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. Bunny-chan

    Determining a trigonometric limit

    Homework Statement Calculate the following limit: Homework EquationsThe Attempt at a Solution I don't know how to proceed with this. I've tried to multiply by the conjugate, and to simplify the expression (x+\pi) to u, but I wasn't very sucessful. To what kind of algebric device I could...
  2. shihab-kol

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  3. Bunny-chan

    Book demonstration about trigonometric relations

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  4. Quantum Velocity

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  5. Eclair_de_XII

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    Additionally, what topics from that same course are relevant to probability? I ask because I'm afraid I might forget some of the topics from my calculus series after one semester of disuse. I mean, I know I should probably brush up on my calculus skills in preparation for any math class that...
  6. H

    Calculating the equations of motion for particle in parabola

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  7. D

    A Dirac Delta and Residue Calculus

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  8. jlmccart03

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  9. cathal84

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  10. R

    Integral form of Particular solution question

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  11. D

    Area between 2 curves, Volume around X and Y, Centroid

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  12. kupid

    MHB Calculus & Diff. Eqn: Beginner Qs on Function, Derivative & Gradient

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  13. ccaatt

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  14. W

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  15. P

    I Multivariable Calculus Project: Spacetime/Black Holes

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  16. G

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  17. S

    Calculus Good textbooks for really learning calculus?

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  18. D

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  19. U

    B Integrating to find surface area/volume of hemisphere

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  20. Harshna

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  21. J

    A Is the pole in this integrand integrable?

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  22. CrunchBerries

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  23. T

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  24. Eclair_de_XII

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  25. Puff Cube

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  26. patric44

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  27. doktorwho

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  28. Greg Bernhardt

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  29. O

    Portions of Calculus to Review for Intro. to Prob & Stats

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  30. W

    Connecting Vector Calculus to Maxwell's Equations

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  31. D

    [Calc] First max and min values of an underdamped oscillation

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  32. D

    Determine the truth of the following statements

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  33. doktorwho

    Integral that is reduced to a rational function integral

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  34. jlmccart03

    Series: Determine if they are convergent or divergent

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  35. doktorwho

    Best resources for learning Integrals

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  36. E

    How is this mathematically rigorous?

    In the solution of this problem(121), dW = (kmgcosΦ + mgsinΦ) ds, where ds is the differential element along the curve. Now they have done kmg dscosΦ + mg ds(sinΦ) = kmgdx +mgdy. Makes sense intuitively, but I want to know how this is rigorous. What I'm thinking is, the curve is broken into N...
  37. E

    I Rigorous Explanation of dW in Problem 121

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  38. Schaus

    Find the equation of the tangent line of the curve

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  39. karush

    MHB Splitting a 352MB Calculus Textbook into Chapters

    I have calculus textbook that is 352MB I want to split it into chapters the book is 1050 pages I used one the free online splitters to cut out a chapter earlier. but now I can't find it. there are MB limits so I'm over I thought the acrobat reader on the University pc would do it but the...
  40. C

    I Limits of integration on Polar curves

    General question, how do you determine the limits of integration of a polar curve? Always found this somewhat confusing and can't seem to find a decent explanation on the internet.
  41. B

    I Why dy/dx is not a ratio?

    I read people saying that dy/dx is not a ratio because it is a limit or standard part of a ratio. $${dy\over dx} = \lim_{h \to 0} {f(x +h) - f(x) \over h}, \ \ \ {dy\over dx} = st\left( {f(x +h) - f(x) \over h}\right)$$ what I get is ##{f(x +h) - f(x) \over h}## is a ratio but putting a limit...
  42. C

    AP Calculus BC: Differentiability and continuity

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  43. R

    B Instantaneous speed without using calculus

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  44. E

    Understanding Odd and Even Functions in Double Integrals

    Homework Statement Hi, I am not asking for solution for any problem as i already have the given solution for the problem. Instead, what i want clarify is what do they mean by the odd and even function and how do they get 0? Also, is there a need to change the order from dxdy to dydx?
  45. Kaura

    Extrema of Two Variable Bounded Function

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  46. Schaus

    Finding discontinuities in functions

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  47. K

    I Limits to directly check second order differentiability

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  48. cg78ithaca

    A Modeling diffusion and convection in a complex system

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  49. D

    Differential calculus ,Successive differentiation

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  50. doktorwho

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