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Online Resource: Calculus
The site is maintained by George Alexander.
Technical expertise by the AMATYC Website Coordinator.
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With the changing nature of the Internet, these sites may no
longer exist or they may exist in different formats. To suggest
new sites for inclusion, to report bad links, or to comment on
any of the listings in this resource, please use the feedback
form.
History of Calculus
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Real Analysis/Advanced Topics
- Introduction
to Generalized Calculus
This paper written by David Manura supports this theory, "Elementary
calculus is only one of many calculuses, characterized by a
line, but there are other non-linear calculus's which have their
own set of properties. To investigate these non-linear calculus's,
we need to define what a calculus is. He then defines calculus
as "a system composed of the four building blocks: the discrete
limit, continuous limit, discrete iteration and continuous iteration."
- Introduction
to The Gauge Integral
Thoroughly discusses the various properties of an alternative
integration theory and its relationship with the Lebesgue and
Riemann integrals.
- Unified Analysis
The authors explore a new point of view on the calculus, inspired
by the realization that a stronger definition of the limit can
banish divergence from the logical foundations of the subject.
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Reform Calculus
- Mathematics Archive
at the University of Kentucky
Materials available on the Mathematics Archives are classified
into five main categories: Topics in Mathematics: Teaching materials,
software, WWW links organized by Mathematical Topics. and a
Searchable database.
- SimCalc: Simulations
for Calculus Learning
The SimCalc Project aims to democratize access to the Mathematics
of Change for mainstream students by combining advanced simulation
technology with innovative curricular solutions that begin in
the early grades and includes powerful ideas extending beyond
classical calculus.
- VRML Calculus
Uses three dimensional animated graphics to visually explore
calculus concepts for enhanced learning of material.
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Real World Problems
-
Barry Spieler's Calculus Projects
This site frames problems in letters to students playing the
role of consultant.
- Calculus
and Disease Prediction
At this site the author takes a single context--an infectious
disease spreading through a population--to see how calculus
emerges and how it is used.
- Complex,
Technology Based Problems in Calculus
This site 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.
- University
of Minnesota Calculus Initiative
The Geometry Center is assisting in the development of interactive
technology-based modules for the engineering calculus sequence.
These modules emphasize geometric concepts of calculus while
examining applications of mathematics to the physical and life
sciences.
- Writing
In Mathematics
The problems are presented as a series of letters to the calculus
students, a lot more fun then traditional problems.
-
Wumpus World
Looks at the use of calculus in game theory and contains a description
of a game where calculus can be used to choose moves.
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Reference Information and Resources
-
AB Calculus and BC
Calculus
Advanced Placement Program of the College Board with AP Exam
information, topic outlines, calculator policies, and sample
free response questions.
- Automatic Calculus Derivatives
and Integrals
A powerful site that will find the derivative
and integral for standard functions (small fee for integration).
- Calculus and Mathematica
Using the software Mathematica, University of Illinois Urbana-Champaign
offers calculus courses in which students need not be on college
campus. These courses emphasize experimentation and real-time
visualization to learn fundamental calculus concepts and ideas.
- Calculus Hater’s
Home Page
Links to surviving calculus class, books that might help and
unite with other calculus haters, for further study and other
interesting sites.
- Computer Texts
for Business mathematics
This project was an ICTCM 2000 Awards Nomination. This course
was created at the University of Arizona to replace a finite
mathematics and brief calculus sequence required of all undergraduate
business students. The two course which replace them are project
oriented. The materials can be downloaded from the website.
- Department of Mathematical
Sciences, Michigan Technological University
Contains Mathematica Notebook information used in various courses
in calculus, which can be downloaded to use with Mathematica.
- Dave's
Math Tables
Integrals, a collection of mathematical tables, proofs, and
theorems covering Calculus.
- Favorite
Mathematical Constants
A listing of mathematical constants, from the very basic, such
as 'zero', to the advanced. Good reference resource.
- I
Love Calculus
Series of links to other calculus sites
- Integrator
Enter in any function of x and it will return the integral.
-
Internet Calculus
University of Pittsburgh provides a practice Calculus Examination
and solutions
-
MA 1002 Analysis and Advanced Calculus
Teaches an advanced course in Calculus covering theory and solutions.
- PCPOW - Calculus
Contest
Submit the correct answer to the "Calculus Problem of the Week"
and win prizes
- S.O.S.
Mathematics - Calculus
Contains descriptions of many operations used in calculus. Use
as reference or review tool.
Slope/Rate of Change
- Applications
of Derivatives
Detailed presentation of the applications of derivatives in
the following areas: Rates of Change, Approximation , Optimization
, Graphing, Tangent Lines Parametric Equations Polar Coordinates.
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Tutorials
- Calculus
Homepage
Links to the following: General Calculus, Advanced Placement
Calculus, Calculus On-Line Tutorials, Calculus Grading, Calculus
Books and Reviews, Calculator Resources, Other Calculus Resources.
- Calculus
Made Easier
- Calculus on the
Web
This site provides books, tests, and exercises for learning
and practicing various Calculus concepts. Generates detailed
solutions and explanations to math problems.
- Calculus Page
Resources for the calculus students, as an aid in preparing
for exams, and their instructors at UC Davis along with links
to other websites.
-
CyberCalc Index
An online tutorial on Calculus that includes: Review of Needed
Topics, Limits and Continuity and Derivatives.
- Derivatives
Learn basic differentiation with interactive LiveMath examples
and historical commentary.
- e-Calculus
Home page
Some highlights of the site are e-Calculus, a Calculus 1 tutorial;
Algebra Review in Ten Lessons, and some Mathematical Games.
Note: All materials available at this site are in PDF format.
-
Elementary Calculus
Learn calculus with this easy to follow tutorial covering many
topics, basic operations and practice problems.
- Finite
Mathematics and Applied Calculus Resource Page
Stefan Waner’s and Steven R. Costenoble’s on-line
tutorials written specifically for users of their books, Finite
Mathematics, Applied Calculus, and Finite Mathematics and Applied
Calculus. Yet the material is sufficiently generic so as to
be useful to any student or faculty member, regardless of the
textbook being used
- Graphics
for the Calculus Classroom
Contains still and animated images illustrating various concepts
and problems in calculus. Each image is accompanied by explanations
of the problem, including the appropriate formulas
- Graphing
Cubic Polynomials
Contains a Java based interactive function in calculus that
allows you to change the values of variable to see how it affects
the outcome of a graph of a cubic polynomial. Requires a Java
enabled browser
- Interactive
Real Analysis
An interactive textbook for Real Analysis and Advanced Calculus
that deals with sets, sequences, series, continuity, differentiability,
integratebility (Riemann and Lebesgue), topology, and many other
topics.
-
Interactive Textbook for PFP 96
Contains tutorials and exercises for linears, quadratics, exponentials,
trigonometrics; Derivatives: velocity, acceleration and growth;
Differential equations: Newton's Laws, Rocket motion, chaotic
systems; Forces and vectors. Numerous worked problems.
- Karl's Calculus Tutor
In-depth help understanding the details of calculus most people
don't care to know. "This tutorial is intended to provide you
with clear, concrete, down-to-earth explanations of the material
commonly encountered in the most dreaded of introductory undergraduate
courses: calculus"
- Learning
Calculus
This is not a tutorial, but it gives tips on how to approach
the learning process. Refer your students to this site for helpful
hints on being a successful calculus student, or use as the
handouts with modifications for your classes
-
Limits
- Mr. Kelley's AP Calculus
Home Page
This zany site can lift the spirits and fortify the mind of
anybody attempting to master calculus and/or prepare for the
AP Calculus test. You can get your math problems from algebra
to calculus answered by students from Mr. Kelley's AP Calculus
class or try to solve the calculus problem of the week
- School of
Math Online Resources
Contains Java applets that illustrate various concepts in calculus,
based on courses taught at Georgia Tech. Also includes worksheet
information for use with the Maple software program.
- Topics
in Calculus
Notes to help students learn how to apply and understand the
concepts of calculus. A total of fifteen topics are covered
and include differentials, max-min problems, exponential growth,
and the Potential Function of a Vector Field.
- Visual
Calculus
At this calculus site you will find tutorials complete with
animations and movies that visually define terms, solve problems,
and demonstrate how to use a graphical calculator
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