1. Math History This guide to the history of calculus is keyed to the chapters and content of the 10th edition of Thomas' Calculus. http://occ.awlonline.com/bookbind/pubbooks/thomas_awl/chapter1/medialib/custom3/

Thomas' Calculus This guide to the history of calculus is keyed to the chapters and content of the 10th edition of Thomas' Calculus . This electronic document highlights important events and people in the development and use of calculus. Learn about the history of calculus The history of calculus is rich and full of considerable human effort. By investigating this guide, through the sections containing a timeline, essays on the development of the major elements and topics of the subject, biographies of over 100 contributors and users of the subjects, and a set of over 100 problems (questions keyed to chapters in the book) to investigate in the history of calculus, you can learn more about the subject and how it has been used to help society. Use with the textbook These history modules (topic essays and biographies) can be used to supplement a reading assignment or lecture or with the problem exercises can supplement the outside class work. They are excellent sources for written or oral projects. The textbook contains icons that indicate good places where history modules can be used.

2. History Of Calculus THE history of calculus The beginnings of integration can be recognised in the work of the ancient Greeks (Euclid, Archimedes ) in finding areas of curved regions and volumes of curved solids. http://www.scit.wlv.ac.uk/university/scit/modules/mm2217/hc.htm

THE HISTORY OF CALCULUS (Summary) The beginnings of integration can be recognised in the work of the ancient Greeks (Euclid, Archimedes ) in finding areas of curved regions and volumes of curved solids. The beginnings of differentiation were much later, in the work of the early 17th century on tangents to curves and instantaneous rates of change. The recognition that these two processes are inverses of each other (the "Fundamental Theorem of Calculus") and the major initial development of the theory occurred in the late 17th century, mainly in the work of Newton (1642-1727) and Leibniz (1646-1716). All calculus was based on the concept of a limit, a concept which was not well understood until the 19th century (in the work of Cauchy, Riemann, Weierstrass and others) and until then the results in the calculus were founded on an unsound, non- rigorous basis. (e.g. one intuitive idea was that the gradient of the tangent to the curve at (x,y) is the gradient of the chord, i.e. when x = 0.

3. The History Of The Calculus And The Development Of Computer Algebra Systmes THE DEVELOPMENT OF CALCULUS. Introduction. Calculus history of calculus (Summary). The beginnings of Integration http://www.math.wpi.edu/IQP/BVCalcHist/calctoc.html

The History of the Calculus and the Development of Computer Algebra Systems Introduction History of the Integral from the 17 th Century ... Conclusions A. Bibliography Return to the Main Page

4. 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. Highlights in the history of calculus by Richard Walker. http://www.math.nus.edu.sg/aslaksen/teaching/calculus.shtml

Why Calculus? Sir Isaac Newton, 1643-1727 Gottfried Wilhelm von Leibniz, 1646-1716 Objectives of the Module Topics to be Covered ... Project Topics Back to Helmer Aslaksen's home page. Objectives of the Module 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. Topics to be Covered 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.

5. Why Study Calculus? A Brief History Of Math Why Do We Study calculus? a brief look at some of the history of mathematics The question I am asked most often is, "why do we study this?" (or its variant, "will this be on the exam?"). with the world after calculus. (Probably we should put more history into our calculus courses. There is a growing http://www.math.vanderbilt.edu/~schectex/courses/whystudy.html

Why Do We Study Calculus? or, a brief look at some of the history of mathematics an essay by Eric Schechter version of September 10, 1999 The question I am asked most often is, "why do we study this?" (or its variant, "will this be on the exam?"). Though some students will eventually use integrals and derivatives in their work in physics, chemistry, or economics, most will never use epsilons and deltas. Applied mathematicians may use a theorem such as "the limit of the product is the product of the limits"; we only need epsilons and deltas to prove such theorems. If the applied mathematician takes the attitude that "I trust the pure mathematicians who say they have proved this theorem," then the applied mathematician does not need to study epsilons and deltas at all. But calculus is not a just vocational training course. In part, students should study calculus for the same reasons that they study Darwin, Marx, Voltaire, or Dostoyevsky: These ideas are a basic part of our culture; these ideas have shaped how we perceive the world and how we perceive our place in the world. To understand how that is true of calculus, we must put calculus into a historical perspective; we must contrast the world before calculus with the world after calculus. (Probably we should put more history into our calculus courses. There is a growing movement among mathematics teachers to do precisely that.) The earliest mathematics was perhaps the arithmetic of commerce: If I am willing to trade 3 of my goats for one of your cows, how many goats will 4 cows cost me? The ancient Greeks did a great deal of clever thinking, but very few experiments; this led to some errors. For instance, Aristotle observed that a rock falls faster than a feather, and concluded that heavier objects fall faster than lighter objects. Aristotle's views persisted for centuries, until the discovery of air resistance.

6. Basic Calculus 5. The calculus of Leibniz. 6. The calculus of Newton Part II. calculus and the Sciences. 8. Analysis of Functions http://www.nd.edu/~hahn

7. School Principals Guide To Student Math Improvement A free tutorial that explains difficult algebra, trigonometry and calculus concepts to beginning middle/high school students in a simplified way that they can understand and use. http://members.tripod.com/learnmath/

var TlxPgNm='index'; School Principals Guide to Student Math Improvement Invitation to Mathematics is Math for School Principals. It is an algebra and college prep math tutoring program that extracts clean, fresh, authoritative algebra and math concepts and explains them in a made-simple way. School Principals Guide to Student Math Improvement As a School Principal you are looked upon for leadership to show and direct teachers how to be accountable for high academic standards. Today, any School Principal attempting to meet this difficult goal faces new questions and challenges. To help answer those questions the Educational Research Institute is pleased to bring you a breakthrough Professional Development Mathematics and Science Support Training Program part of the Math 2002' teacher training program, that, for the first time, gives teachers and administrators, an understandable, bare facts, overview of the math knowledge necessary to determine where to take your students to raise the schools academic levels. The use of this breakthrough program is intended to save your school considerable time and money. Why is this Guide Important to School Principals?

8. Multivariable Calculus Lecture notes by Carlos C. Rodriguez, State University of New York at Albany. http://omega.albany.edu:8008/calculus3

Multivariate Calculus With Maple If you were using a Java-enabled browser, you would see an animated scrolling text sign that looks like this: [Preface] [Table of Contents] [Review of Calc1] [Vector Geometry] ... [Found Elsewhere] Last modified: Mon Jan 24 10:57:03 EST 2000

9. ALVIRNE HIGH SCHOOL PROBLEM OF THE WEEK SITE New Hampshire's Alvirne High School web page of sample questions and answers for the advanced placement calculus test. http://www.seresc.k12.nh.us/www/alvirne.html

Alvirne High School Hudson, N.H. Problems of the Week Alvirne's AP Calculus Class invites you to join them in their preparation for the AP Calculus exam . You are Visitor Number since December 18,1995. Our EMAIL ADDRESS HAS CHANGED. IT IS NOW sray@seresc.net Check Out the Solutions for the 2002 Exam Here Alvirne's Aid to the AP Calculus exam Alvirne's Problem of the Week Updated 3/15/03 SUBMIT a problem along with a detailed solution Guest Problem of the Week Updated 3/15/03 Sample Multiple Choice AP Questions Courtesy of AP CALCULUS Class from Greencastle High School, Greencastle, PA. Updated 3/15/03 Teacher and Student Calculus Resources Awards received by the ALVIRNE AP Calculus Page ARCHIVE of 2002-2003 ALVIRNE problems with detailed solutions. ARCHIVE of 2002-2003 GUEST problems with detailed solutions. ARCHIVE of 2001-2002 ALVIRNE problems with detailed solutions. ARCHIVE of 2001-2002 GUEST problems with detailed solutions. ARCHIVE of 2000-2001 ALVIRNE problems with detailed solutions. ARCHIVE of 2000-2001 GUEST problems with detailed solutions. ARCHIVE of 1999-2000 ALVIRNE problems with detailed solutions.

10. On The Pi-Calculus And Linear Logic - Bellin, Scott (ResearchIndex) (CiteSeer) Article by Bellin and Scott showing how classical linear logic may be interpreted in the pi calculus, thus supporting Abramksy's `Proofs as Processes' thesis. http://citeseer.nj.nec.com/bellin92calculus.html

On the pi-Calculus and Linear Logic (1994) (Make Corrections) (4 citations) G. Bellin, P.J. Scott Theoretical Computer Science Home/Search Context Related View or download: profs.sci.univr.it/~be PICALCPAPER.ps Cached: PS.gz PS PDF DjVu ... Help From: profs.sci.univr.it/~bell papers (more) Homepages: G.Bellin P.Scott HPSearch (Update Links) Rate this article: (best) Comment on this article (Enter summary) Abstract: We detail Abramsky's "proofs-as-processes" paradigm for interpreting classical linear logic (CLL) [13] into a "synchronous" version of the -calculus recently proposed by Milner [27, 28]. The translation is given at the abstract level of proof structures. We give a detailed treatment of information flow in proof-nets and show how to mirror various evaluation strategies for proof normalization. We also give Soundness and Completeness results for the process-calculus translations of various... (Update) Context of citations to this paper: More called proof nets, and the dynamics of their normalization can be used to express some aspects of concurrency [Abramsky 1993, Bellin Scott 1992 , Lafont 1989, Lafont 1990] The Curry Howard Isomorphism also states that the types of programs can be seen as formulas, and the ...of) LL into stark relief.

11. Luke Ong Merton College, Oxford Categorical logic, game semantics, type theory, lambda calculus, semantics of programming languages, and sequentiality. http://web.comlab.ox.ac.uk/oucl/people/luke.ong.html

Luke Ong Reader in Computer Science Tutorial Fellow in Computation, Merton College Address Oxford University Computing Laboratory Wolfson Building, Parks Road, Oxford, OX1 3QD, England. Telephone Direct: +44 (0)1865 283522 Department: +44 (0)1865 273838 Fax: +44 (0)1865 273839 EMail Luke.Ong@comlab.ox.ac.uk WWW Work-related information (OUCL) oucl people Updated February 2003 Home Search SiteMap Feedback ... News

12. Progress In PDEs Home Page The main purpose of the meeting is to bring together leading experts in this broad and fastmoving area with the objective of highlighting recent important developments. Particular attention will be paid to developments in PDEs that relate to the sciences and other areas of mathematics such as geometry, the calculus of variations, dynamical systems and stochastic analysis. Edinburgh; 913 July 2001. http://www.ma.hw.ac.uk/icms/current/progpde/

Progress in Partial Differential Equations Edinburgh, 9-13 July 2001 Home page Scientific Programme Speakers' Notes Timetable ... Click here for the report on this meeting in ICMS News 11 The Speakers' Notes section contains notes and some abstracts from speakers at this meeting. Scientific Committee: J. M. Ball (Oxford), A. Grigoryan (Imperial College), S Kuksin (Heriot-Watt) The main purpose of the meeting is to bring together leading experts in this broad and fast-moving area with the objective of highlighting recent important developments. Particular attention will be paid to developments in PDEs that relate to the sciences and other areas of mathematics such as geometry, the calculus of variations, dynamical systems and stochastic analysis. One of the sessions of the meeting, on Tuesday 10 July, will be dedicated to the memory of E. M. Landis and will address qualitative theory of second order elliptic and parabolic PDEs. A memoir of E. M. Landis Session timetable The Workshop is supported by: The Engineering and Physical Sciences Research Council and The European Commission under Framework V REGISTRATIONS CLOSED ON 7 APRIL 2001.

13. Inductive Theorem Prover INKA 4.0 Firstorder theorem prover with induction based on the explicit induction paradigm. It is based on a full first-order calculus, a special variant of the resolution calculus with paramodulation. http://www.dfki.de/vse/systems/inka/

The Inductive Theorem Prover INKA, Version 4.0 Visit also the description of the new INKA 5.0 system The INKA-system 4.0 is a first-order theorem prover with induction which is based on the explicit induction paradigm. It is based on a full first-order calculus (a special variant of the resolution calculus with paramodulation) Main Features: The system possesses a powerful predicate-logic prover component which (as already mentioned) is based on an order- sorted variant of a resolution calculus with paramodulation. A variety of definition principles are offered to define data types (with free constructors as well as with non-free constructors), functions and predicates. For functions and predicates additional definition principles are offered for algorithmic specifications. A built-in recursion analysis ensures the termination of the above mentioned algorithms. The encoded well-founded order relation can then be used to formulate the induction axioms. Sophisticated heuristics based on the notions of rippling and of colouring formulas are used to guide the proof search by proof plans. In either way, if the proof search succeeds or if the proof search fails, the user is offered a (graphical) representation of the proof attempt. The user can interact with the system by giving the system some advice for filling the gap in the proof sketch.

14. Connected Calculus This is an applied calculus tutorial. Some prior calculus knowledge might be helpful. 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.

15. Mathematics Pages Topics Algebra, Geometry, Trigonometry, Analytical Geometry, calculus, Vectors. Teaching material and tests. Pages created by Mehrdad Negahban and the University of Nebraska. http://em-ntserver.unl.edu/Math/mathweb/mathtoc.html

University of Nebraska EngM Instructional Lab Course Notes and Mechanics Readiness Online Pre-Application to Graduate Program Masters Program ... Financial Support for Graduate Studies Department of Engineering Mechanics Welcome to the Mathematics for Mechanics Homepage. Click on any of the topics you're interested in learning about! Algebra Geometry Trigonometry Analytical Geometry ... Vectors Once you feel comfortable with the material, test your skills with the Mechanics Readiness Program Copy and distribute freely for personal use only Department of Engineering Mechanics, University of Nebraska, Lincoln, NE 68588-0526 Department of Engineering Mechanics Phone: (402) 472-2377 W317.4 Nebraska Hall FAX: (402) 472-8292 University of Nebraska-Lincoln E-mail: dgsem@unl.edu Lincoln, NE 68588-0526 Web: http://www.unl.edu/emhome/em.html This page has been visited times since

16. 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/

17. Alan Bain A fairly complete elementary introduction to the basics of stochastic integration with respect to continuous semimartingales by Alan Bain. All the theory usually needed for basic mathematical finance. Sixty pages in dvi, postscript, and pdf. http://www.statslab.cam.ac.uk/~afrb2/

Alan Bain E-mail address: afrb2@cam.ac.uk Research Interests I am interested in the application of probability theory techniques to problems arising from communications networks, in particular the Internet. My recent work has focussed on using fluid limits to model the behaviour of various congestion control schemes. Online Bookshelf A number of useful probability textbooks have recently become available online. Meyn, S. and Tweedie, R., Markov Chains and Stochastic Stability Kelly, F., Reversibility and Stochastic Networks Publications Modelling the Performance of In-Call Probing for Multi-Level Adaptive Applications with Peter Key, Microsoft Research MSR Technical Report , MSR-TR-2002-06. Modelling the Performance of Distributed Admission Control for Adaptive Applications with Peter Key, Microsoft Research MAMA Workshop , June 2001 Stochastic Calculus Notes These notes provide a fairly complete elementary introduction to the basics of stochastic integration with respect to continuous semimartingales (not just with respect to a Brownian Motion). They certainly contain all the theory usually needed for basic mathematical finance (Girsanov's theorem etc.). They do lack the martingale representation theorem. They may be downloaded and print out at about eighty pages. If you find any errors, or feel that there are serious omissions, or even just have some suggestions for improvements, please contact me by email and I shall endeavour to improve them! Contents The notes are available in various forms, but I have had reports of people experiencing trouble with the postscript versions. The idea of producing a PDF version was suggested to me by Noel Vaillant.

18. Karl's Calculus Tutor: Starting Page For 1st Year Calculus Tutorial Introductory information on counting numbers, integers, limits, and derivatives. http://www.karlscalculus.org/

Karl's Calculus Tutor Home Page last update 24-Sep-02 Welcome to Karl's Calculus Tutor Greetings to Fall 2002 Semester Students Enter the tutorial (below) or search this website for a calculus topic. You will find coverage of limits, continuity, derivatives, related rates, optimization, L'Hopital's rule, integration, and much more. There are dozens of problems worked out for you step-by-step. If you are having difficulty with a calculus topic, you are encouraged to go to the appropriate section, look at the text, and then follow along with the worked problems to learn how you can do similar problems on your own. There is also remedial coverage of algebra topics, number systems, exponentials, logs, trig functions and trigonometry, if you are in need of review on these topics. Email help on math problems is available, but please read the instructions for emailing me first. ENTER Karl's Calculus Tutor You can participate in a calculus discussion by posting to Karl's Calculus Forum Go to Karl's Calculus Forum You can email me by clicking this button: Use your own emailer Use form For information about Karl's Calculus Tutor to be emailed to you, put your email address in the blank below and click

19. A Non Functional Calculus: Linear Logic And Concurrency (ResearchIndex) (CiteSeer) This paper proposes the *calculus as an approach that unifies Abramsky's proofs-as-processes approach with Boudol and Berry's Chemical Abstract Machine approach. http://citeseer.nj.nec.com/313007.html

A non functional calculus: linear logic and concurrency (2000) (Make Corrections) Corrado Priami, Ugo Solitro, Cristina Borboni Home/Search Context Related View or download: sci.univr.it/~priami/wwwpa Star.ps.gz Cached: PS.gz PS PDF DjVu ... Help From: sci.univr.it/~priami/Mypapers (more) Homepages: C.Priami U.Solitro HPSearch (Update Links) Rate this article: (best) Comment on this article (Enter summary) Abstract: this paper to an interaction mechanism inspired to the computational behaviour of proof nets, a deduction system of linear logic [7]. In this setting the conclusion of a derivation is the type of the corresponding proof net. The computational mechanism is cut elimination that can only occur between terms with the same type. The relationship between proof nets and processes have already been studied in the literature. Abramsky interprets proof as processes and consider a cut-elimination as... (Update) Similar documents (at the sentence level): Functional Features of a Calculus for Logic and Concurrency - Priami, Solitro (2000) (Correct) Active bibliography (related documents): More All Concurrent Constraints in the Fusion Calculus (Extended Abstract) - Victor, Parrow (1998)

20. Personal Marco Pedicini Institute for Applied calculus, Rome Theoretical computer science, linear logic, geometry of interaction, optimal reductions. http://www.iac.rm.cnr.it/~marco/html

Consiglio Nazionale delle Ricerche ISTITUTO per le APPLICAZIONI del CALCOLO "Mauro Picone" Marco PEDICINI Research Interests: Dynamics of Computational Processes - Linear Logic, Proof Nets and Geometry of Interaction; - Computer Science: Concurrent and Parallel Systems; Quantum Computation FTP-site for Marco Pedicini e-prints. Papers Links and Abstracts Projects Other WWW Experiences: Vincent's Page Jean-Baptiste Joinet Link Hyper Harold Schellinx Laurent , Paris-alien in Marseille Lorenzo Tortora de Falco web site Personal Annotations on www: Mathematics Subject Classification Yahoo Referenced Mathematics Institutes Archivio Gazzetta Ufficiale (Concorsi Laureati) (IAC mirroring del televideo) Archivio Gazzetta Ufficiale Concorsi (Comune di Jesi) (la Repubblica) Reclutamento dal Ministero URST Marco Pedicini: marco@iac.rm.cnr.it

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