What is calculus i: Definition and 52 Discussions

Calculus 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 the latter 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. Later work, including codifying the idea of limits, put these developments on a more solid conceptual footing. Today, calculus has widespread uses in science, engineering, and social science.

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  1. S

    What type of mathematics did you find the most difficult?

    Mathematics tends to be more progressive than any other field. But I've heard some people say that some math classes that they took were more difficult than the most advanced math classes that they took. For instance, I've heard people say that Calculus II is more difficult than Calculus III...
  2. J

    Studying Reading "How to Prove It" right before taking Calculus I -- Question

    If I were to read up to and including Chapter 3, would I be prepared enough to read Spivak's Calculus or at least some single variable calculus text based on proofs? I'm asking because I plan on taking Real Analysis later and I'd like to gain a better understanding of Calculus. I have read...
  3. J

    Courses I only got a B in Calculus I :(

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  4. O

    MHB Calculus I - Relative Growth Rate help

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  5. havonasun

    Courses Deciding Between Calculus I & Calculus w/ Analytic GeometryI

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  6. S

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  7. mr_persistance

    Apostol's Calculus I. 3.12 - Verify Solution.

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  8. D

    Should I Retake Calculus I over the Summer to Prepare for Calculus II?

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  9. A

    MHB Calculus I Simplifying and Substitution

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  10. QuantumCurt

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  11. A

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  12. F

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  13. B

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  14. K

    What should I study to prepare for Calculus I and II

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  15. K

    Calculus I review for Calculus II

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  16. K

    Should I take Calculus I, or Calculus I and II?

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  17. B

    Determine if EVT applies (Calculus I)

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  18. P

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  19. D

    Schools How to study for Calculus I (College)

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  20. T

    Find the General Anti-derivative (Calculus I)

    Homework Statement given f(x) = [x^3+5sqrt(x)]/x^2, find the anti-derivative Homework Equations The Attempt at a Solution Hi I have attempted to solve this by re-writing the equation as a sum of two fractions: x^3/x^2 + 5sqrt(x)/x^2, simplying gives = x + 5/x^3/2 I then...
  21. K

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  22. T

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  23. N

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  24. A

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  25. G

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  26. G

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  27. Dembadon

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  28. mccoy1

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  29. C

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  30. R

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  31. W

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  32. E

    Calculus I: Is it possible to teach myself over winter break?

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  33. R

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  34. R

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  35. R

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  36. P

    I learned calculus I and II using stewart's. I also taught myself

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  37. A

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  38. A

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  39. S

    What's an acceptable grade for Calculus I in university?

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  40. B

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  41. D

    Are there any good video lectures for learning Calculus I?

    Don't know if it's already been posted somewhere else, my apologies if it has been, but I found http://press.princeton.edu/video/banner/8351.html" video lectures by Adrian Banner quite educational. It's not very advanced stuff, but everything is explained very clearly. Good stuff.
  42. S

    Calculus I - without a calculator

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  43. S

    Is Michael Spivak's Calculus I book worth the investment?

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  44. D

    Can I Take Linear Algebra Without Calc. II and Multi-Variable?

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  45. S

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  46. E

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  47. D

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  48. tony873004

    Finding Online Calculus I Resources to Refresh Your Memory

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  49. Orion1

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  50. T

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