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Calculus is a branch of mathematics concerned with two types of functions: derivatives and integrals.

The derivative calculates the rate of change of the function at a point on a curved line. This formula also works for a straight line, as well. A derivative of a function is written by adding a apostrophe like this: f'(x). One of the applications of derivatives is to determine velocity and acceleration of an object in motion.

Integrals measure the area under a curved line graph, such as a half circle. The integral symbol looks like a flattened S.

Derivatives and integrals are related in that they are inverse functions of each other. That means the operations will cancel each other out, such as taking the square root of a squared number will give you the original number.

Applications of integrals include calculating areas of plane regions or surfaces, as well as calculating volumes of solids.

Both derivatives and integrals are defined by using the concept of a limit. An example of a limit is where you have the equation 1/x. If you take x to be very large, then 1/x gets closer to 0.
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Calculus Made Easier - An introduction to the basic concepts. The derivative and integral are explained. Resource links included. Automatic Calculus Solutions - Check calculus homework. Enter a function and click for a step-by-step derivative or integral with each step explained. Visual Calculus - Short descriptions and examples for limits, derivatives, and integrals. Various plug-ins are needed to view some of the pages. A Physicist's View of Teaching Calculus - Topics in calculus that are important in physics Math Shop: Review Questions - Review quizzes for calculus, differential equations, linear algebra and other advanced math fields. World Web Math: Calculus Summary - An overview of calculus ideas. Covered are derivative rules and formulas as well as some basic integration rules. Technology Based Problems - Calculus and differential calculus problems are presented. The possible solution or solutions are given. Dan the Tutor - Features practice exams and worked out solutions covering limits, derivatives and integrals. In PDF format. UBC Calculus Help: Integrals - University of British Columbia course notes. Covers integration and series with applications. Illustrated with interactive Java applets. Graphics for the Calculus Classroom - Graphical demonstrations developed by Douglas N. Arnold for the first year calculus student. Dan's Math at Home Lessons: Calculus - Features step by step lessons to introductory calculus. Included are function and precalculus preview pages. UBC Calculus Help: Derivatives - University of British Columbia course notes. Covers functions, derivatives and applications of derivatives in some detail. Calculus labs or short quizzes are also included. There are many fine illustrations in this tutorial. Dr. Vogel's Gallery of Calculus Pathologies - Discusses instances of functions that are more difficult to apply calculus formulas to. Examples that are included are discontinuous functions and functions with discontinuous derivatives. S.O.S. Math - Calculus - Explains concepts in detail of limits, convergence of series, finding the derivative from the definition and continuity. Some basic formula conversions are given. e-Calculus - A basic calculus tutorial covering limits, derivatives, and integrals in PDF format. CalculusQuest - An online differential calculus textbook including practice activities. Qrhetoric Calculus - Covers the basic derivative functions such as the derivative of polynomials. Some advanced derivative topics are also discussed. The integral is introduced and some practical integral problems such as finding the area and related rates are covered. Harvey Mudd College Tutorials - Topics include precalculus, calculus, multivariable calculus, linear algebra and differential equations. A Calculus Primer - This is a clearly written tutorial with plenty of graphic aids. Meant as an introduction for nonspecialists. Covers many of the basics, including differentiation. The University of Minnesota Calculus Initiative - Offers calculus application examples for the mathematical properties of a rainbow, the fundamental theorem of calculus, methods of maximizing structural beams in a building, and modeling population growth. Includes general formulas to go along with the word problems and a variety of questions in relation to each exercise. Calculus.org - Directory of calculus links for tutorials, homework help, history sample tests, and tips on exam preparation. That's Calculus - Humorous approach to lessons , which are given using Real Player video clips. Topics cover the concept of limit, derivatives, and summation series. Understanding Calculus by Faraz Hussain - A free, complete 360 page book covering all the basics of Calculus. The Calculus Page Problems List - Features topic summaries with practice exercises for derivative and integral calculus. Includes solutions. Authored by D. A. Kouba. Calculus on the Web - An internet tutoring utility for learning and practicing calculus. C.O.W. gives the student or interested user the opportunity to learn and practice problems. Instant feedback for the correctness of answers. Calculus Reference - Offers a reference containing the main theories and equations of calculus Elementary Calculus: An Approach using Infinitesimals - An online book by H. Jerome Keisler. Covers differentiation, continuous functions, integration, limits, applications, infinite series, vector calculus and differential equations. Calculus by Gilbert Strang - Online text covers introduction to derivatives, applications, methods of solving integration problems, polar coordinates, infinite series, partial derivatives, and vector calculus. Calculus - Wikipedia - Contains information of the history, principles, and applications of calculus. Kodawari House - Discusses proofs concerning integrals, Taylor series, e^πi, and the beta function. Distance Calculus - Online course providing tutorials on subjects ranging from precalculus to differential equations. Includes math tools and resource links. MyCalculus: Calculus Problem Solver - Free online calculus problem solver provides answers to homework problems. Alien's Mathematics: Higher Calculus and Super Calculus - Offers downloadable pdf files covering a range of integrals, derivatives and theorems. Intuitive Calculus - This site is dedicated to help students achieve an intuitive grasps of the concepts in basic calculus while still being able to solve the problems they may find in a regular course. Calculus Video Notes - Video tutorials that explain most of the calculus topics. Math24.net - Topics include limits, derivatives, integrals, infinite sequences and Fourier series. Derivative Calculator - An online symbolic derivative calculator that supports partial derivatives and shows the input as a graphical formula. Calculus Notes - eMathHelp - Covers almost all topics in Calculus. Every note has illustrations and a lot of examples. Solitary Road - Calculus - Covers wide range of caclulus topics: from pre-calculus (definition of function) to multivariable calculus (double integrals).
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