two - VectorsAlgebra and Geometry 2.1 Vectors 2.2 Scalar Product 2.3 Vector Product Chapter Three - Vector Functions 3.1 Relations and Functions 3.2 Vector Functions 3.3 Limits and Continuity Chapter Four - Derivatives 4.1 Derivatives 4.2 Geometry of Space CurvesCurvature 4.3 Geometry of Space CurvesTorsion 4.4 Motion Chapter Five - More Dimensions 5.1 The space R n 5.2 Functions Chapter Six - Linear Functions and Matrices 6.1 Matrices 6.2 Matrix Algebra Chapter Seven - Continuity, Derivatives, and All That 7.1 Limits and Continuity

24. Calculus - A To Z Home's Cool Homeschooling Math calculus made easy through online games for young homeschoolers. Links from your Homeschooling Guide http://homeschooling.gomilpitas.com/explore/calculus.htm

YOU ARE HERE: HOMESCHOOLING EXPLORATIONS 4 KIDS MATH Earn your certificate from the comfort of your own computer. Homeschooling Explorations 4 Kids I am Ann Zeise , your guide to the best and most interesting and useful sites and articles about home education on the web. Homeschooling New Kids Links New Kids Links Contact Ann Zeise ... Curriculum Shopping Site Index: A B C D ... Z Advanced Math Math 4 Teens Calculators History of Math High School Math Algebra Geometry Trigonometry Calculus Math 4 Kids Art Math Connection Calendars Clocks Logic Games ... Word Problems Math Curriculum Math Shop Explorations 4 Kids Computer Literacy Drivers Ed Fine Arts General Interest ... Social Studies A to Z Home's Cool Welcome to Homeschooling Articles Beginning to Homeschool Chat Room ... Unschooling Calculus AP Calculus We have selected relevant material from MIT's introductory courses to support students as they study and educators as they teach the AP Calculus curriculum. Calculus Graphics These are excerpts from a collection of graphical demonstrations I developed for first year calculus.

25. Fractional Calculus Provides the Riemann-Liouville definition of the fractional integral, a definition of fractional derivatives, and a list of applications of the calculus. http://people.tuke.sk/ivo.petras/FC.html

Fractional Calculus (differentiation and integration of arbitrary non-integer order) Key words: fractional calculus fractional integral fractional derivatives fractional differential equations 1. Introduction The term fractional calculus is no new. It is a generalization of the ordinary differentiation and integration to non-integer (arbitrary) order. The subject is as old as the calculus of differentiation and goes back to times when Leibniz Gauss , and Newton invented this kind of calculation. In a letter to L`Hospital in 1695 Leibniz raised the following question: "Can the meaning of derivatives with integer order be generalized to derivatives with non-integer orders?" The story goes that L`Hospital was somewhat curious about that question and replied by another question to Leibniz. "What if the order will be 1/2?" Leibniz in a letter dated September 30, 1695 replied: The translation reads: "It will lead to a paradox, from which one day useful consequences will be drawn." The question raised by Leibniz for a fractional derivative was an ongoing topic in the last 300 years. Several mathematicians contributed to this subject over the years. People like Liouville Riemann , and Weyl made major contributions to the theory of fractional calculus. The story on the fractional calculus continued with contributions from

26. Integral - Wikipedia, The Free Encyclopedia Integration is an important concept in mathematics and, together with differentiation, is one of the two main operations in calculus. Given a function ƒ of a real variable x and an http://en.wikipedia.org/wiki/Integral_calculus

Integral From Wikipedia, the free encyclopedia   (Redirected from Integral calculus Jump to: navigation search This article is about the concept of integrals in calculus . For the set of numbers, see integer . For other uses, see Integral (disambiguation) A definite integral of a function can be represented as the signed area of the region bounded by its graph. Topics in Calculus Fundamental theorem Limits of functions Continuity ... Identities Rules: Power rule Product rule Quotient rule Chain rule ... Integral calculus Integral Lists of integrals Improper integrals Integration by: parts disks cylindrical shells ... Jacobian Integration is an important concept in mathematics and, together with differentiation , is one of the two main operations in calculus . Given a function of a real variable x and an interval a b ] of the real line , the definite integral is defined informally to be the net signed area of the region in the xy -plane bounded by the graph of , the x -axis, and the vertical lines x a and x b The term integral may also refer to the notion of antiderivative , a function F whose derivative is the given function . In this case, it is called an

27. Calculus Help | Homeschool Online Lessons Get calculus help via online videos. Create your homeschool curriculum using homeschool online lessons. calculus online video courses will make your home school a success. http://www.thinkwell.com/homeschool/product/calculus

28. Applications Of Fractional Calculus Provides information of the practical uses of the calculus. http://www.icp.uni-stuttgart.de/Jahresberichte/01/node66.html

Next: Fractional Dynamics in the Up: Scientific Report Previous: The Broad Histogram Method: Contents Applications of Fractional Calculus The idea of generalizing the concepts of differentiation and integration to noninteger (fractional) orders has a long mathematical history. In mathematics one learns very early that the -th derivative of is for . It is little known, however, that this rule can be naturally generalized to noninteger orders such that for arbitrary real (and complex) . Over the centuries many mathematicians have built up a large body of mathematical knowledge on fractional integrals and derivatives. Although fractional calculus is a natural generalization of calculus, and although its mathematical history is equally long, it has, until recently, played a negligible role in physics. This situation is beginning to change and there has been some interest in Applications of Fractional Calculus in Physics. Our Institute has published a book concerning this topic which was well received by the scientific public (see section Many applications of fractional calculus in physics amount to replacing the time derivative in an evolution equation with a derivative of fractional order. This is not merely a phenomenological procedure providing an additional fit parameter. Rather fractional derivatives seem to arise generally and universally, and for deep mathematical reasons. One central result of the work at our institute has been the fact that fractional derivatives arise as the infinitesimal generators of a class of translation invariant convolution semigroups. These semigroups appear universally as attractors for coarse graining procedures or scale changes. They are parametrized by a number in the unit interval corresponding to the order of the fractional derivative. Ongoing work concentrates on applications of fractional time evolutions in particular to diffusion phenomena and glassy relaxation.

29. Math.com Homework Help Calculus Free math lessons and math homework help from basic math to algebra, geometry and beyond. Students, teachers, parents, and everyone can find solutions to http://www.math.com/homeworkhelp/Calculus.html

30. Calculus | Define Calculus At Dictionary.com , lus es. 1. Mathematics . a method of calculation, esp. one of several highly systematic methods of treating problems by a special system of algebraic notations, as http://dictionary.reference.com/browse/Calculus

31. Newton Vs. Leibniz; The Calculus Controversy Newton vs. Leibniz; The calculus Controversy Like most discoveries, calculus was the culmination of centuries of work rather than an instant epiphany. http://www.angelfire.com/md/byme/mathsample.html

Newton vs. Leibniz; The Calculus Controversy Like most discoveries, calculus was the culmination of centuries of work rather than an instant epiphany. Mathematicians all over the world contributed to its development, but the two most recognized discoverers of calculus are Isaac Newton and Gottfried Wilhelm Leibniz. Although the credit is currently given to both men, there was a time when the debate over which of them truly deserved the recognition was both heated and widespread. As the renowned author of Principia (1687) as well as a host of equally esteemed published works, it appears that Newton not only went much further in exploring the applications of calculus than Leibniz did, but he also ventured down a different road. Leibniz and Newton had very different views of calculus in that Newton�s was based on limits and concrete reality, while Leibniz focused more on the infinite and the abstract (Struik, 1948). However, regardless of the divergent paths these two scholars chose to venture down, the question of who took the first step remained the primary issue of debate. Unaware that Newton was reported to have discovered similar methods, Leibniz discovered �his� calculus in Paris between 1673 and 1676 (Ball, 1908). By 1676, Leibniz realized that he was onto something �big�; he just didn�t realize that Newton was on to the same big discovery because Newton was remaining somewhat tight lipped about his breakthroughs. In fact, it was actually the delayed publication of Newton�s findings that caused the entire controversy. Leibniz published the first account of differential calculus in 1684 and then published the explanation of integral calculus in 1686 (Boyer, 1968).

32. CVGMT: Preprints on various topics on the calculus of variations. http://cvgmt.sns.it/

Home People News Preprints ... Help Welcome to the HomePage of the Research Group in Calculus of Variations and Geometric Measure Theory at Pisa. Look here to know more about us. Please, feel free to download and use all the material you find interesting. If you want to receive regularly the group news, subscribe to our mailing list in the Mail section. Registered users can: Ennio De Giorgi's HomePage Calculus of Variations Seminars at the Math. Dept. of University of Pisa PostDoc Positions at the SNS Pisa 16 Jan 2011 - 15 Jan 2013 Latest News Added to the Preprint Server (Meeting Announcement) 5 Jan 2011 - 7 Jan 2011 "Kinetic theory, optimal transport, probability, geometry: old and new", Conference in the honor of C�dric Villani, Fields medalist 2010 New Papers Added to the Preprint Server P. Koskela M. Miranda Jr. N. Shanmugalingam International Mathematical Series (N.Y.) Geometric properties of planar BV-extension domains N. Fusco F. Maggi A. Pratelli (Submitted Paper) On the isoperimetric problem with respect to a mixed Euclidean-Gaussian density F. Maddalena D. Percivale F. Tomarelli (Preprint) Adhesive Flexible Material Structures F. Ferrari -

33. Math Forum: Calculus The best Internet resources for calculus classroom materials, software, Internet projects, and public forums for discussion. http://mathforum.org/calculus/

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 ... Help http://mathforum.org/ The Math Forum is a research and educational enterprise of the Goodwin College of Professional Studies

34. Mathematics Archives - Topics In Mathematics - Calculus calculus Resources OnLine ADD. KEYWORDS Initiatives, Projects and Programs, Articles, Posters, Discussions, Software, Publisher sites, Other listings of calculus http://archives.math.utk.edu/topics/calculus.html

Topics in Mathematics Calculus Calculus Resources On-Line ADD. KEYWORDS: Initiatives, Projects and Programs, Articles, Posters, Discussions, Software, Publisher sites, Other listings of calculus resources Aid for Calculus ADD. KEYWORDS: Solving problems in calculus AP Calculus on the Web ADD. KEYWORDS: Textbooks, 1998 Syllabus, Approved Calculators, Resources Are You Ready for Calculus? What you should know! Area of a Circle SOURCE: Tom Richmond, Western Kentucky University TECHNOLOGY: Animated Gif Basic EXCEL-skills for calculus and differential equations ADD. KEYWORDS: Sample worksheets, Sample problems / skills Better File Cabinet ADD. KEYWORDS: Database of calculus problems SOURCE: Eric Hsu and University of Texas at Austin Bisection Method Tutorial Cal Poly Linked Curriculum Program Interdisciplinary Projects ADD. KEYWORDS: Projects Calculus Calculus I Home Page ADD. KEYWORDS: Sample CBL Experiment: Newton's Law of Cooling, TI-85 Programs and CBL Experiment Data, Mathematica Notebooks Calculus 1 - Problems and Solutions ADD. KEYWORDS:

35. 49: Calculus Of Variations And Optimal Control; Optimization calculus of variations and optimal control. Optimization. http://www.math.niu.edu/~rusin/known-math/index/49-XX.html

Search Subject Index MathMap Tour ... Help! ABOUT: Introduction History Related areas Subfields POINTERS: Texts Software Web links Selected topics here 49: Calculus of variations and optimal control; optimization Introduction Calculus of variations and optimization seek functions or geometric objects which are optimize some objective function. Certainly this includes a discussion of techniques to find the optima, such as successive approximations or linear programming. In addition, there is quite a lot of work establishing the existence of optima and characterizing them. In many cases, optimal functions or curves can be expressed as solutions to differential equations. Common applications include seeking curves and surfaces which are minimal in some sense. However, the spaces on which the analysis are done may represent configurations of some physical system, say, so that this field also applies to optimization problems in economics or control theory for example. History Applications and related fields See also (for numerical optimization)

36. Pauls Online Notes : Calculus I Here are my online notes for my calculus I course that I teach here at Lamar University. Despite the fact that these are my �class notes�, they should be http://tutorial.math.lamar.edu/Classes/CalcI/CalcI.aspx

MPBodyInit('CalcI_files') Paul's Online Math Notes Online Notes / Calculus I You can navigate through this E-Book using the menu to the left. For E-Books that have a Chapter/Section organization each option in the menu to the left indicates a chapter and will open a menu showing the sections in that chapter. Alternatively, you can navigate to the next/previous section or chapter by clicking the links in the boxes at the very top and bottom of the material. Also, depending upon the E-Book, it will be possible to download the complete E-Book, the chapter containing the current section and/or the current section. You can do this be clicking on the E-Book Chapter , and/or the Section link provided below. For those pages with mathematics on them you can, in most cases, enlarge the mathematics portion by clicking on the equation. Click the enlarged version to hide it. E-Book Review Calculus I (Math 2413) Here are my online notes for my Calculus I course that I teach here at Lamar University.  Despite the fact that these are my “class notes”, they should be accessible to anyone wanting to learn Calculus I or needing a refresher in some of the early topics in calculus.  I’ve tried to make these notes as self contained as possible and so all the information needed to read through them is either from an Algebra or Trig class or contained in other sections of the notes.

37. E-Calculus Home Page A basic calculus tutorial covering limits, derivatives, and integrals in PDF format. http://www.math.uakron.edu/~dpstory/e-calculus.html

A Note on the Retirement of D. P. Story Last Update: 5/01/2006 While the navigation system is out of order, here is a list of direct links to the tutorial files. Root Directory mainmenu.pdf maintut.pdf Calculus 1 Directory c1_menu.pdf Functions c1f_t.pdf c1f_t1.pdf Limits c1l_t.pdf c1l_t1.pdf c1l_t2.pdf c1l_tp.pdf Continuity c1c_t.pdf c1c_tp.pdf Differentiation c1d_t.pdf c1d_t1.pdf c1d_tp.pdf Integration c1i_t.pdf c1i_t1.pdf c1i_tp.pdf c1i_a.pdf ... What's New Get the Latest version of Acrobat Reader 5.0. Click on the Get Acrobat Icon above to go to the download area. e-Calculus is a Calculus I tutorial written in TeX and converted to the Adobe Portable Document Format (PDF). Features include verbose discussion of topics , typeset quality mathematics, user interactivity in the form of multiple choice quizzes, in-line examples and exercises with complete solutions, and pop-up graphics. If you are a first time user, be sure to check out the section entitled Important Components and the section Important Information directly below it before you start e-Calculus e-Calculus is viewed in the PDF format. This requires that you have

38. Calculus Online Book A free, complete 360 page book covering all the basics of calculus. http://www.understandingcalculus.com/

Understanding Calculus Home Testimonials Table of Contents Preface ... Share page with friends Your Name: Friend Emails: Your Email - optional: Understanding Calculus Understanding Calculus is a complete online introductory book that focuses on concepts. Integrated throughout the e-book are many engineering applications aimed at developing the student's scientific approach towards problem solving. The book has as much to do with calculus as with philosophy. My motivation in writing it was to prove to myself that I could understand a complex subject like calculus by applying simple rules of logic and reason. As Henry Ford said, " Nothing is particularly hard if you divide it into small jobs ". I have now forgotten a lot of the calculus, but what remains is that sense that anything can be understood. Too much of the world is complicated by layers of evolution. If you understand how each layer is put down then you can begin to understand the complex systems that govern our world. Charles Darwin wrote in 1859 in his On The Origin of Species " When we no longer look at an organic being as a savage looks at a ship, as at something wholly beyond his comprehension; when we regard every production of nature as one which had a history; when we contemplate every complex structure and instinct as the summing up of many contrivances, each useful to the possessor, nearly in the same as when we look at any great mechanical invention as the summing of the labour, the experience, the reason, and even the blunders of numerous workmen; when we thus view each organic being, how far more interesting, I speak from experience, will the study of natural history become! "

39. Connected Calculus An applied calculus tutorial covering topics such as curve fitting, series, and optimization. http://www.math.montana.edu/frankw/ccp/calculus/topic.htm

The Connected Curriculum Project Contents Models, Data, and Curve Fitting Estimation and Limits Sequences and Discrete Dynamical Systems Derivatives and Differention ... Numerical Methods Models, Data, and Curve Fitting A Guide to this Chapter. The Mean and the Median Linear Models Linear Regression Quadratic Models Exponential Models Logistic Models Periodic Models Contents Estimation and Limits A Guide to this Chapter. Introduction When is it Safe to Drink the Water? A Descriptive Look Estimation and Limits Area ... Contents Sequences and Discrete Dynamical Systems A Guide to this Chapter. Quickstart Population Models Exponential Models Exponential Models with Immigration Linear Dynamical Systems ... Contents Derivatives and Differention A Guide to this Chapter. Introduction Curved Mirrors Comparing a Function with its Derivative Computing the Derivative as a Limit Visualizing the Derivative as a Limit Sometimes There Isn't a Tangent Interpretation Powers Linearity of the Derivative Polynomials Derivatives of the Trigonometric Functions Product Rule Quotient Rule Chain Rule Inverse Function Rule Derivatives of the Inverse Trigonometric Functions The Exponential Function Logarithms Implicit Differentiation Related Rates Mean Value Theorem Higher Order Derivatives Partial Derivatives Directional Derivatives The Gradient Contents Graphing A Guide to this Chapter.

40. Some Multivariable Calculus Ideas Various calculus problems are solved and plotted on a 3D graph. http://www.ma.iup.edu/MathDept/Projects/CalcDEMma/veccalc/veccalc.html

Some Multivariable Calculus Ideas This is an evaluated Mathematica notebook. Since the notebook is intended to be interactive, it may be helpful to also view the unevaluated version Gary S. Stoudt Mathematics Department Indiana University of PA Indiana, PA 15705 GSSTOUDT@grove.iup.edu Functions to Initialize Purpose Parametric Curves Vector Functions and Curves ... Line Integrals Go up to Calculus and Differential Equations Project Description

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