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MIT OpenCourseWare · series 5 of 10

18.01 Single Variable Calculus

David Jerison: differentiation, integration, techniques of integration and series. Fall 2006.

35 lectures0 min

Episodes

  1. Lec 1

    Derivatives, slope, velocity, rate of changeNot yet

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  2. Lec 2

    Limits, continuity; Trigonometric limitsNot yet

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  3. Lec 3

    Derivatives of products, quotients, sine, cosineNot yet

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  4. Lec 4

    Chain ruleNot yet

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  5. Lec 5

    Implicit differentiation, inversesNot yet

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  6. Lec 6

    Exponential and log; Logarithmic differentiation; hyperbolic functionsNot yet

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  7. Lec 7

    Hyperbolic functions (cont.) and exam 1 reviewNot yet

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  8. Lec 9

    Linear and quadratic approximationsNot yet

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  9. Lec 10

    Approximations (cont.); curve sketchingNot yet

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  10. Lec 11

    Max-min problemsNot yet

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  11. Lec 12

    Related ratesNot yet

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  12. Lec 13

    Newton's method and other applicationsNot yet

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  13. Lec 14

    Mean value theorem; InequalitiesNot yet

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  14. Lec 15

    Differentials, antiderivativesNot yet

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  15. Lec 16

    Differential equations, separation of variablesNot yet

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  16. Lec 18

    Definite integralsNot yet

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  17. Lec 19

    First fundamental theorem of calculusNot yet

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  18. Lec 20

    Second fundamental theoremNot yet

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  19. Lec 21

    Applications to logarithms and geometryNot yet

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  20. Lec 22

    Volumes by disks and shellsNot yet

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  21. Lec 23

    Work, average value, probabilityNot yet

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  22. Lec 24

    Numerical integrationNot yet

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  23. Lec 25

    Exam 3 reviewNot yet

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  24. Lec 27

    Trigonometric integrals and substitutionNot yet

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  25. Lec 28

    Integration by inverse substitution; completing the squareNot yet

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  26. Lec 29

    Partial fractionsNot yet

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  27. Lec 30

    Integration by parts, reduction formulaeNot yet

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  28. Lec 31

    Parametric equations, arclength, surface areaNot yet

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  29. Lec 32

    Polar coordinates; area in polar coordinatesNot yet

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  30. Lec 33

    Exam 4 reviewNot yet

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  31. Lec 35

    Indeterminate forms - L'Hospital's ruleNot yet

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  32. Lec 36

    Improper integralsNot yet

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  33. Lec 37

    Infinite series and convergence testsNot yet

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  34. Lec 38

    Taylor's seriesNot yet

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  35. Lec 39

    Final reviewNot yet

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