Calculus Lecture Notes calculus Lecture Notes. To view the following notes, you must have Adobe Reader . Mac, DOS, Windows and SUN versions are available for download from Adobe http://www.math.scar.utoronto.ca/calculus/Redbook/
FREE Mathematics How-to Library - Math Homework Help Math Tutor Software Offers help with algebra, geometry, calculus, fractions, money, and trigonometry problems. Includes worked examples and files for download with more information and exercises. http://www.teacherschoice.com.au/mathematics_how-to_library.htm
Extractions: Teachers' Choice Software home page Stuck on your homework ? No problem! Get help FAST with your mathematics and physics questions. We provide personalized , professional tutoring in high school mathematics and physics. We can help you now ! Select a category from the table below, or scroll this page to view the topic headings.
Earliest Uses Of Symbols Of Calculus Gives background for notations that are commonly used like the integral and delta signs. http://members.aol.com/jeff570/calculus.html
Extractions: Earliest Uses of Symbols of Calculus Last revision: Dec. 1, 2004 Derivative. The symbols dx, dy, and dx/dy were introduced by Gottfried Wilhelm Leibniz (1646-1716) in a manuscript of November 11, 1675 (Cajori vol. 2, page 204). f'(x) for the first derivative, f''(x) for the second derivative, etc., were introduced by Joseph Louis Lagrange (1736-1813). In 1797 in Théorie des fonctions analytiques the symbols f'x and f''x are found; in the Oeuvres, Vol. X , "which purports to be a reprint of the 1806 edition, on p. 15, 17, one finds the corresponding parts given as f(x), f'(x), f''(x), f'''(x) " (Cajori vol. 2, page 207). In 1770 Joseph Louis Lagrange (1736-1813) wrote for in his memoir Nouvelle méthode pour résoudre les équations littérales par le moyen des séries Oeuvres, Vol. III In 1772 Lagrange wrote u' du dx and du u'dx in "Sur une nouvelle espèce de calcul relatif à la différentiation et à l'integration des quantités variables," Nouveaux Memoires de l'Academie royale des Sciences et Belles-Lettres de Berlin Oeuvres, Vol. III
Mathematical Sciences, Richard Statman Carnegie Mellon University Theory of computation, lambda calculus, combinatory logic. http://www.math.cmu.edu/people/fac/statman.html
Extractions: E-mail: statman@cs.cmu.edu 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. The omega rule is sigma-zero-three hard (with Benedetto Intrigilia), LICS'04 On the lambda Y calculus, LICS '02 Church's lambda delta calculus, LPR '00 The word problem for combinators, RTA '00
Refinement Calculus Refinement calculus Tutorial. The refinement calculus is a formalisation of the stepwise refinement method of program construction. http://www.ecs.soton.ac.uk/~mjb/refcalc-tut/home.html
Extractions: The refinement calculus is a formalisation of the stepwise refinement method of program construction. The required behaviour of the program is specified as an abstract, possibly non-executable, program which is then refined by a series of correctness-preserving transformations into an efficient, executable program. We give an introduction to the application of the refinement calculus by using it to derive a few example programs. You may need to take a quick look at the Logical Notation and Mathematical Notation used in this tutorial, before going on to the Specification and Programming Notation Note that the specification notation used here is closer to the style of Back and Morris , rather than that of Morgan , though the differences are minor. In the refinement calculus, specifications are written as abstract programs usually in the form of specification statements. For example, a program that assigns x an arbitrary element from set S , provided S is not empty, may be specified as: We write to say that program is refined by program . This means that is a correct implementation of . Since refinement is transitive, a refinement step can always be broken up into a number of smaller steps, i.e.
Extractions: In my opinion, calculus is one of the major intellectual achievements of Western civilization - in fact of world civilization. Certainly it has had much more impact in shaping our world today than most of the works commonly included in a Western Civilization course books such as Descartes's Discourse on Method or The Prince by Machiavelli. But at most universities, we have taken this magnificent accomplishment of the human intellect and turned it into a boring course. Sawyer's little book What Is Calculus About? (Another book in the same vein, but more recent, is The Hitchhiker's Guide to Calculus by Michael Spivak.) For many of us mathematicians, calculus is far removed from what we see as interesting and important mathematics. It certainly has no obvious relevance to any of my own research, and if it weren't for the fact that I teach it, I would long ago have forgotten all the calculus I ever learned. But we should remember that calculus is not a mere ``service course.'' For students, calculus is the gateway to further mathematics. And aside from our obligation as faculty to make all our courses interesting, we should remember that if calculus doesn't seem like an interesting and worthwhile subject to students, then they are unlikely to see mathematics as an attractive subject to pursue further.
The Join-calculus Language The joincalculus is an experimental language based on the homonymous process The join calculus language this system contains a compiler and an http://pauillac.inria.fr/join/
Extractions: [an error occurred while processing this directive] The join-calculus is an experimental language based on the homonymous process calculus. It provides a simple support for distributed programming. The join-calculus programming model features concurrent processes running on several machines, static type-checking, global lexical scope, transparent remote communication, agent-based mobility, and some failure-detection. We have developped two implementations of the Join-Calculus in the Objective-CAML envirronment. Our model of concurrency: The reflexive chemical abstract machine and the join-calculus , by Cédric Fournet and Georges Gonthier, POPL'96.
Marta Sanz-Solé's Home Page Universitat de Barcelona. Random fields; Malliavin calculus; Anticipative calculus; Small perturbations of dynamical sytems; Stochastic partial differential equations. Publications, lecture notes. http://orfeu.mat.ub.es/~sanz/
UBC Calculus Help Integrals University of British Columbia course notes. Covers integration and series with applications. Illustrated with interactive Java applets. http://www.ugrad.math.ubc.ca/coursedoc/math101/
Technology Based Problems calculus and differential calculus problems are presented. The possible solution or solutions are given. http://www.rose-hulman.edu/Class/CalculusProbs/
Extractions: Welcome to the Complex, Technology Based Problems in Calculus Home Page We offer complex, technology-based problems in calculus with applications in science and engineering. These problems have a higher level of complexity than traditional text book problems and foster use of a computer algebra system. Each problem set includes discussions of related teaching issues and solutions worked in Mathematica By category: Choose from categories that best describe the problem type desired. Full text word search: All problems with the string you enter will be listed. Keyword search: All problems come with a list of key words provided by the author(s). All matches will be listed. Alphabetically: If you know the file name for a problem set, you can find it in alphabetical order.
Why Calculus? The goal of the course is to show why calculus has served as the principal quantitative language of science for more than three hundred years. http://www.math.nus.edu.sg/aslaksen/teaching/calculus.html
Extractions: Sir Isaac Newton, 1643-1727 Gottfried Wilhelm von Leibniz, 1646-1716 Back to Helmer Aslaksen's home page. The goal of the course is to show why calculus has served as the principal quantitative language of science for more than three hundred years. How did Newton and Leibniz transform a bag of tricks into a powerful tool for both mathematics and science? Why is calculus so useful in geometry, physics, probability and economics? Why are mathematicians so concerned with rigor in calculus? Since calculus is about calculating, what is the relationship between calculus and computers? What is the relationship between calculus and new topics like chaos and nonlinearity? If you want to understand what calculus is really about, then this is the course for you. Ancient peoples, driven by natural curiosity and the demands of applications, confronted the problems of finding areas and volumes of various shapes. Their methods of solving these problems may be regarded as precursors to integration . Outstanding in this regard was the work of the Greeks, exemplified by Archimedes' solutions to numerous problems of quadrature, and the works of the Chinese mathematicians Liu Hui and Zu Chongzhi. Concepts resembling differentiation did not arise until much later.
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/
PCPOW Home Page (Kent, WA), PCPOW (Prob/Stats and calculus Problems of the Week) calculus Question Stats Question Check our archives for problems from last year. http://www.kent.k12.wa.us/pcpow/
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
Extractions: 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. 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.
Calculus - Wikibooks The logarithmic spiral a function derived from calculus concepts of the We at the Wikibook of calculus aim to write a quality textbook to http://en.wikibooks.org/wiki/Calculus
Extractions: through Infinite Series. The logarithmic spiral a function derived from calculus concepts of the nautilus's shell demonstrates the universality of mathematics. We at the Wikibook of Calculus aim to write a quality textbook to facilitate mastering the topics of differentiation, integration, infinite series, conics, and parametric and polar equations. Please contribute wherever you feel the need. Further Analysis Formal Theory of Calculus Retrieved from " http://en.wikibooks.org/wiki/Calculus Categories Mathematics Calculus Views Personal tools Navigation Search Toolbox What links here Related changes Upload file Special pages ... Permanent link This page was last modified 03:36, 11 August 2005.
Webmath Offers interactive homework help in prealgebra, algebra, geometry, trigonometry, calculus, statistics, and real world math. From DiscoverySchool.com. http://www.webmath.com/
Extractions: Welcome to Webmath! Are you stuck on a math problem? We'd like to help you solve it. Here are three options we can offer you: Click on one of the tabs above. You'll find over 100 instant-answer, self-help, math solvers, ready to provide you with instant help on your math problem. Find a problem that's similar to yours by browsing through more than 1,300 completely solved math problems. Ask a math expert about your math problem. Quick jump to math help: Click to select Ask a Math Expert Calculus, Derivatives Calculus, Integration Calculus, Quotient Rule Calculus, Solved Integrals Coins, Counting Combinations, Finding all Complex Numbers, Adding of Complex Numbers, Calculating with Complex Numbers, Multiplying Complex Numbers, Powers of Complex Numbers, Subtracting Conversion, Area Conversion, Lengths Conversion, Mass Conversion, Power Conversion, Speed Conversion, Temperatures Conversion, Volume Data Analysis, Finding the Average
Java + Calculus Java + calculus. Some Java applets for experimenting with graphs of functions, and notions like limits, tangents, derivatives, arc length, and area. http://www.math.utah.edu/~carlson/teaching/java/calculus/
Charles Stewart Technische Universität Berlin, Theory and Formal Specifications group Proof theoretic semantics, lambda calculus, linear logic, theoretical computer science, philosophy of language. http://www.linearity.org/cas/
Extractions: I am a postdoctoral researcher in theoretical computer science associated with the International Centre for Computational Logic 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. My research interests include: Programming language theory: Graph transformation: Graph transformation and the design of distributed algorithms;
An Introduction To Lambda Calculus And Scheme We can use Lambdacalculus to describe such a function The Scheme programming language is essentially the lambda-calculus outlined above, plus http://www.jetcafe.org/~jim/lambda.html
Extractions: This talk was given at the JPL Section 312 Programming Lunchtime Seminar. A function accepts input and produces an output. Suppose we have a "chocolate-covering" function that produces the following outputs for the corresponding inputs: peanuts -> chocolate-covered peanuts rasins -> chocolate-covered rasins ants -> chocolate-covered ants We can use Lambda-calculus to describe such a function: Lx.chocolate-covered x This is called a lambda-expression. (Here the "L" is supposed to be a lowercase Greek "lambda" character). If we want to apply the function to an argument, we use the following syntax: (Lx.chocolate-covered x)peanuts -> chocolate-covered peanuts Functions can also be the result of applying a lambda-expression, as with this "covering function maker": Ly.Lx.y-covered x We can use this to create a caramel-covering function: (Ly.Lx.y-covered x)caramel -> Lx.caramel-covered x Functions can also be the inputs to other functions, as with this "apply-to-ants" function:
