Geometry.Net - Science: Calculus

Calculus@Internet
Tutorials on calculus subjects ranging from precalculus to differential equations. Math tools and resource links.
http://www.calculus.net/
ALVIRNE HIGH SCHOOL PROBLEM OF THE WEEK SITE
Problems presented by Alvirne High School students and guests as they prepare for the Advanced Placement exam in calculus. Alvirne's AP calculus Class invites you to join them in their preparation
http://www.seresc.k12.nh.us/www/alvirne.html
Visual Calculus
Short descriptions and examples for limits, derivatives, and integrals. Various plug-ins are needed Category Science Math calculusTutorials. Precalculus. Limits and Continuity. Derivatives. Applications ofDifferentiation. Integration. Applications of Integration. Sequences and Series.
http://archives.math.utk.edu/visual.calculus/
Arnold, Douglas N. - Calculus GraphicsCollection Of Animated Graphical Demonstra
Get prices and ordering details about math tutorials and courses available from the Univ of Illinois at UrbanaChampaign and Ohio State Univ.
http://www.math.psu.edu/dna/graphics.html
Mathematics Archives Calculus Resources On-Line
Math Archives calculus Resources On-line. Welcome to the calculus Resources On-linearea of the Mathematics Archives. Other listings of calculus resources.
http://archives.math.utk.edu/calculus/crol.html

Extractions: TEXT-BASED MENU Welcome to the Calculus Resources On-line area of the Mathematics Archives. This area contains information and links to numerous Internet resources, which could be used for teaching and learning of calculus. If you would like to suggest adding information to this area, or have comments or questions, please contact Przemyslaw Bogacki , the calculus moderator. Here is the contents of the Calculus Resources On-line area: Articles, Posters, Discussions Software vendors and other platform-specific sites Publisher sites ... Other listings of calculus resources Mathematics Archives software collection contains numerous shareware and freeware programs useful for teaching and learning of calculus. In addition to the "calculus" directories in the Mac and Windows/MS-DOS areas, interesting programs may be found elsewhere (e.g., in the directories "Advanced Calculus", "Graphing Programs", etc.).
Finite Mathematics And Applied Calculus Resource Page
Offers interactive tutorials, game theory simulator, quizzes and exercises on finite mathematics and applied calculus.
http://www.hofstra.edu/~matscw/realworld.html
Calculus On The Web
An internet tutoring utility for learning and practicing calculus. COW gives the student or interested Category Science Math calculusWelcome to calculus on the Web. The COW Library calculus on the Web ispartially supported by the National Science Foundation. A project of
http://www.math.temple.edu/~cow/
Karl's Calculus Tutor: Starting Page For 1st Year Calculus Tutorial
Covers calculus of limits, continuity and derivatives in some detail. Also covers integrals and methods Category Science Math calculusA place for a 1st year calculus student to come when he or she needs ahelping hand. Emailhelp available. Karl's calculus Tutor. Home Page.
http://www.karlscalculus.org/

Extractions: last update 24-Sep-02 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. 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
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

Extractions: 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, multivectors and Clifford algebra.
Coolmath.com - An Amusement Park Of Mathematics... And More!
An amusement park of mathematics. Puzzles and number problems, fractals, geometry, calculus, algebra, online games, online calculators, and links.
http://www.coolmath.com/
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/

Extractions: About MacTech Home Page Subscribe to MacTech! ... Webmaster Feedback Volume Number: Issue Number: Column Tag: Lisp Listener Abe Lincoln 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.
Calculus
InfoPlease article defining calculus, differential calculus, and integral calculus.
http://kids.infoplease.lycos.com/ce6/sci/A0809858.html

Extractions: calculus calculus, branch of mathematics that studies continuously changing quantities. The calculus is characterized by the use of infinite processes, involving passage to a limit Newton and the German mathematician G. W. Leibniz , working independently, developed the calculus during the 17th cent. The calculus and its basic tools of differentiation and integration serve as the foundation for the larger branch of mathematics known as analysis . The methods of calculus are essential to modern physics and to most other branches of modern science and engineering. Sections in this article:
Calculus And Mathematica At UIUC
A Mathematicabased calculus course.Category Science Math Software Mathematica
http://www-cm.math.uiuc.edu/
Vrml.calculus.net - Virtual Reality & Calculus
Special Notes about Using the VRML Plugin Live3D Part I calculus, VR,and Three Dimensions. Part II Applications via calculus and VR.
http://www.calculus.net/vrml/

Extractions: To quicly click through the viewpoints of the world: Click on the world Keystroke: CONTROL-RIGHTARROW Torsion of a curve is usually taught via formulas involving the cross-product of the velocity and acceleration vectors. With a CAS animation, we may watch a point travel along a curve, and view the length of the binormal change, coupled with the twisting of the TNB frame. With a VR animation, we may actually ride along the curve and experience the torsion. Of course the formulas are required for mathematical analysis, but what are the benefits for students in experiencing the changes in torsion? Does this effect the way we teach TNB analysis? How Will Virtual Reality Change Vector Calculus? One goal of this book is to address this question, via exploring many of the topics of three-dimensional calculus using the power of virtual reality a la VRML. Until recently, all of multivariable/vector calculus was taught algebraically. Now many courses utilize computers via computer algebra systems and graphing tools to visually investigate the geometry of curves and surfaces in 3-space. Virtual Reality/VRML holds many possibilities for extending the visual investigation experience. The incorporation of CAS's forced many changes in the curriculum for 3D calculus over the last five years; we ask: how will VR change it in the next five years?
Focus On Calculus:
Topics in calculus that are important in physics
http://omega.albany.edu:8008/mat214dir/Baierlein.html

Extractions: What topics in calculus would physicists like to see their students learn? A lot of topics, of course, but the need to economize in this article forces me to economize in what I might ask of a calculus teacher, who is strapped for time, if not for space. Here are some highlights- some areas of especial concern to the study of physics. Exponentials and logarithms That the derivative of an exponential function is proportional to the function itself is the most important property of those functions. A physicist would like to start with that property, as displayed here: Numerical exploration with base (b=2) yields a coefficient of b X that is less than 1; trying (b = 10) yields a coefficient greater than 1. In between 2 and 10 there ought to be a number that yields 1, and thereby e enters the scene. Then it is a matter of small, relatively easy steps to develop the topic and to finish with ln y as the integral of one-over-x dx. That logarithmic relation always puzzles students, and so it is best to place it last, not at the start, where it might derail the entire development. Expansions and approximations Almost every ``exactly-solved'' problem in physics is based on some initial approximation. To be sure, solutions have become famous as exact solutions to nonlinear differential equations, but those equations themselves are merely approximations to more fundamental equations. Physics students need to become handy with the Taylor expansion and the binomial expansion. Their level of expertise should enable them to apply those expansions to functions like
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/
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: Oct. 5, 2001 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 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 In 1772 Lagrange wrote u' du dx and du u'dx Nouveaux Memoires de l'Academie royale des Sciences et Belles-Lettres de Berlin. History of Mathematics that Arbogast introduced this symbol, but it seems he does not show this symbol in A History of Mathematical Notations. D was used by Arbogast in the same work, although this symbol had previously been used by Johann Bernoulli (Cajori vol. 2, page 209). Bernoulli used the symbol in a non-operational sense (Maor, page 97). Partial derivative.
Calculus.org - THE CALCULUS PAGE .
calculus.org THE calculus PAGE. Editorial Board. Sponsors. 2003 calculus Prize.The 2003 $1000 calculus Prize competition for High School Students is now open.
http://www.calculus.org/
E-Calculus Home Page
calculus on the Web The COW Library Click on a button below to open a book General information desk. Contents of the COW library If you wish to log in for a recorded session, click on the Login button. calculus on the Web is
http://www.math.uakron.edu/~dpstory/e-calculus.html

Extractions: 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 Acrobat Reader 3.0
Perl Contains The Lambda-Calculus
Explains why this computer program is well suited to apply to functional application.
http://perl.plover.com/lambda/

Extractions: -Calculus (pronounced `lambda calculus') is a model of computation invented by Alonzo Church in 1934. It's analogous to Turing machines, but it's both simpler and more practical. Where the Turing machine is something like a model of assembly language, the -calculus is a model of function application. Like Turing machines, it defines a simplified programming language that you can write real programs in. Writing Turing machine programs is like writing in assembly language, but writing -calculus programs is more like writing in a higher-level language, because it has functions. The two legal operations in the -calculus are to construct a function of one argument with a specified body, and to invoke one of these functions on an argument. What can be in the body of the function? Any legal expression, but expressions are limited to variables, function constructions, and function invocations. What can the argument be? It has to be another function; functions are all you have. With this tiny amount of machinery, we can construct a programming language that can express any computation that any other language can express. Unlike most popular programming languages, Perl is powerful enough to express the

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