161. Visual Calculus Short descriptions and examples for limits, derivatives, and integrals. Various plugins are needed to view some of the pages. http://archives.math.utk.edu/visual.calculus/

Tutorials Pre-Calculus Limits and Continuity Derivatives Applications of Differentiation ... Sequences and Series Information What? Who? How? Awards ... Help Page

162. Project Links | Home Contains modules for probability and statistics, discreet math, linear systems and advanced calculus. Developed by the Rensselaer Polytechnic Institute. http://links.math.rpi.edu/

Overview Background on the people involved in the project. Assumptions How we intend these modules to be used in the classroom. Hardware and software requirements. For Instructors Information for instructors using our materials. The Project Links Modules by general applied topic by general mathematics topic Hardware and Software Guidelines Recommendations for setting up your computer to maximize your time with Project Links. Developers' Connection Documentation and services for current developers and programmers, and for those with new module ideas. Jobs with Project Links Information for those RPI students with programming skills in Java, HTML, and Director. 2001 ASME Curriculum Innovation Award 2000 NEEDS Premier Award for Excellence in Engineering Education [2/24/03]: The website has been updated. The electromagtic field applets have been fixed, and a preliminary version of the module "compatibility mode" has been deployed.

163. 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.

164. New Calculus With Maple V Homepage Address The online texts listed serve as supplements for studying calculus and Differential Equations. http://www2.ncsu.edu/eos/info/maple_info/www/

165. Calculus Bible The calculus Bible by G. S. Gill. http://www.math.byu.edu/Math/CalculusBible/

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166. The Fusion Calculus: Expressiveness And Symmetry In Mobile Processes - Parrow, V (CiteSeer) This PhD thesis proposes the fusion calculus as a simplified picalculus with many formal advantages. http://citeseer.nj.nec.com/parrow98fusion.html

The Fusion Calculus: Expressiveness and Symmetry in Mobile Processes (1997) (Make Corrections) (46 citations) Joachim Parrow, Björn Victor Logic in Computer Science Home/Search Context Related View or download: sics.se/~joachim/fusionfull.ps.gz Cached: PS.gz PS PDF DjVu ... Help From: sics.se/~joachim/cv (more) (Enter author homepages) Rate this article: (best) Comment on this article (Enter summary) Abstract: We present the fusion calculus as a significant step towards a canonical calculus of concurrency. It simplifies and extends the -calculus. The fusion calculus contains the polyadic -calculus as a proper subcalculus and thus inherits all its expressive power. The gain is that fusion contains actions akin to updating a shared state, and a scoping construct for bounding their effects. Therefore it is easier to represent computational models such as imperative and concurrent constraints... (Update) Context of citations to this paper: More ...preserves transitions. We report here the reduction semantics for the recursion free fragment of the guarded fusion calculus from whose syntax in BNF like style is P : j :P :Q j P 1 jP 2 j (x)P with ; being either u x for the input or u x for the

167. Mathematical Sciences, Richard Statman Carnegie Mellon University Theory of computation, lambda calculus, combinatory logic. http://www.math.cmu.edu/people/fac/statman.html

Faculty Visiting Faculty Staff Graduate Students ... Home Richard Statman Professor Ph.D., Stanford University Office: Wean Hall 7214 Phone: (412) 268-8475 E-mail: statman@cs.cmu.edu Research My principal research interests lie in the theory of computation with special emphasis on symbolic computation. In particular, my current research involves lambda calculus and combinatory algebra. This area underwent extensive development in the first half of this century, and then lay dormant until Dana Scott's fundamental work in the 1970's. Part of what has emerged from Scott's work is that lambda calculus forms the foundation of functional programming at both the semantic and syntactic levels. As a result, the area has been revived by an influx of theoretical problems directly related to design and implementation issues. Selected Publications Church's lambda delta calculus, LPR '00 The word problem for combinators, RTA '00 Marginalia to a theorem of Jacopini, TLCA '99 Statman, R., "On Sets of Solutions to Combinator Equations," to appear in Theoretical Computer Science. Statman, R., "The Word Problem for Smullyan's Lark Combinator is Decidable," to appear in the Journal of Symbolic Computation.

168. Simone Martini University of Bologna, Italy Type systems for programming languages, logic in computer science, lambda-calculus. http://www.cs.unibo.it/~martini/

home contact teaching publications ... Dipartimento di Scienze dell'Informazione Simone Martini Simone Martini Professor of Computer Science Simone Martini received the Laurea degree in Scienze dell'Informazione and the Dottorato di Ricerca in Informatica (Ph.D. in Computer Science) from . He has been visitor at Digital Equipment Corporation, Systems Research Center in Palo Alto, at Stanford University , Department of Computer Science, and at His research interests are in the logical foundations of programming languages. He has written papers in lambda-calculus, type theory, linear and resource logics.

169. Calculus Made Easier: A Calculus Tutorial A tutorial covering limits, derivatives and integrals. Includes related resource links. http://wtv-zone.com/Angelaruth49/Calculus.html

Calculus Made Easier by Angela Olson Earth Image by NASA Math Graphics by Douglas N.Arnold at http://www.math.psu.edu/dna/graphics.html Index Introduction The Derivative Integration Helpful Links And Resources There are two components to calculus. One is the measure the rate of change at any given point on a curve. This rate of change is called the derivative. The simplest example of a rate of change of a function is the slope of a line. We take this one step further to get the rate of change at a point on a line. The other part of calculus is used to measure the exact area under a curve. This is called the integral. If you wanted to find the area of a semicircle, you could use integration to get the answer. The two parts; the derivative and the integral are inverse functions of each other. That is, they cancel each other out. Just as (x =x, the derivative of (integral (x)) = x and derivative of (integral (f (x)) = f(x). The derivative is a composite function. This means it is a function acting on another funcion. In fact, the function, is the input instead of just x. The derivative, then takes a type of formula and turns it into another simiilar type of formula. So, a polynomial will always yield a polynomial derivative. A trigonomic function will always yield a trigonomic derivative. There are a few exceptions, but this is generally the case. This is also true for the integral. Back To Top Geometrically, the derivative can be perceived as the slope of the tangent line to a curve at a given point. This is roughly how steep the curve is at a given point. We can easily find the rate of change of a line just by finding the slope. But, most formulas are not as simple as a line and they're usually curved. We use the basic formula of a line to get the derivative. If you remember the slope of a line is:

170. Math Notes Quick reference for basic algebra, trigonometry, geometry, calculus, and physics formulas. Includes online calculators. http://www.geocities.com/tvtronix/mathnotes/

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171. Math Forum: Algebra & Calculus Sketches - Ruth Carver For calculus, gives the tangent line problem and its solution. http://www.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/

172. Analysis 2.3 Analysis is a tool that can draw 2D and 3D graphs of functions with different characteristics. Implicit f(x,y)=g(x,y)form curves are plot in a xy plane. Free download for all Windows versions http://www.geocities.com/leibowitz.geo/analysis_en.html

Analysis 2.3beta2 by Davide Bucci Download Analysis 2.3beta2 is the last version of a computer program to which I have worked for more than five years. Initially conceived as a simple tool for function plotting in high school, by now it has become a really powerful instrument that can be used on first and second year calculus courses at the university. The program sources can be downloaded on the web under the terms of the GNU General Public License v. 2. Analysis is obviously more little and less powerful of a lot of terrible math program that you can find (and pay!), but it requires a fraction of the time necessary to be skilled in and it is really smart, rapid and easy to use: you can run it by a 1.44 MB diskette on old computers! Is that the thing that is more interesting: it is really good for helping you in verifying your exercises without forcing you in using complex functions on terrible computer programs. This document is part of the official documentation and can be printed if you want to have a short resume of the principal possibilities of Analysis. Who used a previous version of the software, will find a lot of news that would probably appreciate; there is also the possibility of choosing the language used by the program between English, French and Italian. Whoever would like to help me and translate Analysis in other languages can find me at

173. Elementary Calculus Elementary calculus An Approach a book by H. Jerome Keisler originally published by Prindle, Weber Schmidt (2nd ed 1986) http://www.math.wisc.edu/~keisler/calc.html

Elementary Calculus: An Approach Using Infinitesimals On-line Edition, by H. Jerome Keisler This is a calculus textbook at the college Freshman level based on Abraham Robinson's infinitesimals, which date from 1960. Robinson's modern infinitesimal approach puts the intuitive ideas of the founders of the calculus on a mathematically sound footing, and is easier for beginners to understand than the more common approach via limits. The whole book in one large file (24 megabytes) Single chapters in much smaller files: Preface to First and Second Editions Contents and Introduction Chapter 1 Real and Hyperreal Numbers Chapter 2 Differentiation Chapter 3 Continuous Functions Chapter 4 Integration Chapter 5 Limits, Analytic Geometry, and Approximations Chapter 6 Applications of the Integral Chapter 7 Trigonometric Functions Chapter 8 Exponential and Logarithmic Functions Chapter 9 Infinite Series Chapter 10 Vectors Chapter 11 Partial Differentiation Chapter 12 Multiple Integrals Chapter 13 Vector Calculus Chapter 14 Differential Equations Appendix Epilogue

174. A Curry-Howard Foundation For Functional Computation With Control - Ong, Stewart Article by C.H. L. Ong and C. A. Stewart which presents a call-by-name variant of Parigot's lambda-mu calculus. The calculus is proposed as a foundation for first-class continuations and statically scoped exceptions in functional programming languages. http://citeseer.nj.nec.com/ong97curryhoward.html

A Curry-Howard foundation for functional computation with control (1997) (Make Corrections) (36 citations) C.-H. L. Ong, C. A. Stewart Home/Search Context Related View or download: comlab.ox.ac.uk/pub/Docu popl97.ps.gz Cached: PS.gz PS PDF DjVu ... Help From: comlab.ox.ac.uk/ou publications (more) Homepages: C.Ong HPSearch (Update Links) Rate this article: (best) Comment on this article (Enter summary) Abstract: We introduce the type theory ¯ v , a call-by-value variant of Parigot's ¯-calculus, as a Curry-Howard representation theory of classical propositional proofs. The associated rewrite system is Church-Rosser and strongly normalizing, and definitional equality of the type theory is consistent, compatible with cut, congruent and decidable. The attendant call-by-value programming language ¯pcf v is obtained from ¯ v by augmenting it by basic arithmetic, conditionals and fixpoints. We study the... (Update) Context of citations to this paper: More ...formal ways of reasoning about them would be useful. One possibility is equational reasoning using control calculi such as C [2] or The counterexample in Section 3 shows the limitations of these calculi, however, in that their equational theories are not consistent...

175. Charles Stewart Technische Universit¤t Berlin, Theory and Formal Specifications group Proof theoretic semantics, lambda calculus, linear logic, theoretical computer science, philosophy of language. http://www.linearity.org/cas/

Charles Alexander Stewart Personal Information I am a postdoctoral researcher in theoretical computer science associated with the Institute of Artifical Intelligence at Technische Universitaet Dresden. In the past, I have been associated with the Theory and Formal Specifications group of Technische Universitaet Berlin, the Linear Naming and Computation section of the Church Project at Boston University, the Department of Computer Science at Brandeis University, and the Foundations of Computation section of the Programming Research Group at Oxford University. Research Interests My research interests include: Structural proof theory: Deep inference and the Calculus of structures; Natural deduction, sequent calculus, and applications to programming language design and implementation; Modal logic and display logic; Programming language theory: Optimal reductions in the lambda calculus; Linear naming and graph reduction, interaction nets; Continuations in theory and practice; Relationships between functional and logic programming; Graph transformation: Graph transformation and the design of distributed algorithms;

176. ResearchIndex Proof Theoretic Approach To Specification Languages Thesis studies FORUM as specification language. FORUM is a higher order logic based on the logical connectives of Linear Logic. Initial example demonstrates that FORUM is well suited to specify concurrent computations by specifying the higher order Ÿ calculus. http://citeseer.nj.nec.com/chirimar95proof.html

177. Math Index Covers derivative and integral conversions as well as calculus rules. Includes practice exercises. http://cne.gmu.edu/modules/dau/calculus/calculus_frm.html

178. Calculus History Interested in how calculus became what it is today? This site offers a historical account of the progression of the study from its infancy to its present state. http://www-gap.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.

179. MathServ Calculus ToolKit Online calculators for several calculus functions. http://math.vanderbilt.edu/~pscrooke/toolkit.shtml

The MathServ Calculus Toolkit 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 August 17, 2000.

180. AMS Online Books/SURV53 The Convenient Setting of Global Analysis foundations of differential calculus in infinite dimensions with applications to differential geometry and global analysis by Andreas Kriegl and Peter W. Michor published by AMS in 1997. Whole book or chapters in crosslinked PDF. http://www.ams.org/online_bks/surv53/

Title List Help AMS Home AMS Bookstore The Convenient Setting of Global Analysis by Andreas Kriegl and Peter W. Michor Publication Date: 1997 Number of pages: 618 pp. Publisher: AMS ISBN: 0-8218-3396-0 SURV/53.E Download Complete Book - FREE Download Individual Chapters Frontmatter Title Contents Preface Introduction Calculus of Smooth Mappings Calculus of Holomorphic and Real Analytic Mappings Partitions of Unity ... References and Index The online version differs from the printed book. Minor corrections have been incorporated into the online version. Comments: webmaster@ams.org Privacy Statement Search the AMS

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