Directory of Calculus Resources

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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.

Subcategories

• Calculus of Variations
• Differential Equations
• Differential Geometry
• Fractional Calculus
• High School Math
• History
• Integral Tables
• Multivariable Calculus
• Software

Resources in This Category

• A Calculus Primer

  http://www.arachnoid.com/calculus/
  This is a clearly written tutorial with plenty of graphic aids. Meant as an introduction for nonspecialists. Covers many of the basics, including differentiation.

• A Physicist's View of Teaching Calculus

  http://omega.albany.edu:8008/mat214dir/Baierlein.html
  Topics in calculus that are important in physics

• Alien's Mathematics: Higher Calculus and Super Calculus

  http://fractional-calculus.com/
  Offers downloadable pdf files covering a range of integrals, derivatives and theorems.

• Automatic Calculus Solutions

  http://www.calc101.com/
  Check calculus homework. Enter a function and click for a step-by-step derivative or integral with each step explained.

• Calculus - Wikipedia

  http://en.wikipedia.org/wiki/Calculus
  Contains information of the history, principles, and applications of calculus.

• Calculus by Gilbert Strang

  http://ocw.mit.edu/ans7870/resources/Strang/strangtext.htm
  Online text covers introduction to derivatives, applications, methods of solving integration problems, polar coordinates, infinite series, partial derivatives, and vector calculus.

• Calculus Made Easier

  http://www.wtv-zone.com/Angelaruth49/Calculus.html
  An introduction to the basic concepts. The derivative and integral are explained. Resource links included.

• Calculus Notes - eMathHelp

  http://www.emathhelp.net/notes?sid=40
  Covers almost all topics in Calculus. Every note has illustrations and a lot of examples.

• Calculus on the Web

  http://cow.math.temple.edu/
  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

  http://www.allaboutcircuits.com/vol_5/chpt_6/index.html
  Offers a reference containing the main theories and equations of calculus

• Calculus Video Notes

  http://integralcalc.com/
  Video tutorials that explain most of the calculus topics.

• Calculus.org

  http://www.calculus.org/
  Directory of calculus links for tutorials, homework help, history sample tests, and tips on exam preparation.

• CalculusQuest

  http://oregonstate.edu/instruct/mth251/cq/
  An online differential calculus textbook including practice activities.

• Dan the Tutor

  http://members.shaw.ca/danthetutor/
  Features practice exams and worked out solutions covering limits, derivatives and integrals. In PDF format.

• Dan's Math at Home Lessons: Calculus

  http://home.earthlink.net/~djbach/calc.html
  Features step by step lessons to introductory calculus. Included are function and precalculus preview pages.

• Derivative Calculator

  http://www.derivative-calculator.net/
  An online symbolic derivative calculator that supports partial derivatives and shows the input as a graphical formula.

• Distance Calculus

  http://www.distancecalculus.com/
  Online course providing tutorials on subjects ranging from precalculus to differential equations. Includes math tools and resource links.

• Dr. Vogel's Gallery of Calculus Pathologies

  http://www.math.tamu.edu/~tom.vogel/gallery/gallery.html
  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.

• e-Calculus

  http://www.math.uakron.edu/~dpstory/e-calculus.html
  A basic calculus tutorial covering limits, derivatives, and integrals in PDF format.

• Elementary Calculus: An Approach using Infinitesimals

  http://www.math.wisc.edu/~keisler/calc.html
  An online book by H. Jerome Keisler. Covers differentiation, continuous functions, integration, limits, applications, infinite series, vector calculus and differential equations.

• Graphics for the Calculus Classroom

  http://www.ima.umn.edu/~arnold/graphics.html
  Graphical demonstrations developed by Douglas N. Arnold for the first year calculus student.

• Harvey Mudd College Tutorials

  http://www.math.hmc.edu/calculus/tutorials/
  Topics include precalculus, calculus, multivariable calculus, linear algebra and differential equations.

• Intuitive Calculus

  http://www.intuitive-calculus.com/
  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.

• Kodawari House

  http://www2.math-4-u.com/math/math.html
  Discusses proofs concerning integrals, Taylor series, e^πi, and the beta function.

• Math Shop: Review Questions

  http://www.math.ucla.edu/~ronmiech/
  Review quizzes for calculus, differential equations, linear algebra and other advanced math fields.

• Math24.net

  http://www.math24.net
  Topics include limits, derivatives, integrals, infinite sequences and Fourier series.

• MyCalculus: Calculus Problem Solver

  http://www.mycalculus.com/
  Free online calculus problem solver provides answers to homework problems.

• Qrhetoric Calculus

  http://www.qcalculus.com/
  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.

• S.O.S. Math - Calculus

  http://www.sosmath.com/calculus/calculus.html
  Explains concepts in detail of limits, convergence of series, finding the derivative from the definition and continuity. Some basic formula conversions are given.

• Solitary Road - Calculus

  http://solitaryroad.com/cal.html
  Covers wide range of caclulus topics: from pre-calculus (definition of function) to multivariable calculus (double integrals).

• Technology Based Problems

  http://www.rose-hulman.edu/Class/CalculusProbs/
  Calculus and differential calculus problems are presented. The possible solution or solutions are given.

• That's Calculus

  http://www.math.dartmouth.edu/~matc/eBookshelf/calculus/CalculusVideo/welcome.html
  Humorous approach to lessons , which are given using Real Player video clips. Topics cover the concept of limit, derivatives, and summation series.

• The Calculus Page Problems List

  http://www.math.ucdavis.edu/~kouba/ProblemsList.html
  Features topic summaries with practice exercises for derivative and integral calculus. Includes solutions. Authored by D. A. Kouba.

• The University of Minnesota Calculus Initiative

  http://www.geom.uiuc.edu/education/calc-init/
  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.

• UBC Calculus Help: Derivatives

  http://www.ugrad.math.ubc.ca/coursedoc/math100/
  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.

• UBC Calculus Help: Integrals

  http://www.ugrad.math.ubc.ca/coursedoc/math101/
  University of British Columbia course notes. Covers integration and series with applications. Illustrated with interactive Java applets.

• Understanding Calculus by Faraz Hussain

  http://www.understandingcalculus.com/
  A free, complete 360 page book covering all the basics of Calculus.

• Visual Calculus

  http://archives.math.utk.edu/visual.calculus/
  Short descriptions and examples for limits, derivatives, and integrals. Various plug-ins are needed to view some of the pages.

• World Web Math: Calculus Summary

  http://web.mit.edu/wwmath/calculus/summary.html
  An overview of calculus ideas. Covered are derivative rules and formulas as well as some basic integration rules.

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