What is Calculus: Definition and 1000 Discussions

Calculus, originally called infinitesimal calculus or "the calculus of infinitesimals", is the mathematical study of continuous change, in the same way that geometry is the study of shape and algebra is the study of generalizations of arithmetic operations.
It has two major branches, differential calculus and integral calculus; the former concerns instantaneous rates of change, and the slopes of curves, while integral calculus concerns accumulation of quantities, and areas under or between curves. These two branches are related to each other by the fundamental theorem of calculus, and they make use of the fundamental notions of convergence of infinite sequences and infinite series to a well-defined limit.Infinitesimal calculus was developed independently in the late 17th century by Isaac Newton and Gottfried Wilhelm Leibniz. Today, calculus has widespread uses in science, engineering, and economics.In mathematics education, calculus denotes courses of elementary mathematical analysis, which are mainly devoted to the study of functions and limits. The word calculus (plural calculi) is a Latin word, meaning originally "small pebble" (this meaning is kept in medicine – see Calculus (medicine)). Because such pebbles were used for counting (or measuring) a distance travelled by transportation devices in use in ancient Rome, the meaning of the word has evolved and today usually means a method of computation. It is therefore used for naming specific methods of calculation and related theories, such as propositional calculus, Ricci calculus, calculus of variations, lambda calculus, and process calculus.

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  1. M

    Studying Learning calculus with a digital copy of a textbook

    Hi, I'm in 12 grade, and I always was a decent student but recently I became more fascinated by learning and I want to learn some math and physics beyond high school level. One or two weeks ago I started the calculus course on mit ocw (18.01sc) (at session 17 right now, right before lecture 7)...
  2. Q

    I Deriving the spherical volume element

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  3. WMDhamnekar

    MHB Multi-variable calculus

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  4. CharlieCW

    How do I deduce some basic thermodynamic identities using multivariate calculus?

    Homework Statement Let x, y and z satisfy the state function ##f(x, y, z) = 0## and let ##w## be a function of only two of these variables. Show the following identities: $$\left(\frac{\partial x}{\partial y}\right )_w \left(\frac{\partial y}{\partial z}\right )_w =\left(\frac{\partial...
  5. Q

    Maximum Horizontal Force of Relativistic Point Charge

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  6. B

    Textbook for calculus of variations? Hamiltonian mechanics?

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  7. M

    Is it possible to integrate acceleration?

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  8. Savian

    Courses Is there a calculus requirement in Europe for Biophysics?

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  9. S

    Calculus Problem: acceleration, speed, and displacement of a particle

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  10. N

    Calculus angular acceleration with respect to theta

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  11. dkeating

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  12. CivilSigma

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  13. KF33

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  14. Adgorn

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  15. navneet9431

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  16. Adgorn

    B Questions regarding polynomial divisions and their roots

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  17. H

    MHB Calculus: Understanding Infinity in Functions

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  18. Philip Koeck

    I Applying a constraint in the calculus of variations

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  19. Q

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  20. Adgorn

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  21. EEristavi

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  22. Adgorn

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  23. J

    B Geodesic dome parametric formula

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  24. CaptainAmerica17

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  25. SebastianRM

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  26. A

    Calculus Multivariable calculus without forms or manifolds

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  27. J

    Courses I only got a B in Calculus I :(

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  28. Adesh

    I How to convert the limit of a series into an integral?

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  29. CaptainAmerica17

    Programs Don't like my calculus class, but want to be a math major....

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  30. astroman707

    Studying What books are good to learn the math in intro physics?

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  31. astroman707

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  32. D

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  33. K

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  34. K

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  35. K

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  36. K

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  37. K

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  38. A

    MHB Solve f(x,y,z): Min & Max Values Subject to Constraint x^2+2y^2+6z^2=81

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  39. topologyfreak

    Studying Should I start with a basic physics book without calculus?

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  40. A

    MHB Solve Lagrange Multipliers Problem w/ e^(9x) - Find (a,b)

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  41. komarxian

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  42. Hawkingo

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  43. Delta2

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  44. T

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  45. B

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  46. T

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  47. jonathanm111

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  48. J

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  49. Javier Lopez

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  50. K

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