Calculus - Khan Academy

1) Newton Leibniz and Usain Bolt

Why we study differential calculus More free lessons at: http://www.khanacademy.org/video?v=EKvHQ

2) Introduction to limits | Limits | Differential Calculus

Introduction to limits

3) Introduction to limits 2 | Limits | Precalculus

Introduction to the intuition behind limits

4) Limit examples (part 1) | Limits | Differential Calculus

Some limit exercises

5) Limit examples (part 2) | Limits | Differential Calculus

More limit examples

6) Limit examples (part 3) | Limits | Differential Calculus

More limit examples

7) Limit examples w/ brain malfunction on first prob (part 4) | Differential Calculus

3 interesting limit examples (correct answer for problem 1 is 3/16 (6/(4*8) NOT 6/(4+8))

8) Squeeze theorem (sandwich theorem) | Limits | Differential Calculus

9) Proof: lim (sin x)/x | Limits | Differential Calculus

Using the squeeze theorem to prove that the limit as x approaches 0 of (sin x)/x =1

10) More limits | Limits | Differential Calculus

More limit examples

11) Epsilon-delta limit definition 1 | Limits | Differential Calculus

Introduction to the Epsilon Delta Definition of a Limit.

12) Epsilon-delta limit definition 2 | Limits | Differential Calculus

Using the epsilon delta definition to prove a limit

13) Derivative as slope of a tangent line | Taking derivatives | Differential Calculus

Understanding that the derivative is just the slope of a curve at a point (or the slope of the tangent line)

14) Calculating slope of tangent line using derivative definition | Differential Calculus

Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/diffe ...

15) The derivative of f(x)=x^2 for any x | Taking derivatives | Differential Calculus

Watch the next lesson: https://www.khanacademy.org/math/differe ...

16) Derivative intuition module | Taking derivatives | Differential Calculus

Sal walking through the derivative intuition module made by Ben Eater Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/diffe ...

17) Calculus: Derivatives 1 | Taking derivatives | Differential Calculus

Finding the slope of a tangent line to a curve (the derivative). Introduction to Calculus.

18) Calculus: Derivatives 2 | Taking derivatives | Differential Calculus

More intuition of what a derivative is. Using the derivative to find the slope at any point along f(x)=x^2

19) Power rule introduction (old) | Taking derivatives | Differential Calculus

Determining the derivatives of simple polynomials.

20) The Chain Rule

Part 4 of derivatives. Introduction to the chain rule.

21) Chain Rule Examples

Examples using the Chain Rule

22) Even More Chain Rule

Even more examples using the chain rule.

23) Product rule | Taking derivatives | Differential Calculus

24) Quotient rule and common derivatives | Taking derivatives | Differential Calculus

25) Derivatives (part 9)

More examples of taking derivatives

26) Proof: d/dx(x^n) | Taking derivatives | Differential Calculus

27) Proof: d/dx(sqrt(x)) | Taking derivatives | Differential Calculus

28) Proof: d/dx(ln x) = 1/x | Taking derivatives | Differential Calculus

Taking the derivative of ln x

29) Proof: d/dx(e^x) = e^x | Taking derivatives | Differential Calculus

Proof that the derivative of e^x is e^x.

30) Proofs of derivatives of ln(x) and e^x | Taking derivatives | Differential Calculus

Doing both proofs in the same video to clarify any misconceptions that the original proof was "circular".

31) Extreme derivative word problem (advanced) | Differential Calculus

32) Implicit Differentiation

Taking the derivative when y is defined implicitly.

33) Implicit Differentiation (part 2)

A hairier implicit differentiation problem.

34) More implicit differentiation

2 more implicit differentiation examples

35) More chain rule and implicit differentiation intuition

More intuition behind the chain rule and how it applies to implicit differentiation.

36) Trig Implicit Differentiation Example

Implicit differentiation example that involves the tangent function

37) Derivative of x^(x^x) | Taking derivatives | Differential Calculus

Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/diffe ...

38) Introduction to l'Hôpital's rule | Derivative applications | Differential Calculus

Introduction to L'Hôpital's Rule Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/diffe ...

39) L'Hôpital's rule example 1 | Derivative applications | Differential Calculus

L'Hôpital's Rule Example 1 Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/diffe ...

40) L'Hôpital's rule example 2 | Derivative applications | Differential Calculus

L'Hôpital's Rule Example 2 Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/diffe ...

41) L'Hôpital's rule example 3 | Derivative applications | Differential Calculus

L'Hôpital's Rule Example 3 Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/diffe ...

42) Maxima Minima Slope Intuition

Intuition on what happens to the slope/derivative and second derivatives at local maxima and minima.

43) Inflection Points and Concavity Intuition

Understanding concave upwards and downwards portions of graphs and the relation to the derivative. Inflection point intuition

44) Monotonicity Theorem

Using the monotonicity theorem to determine when a function is increasing or decreasing.

45) Calculus: Maximum and minimum values on an interval

2 examples of finding the maximum and minimum points on an interval.

46) Graphing using derivatives | Derivative applications | Differential Calculus

Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/diffe ...

47) Another example graphing with derivatives | Differential Calculus

Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/diffe ...

48) Graphing with Calculus

More graphing with calculus.

49) Optimization with Calculus 1

Find two numbers whose products is -16 and the sum of whose squares is a minimum.

50) Optimization with Calculus 2

Find the volume of the largest open box that can be made from a piece of cardboard 24 inches square by cutting equal squares from the corners and turning up the sides.

51) Optimization with Calculus 3

A wire of length 100 centimeters is cut into two pieces; one is bent to form a square, and the other is bent to form an equilateral triangle. Where should the cut be made if (a) the sum of the two are ...

52) Optimization Example 4

Minimizing the cost of material for an open rectangular box.

53) Introduction to rate-of-change problems

Using derivatives to solve rate-of-change problems

54) Equation of a tangent line | Taking derivatives | Differential Calculus

55) Rates-of-change (part 2)

Another (simpler) example of using the chain rule to determine rates-of-change

56) Ladder rate-of-change problem

The classic falling ladder problem

57) Mean value theorem | Derivative applications | Differential Calculus

Intuition behind the Mean Value Theorem

58) The Indefinite Integral or Anti-derivative

An introduction to indefinite integration of polynomials.

59) Indefinite integrals (part II)

Examples of taking the indefinite integral (or anti-derivative) of polynomials.

60) Indefinite Integration (part III)

Integration by doing the chain rule in reverse.

61) Indefinite Integration (part IV)

Integration by substitution (or the reverse-chain-rule)

62) Indefinite Integration (part V)

Introduction to Integration by Parts (kind of the reverse-product rule)

63) Integration by Parts (part 6 of Indefinite Integration)

Example using Integration by Parts

64) Indefinite Integration (part 7)

Another example using integration by parts.

65) Another u-subsitution example

Finding the antiderivative using u-substitution.

66) Introduction to definite integrals

Using the definite integral to solve for the area under a curve. Intuition on why the antiderivative is the same thing as the area under a curve.

67) Definite integrals (part II)

More on why the antiderivative and the area under a curve are essentially the same thing.

68) Definite Integrals (area under a curve) (part III)

More on why the antiderivative and the area under a curve are essentially the same thing.

69) Definite Integrals (part 4)

Examples of using definite integrals to find the area under a curve

70) Definite Integrals (part 5)

More examples of using definite integrals to calculate the area between curves

71) Definite integral with substitution

Solving a definite integral with substitution (or the reverse chain rule)

72) Integrals: Trig Substitution 1

Example of using trig substitution to solve an indefinite integral More free lessons at: http://www.khanacademy.org/video?v=n4EK9

73) Integrals: Trig Substitution 2

Another example of finding an anti-derivative using trigonometric substitution More free lessons at: http://www.khanacademy.org/video?v=fD7Mb

74) Integrals: Trig Substitution 3 (long problem)

Example using trig substitution (and trig identities) to solve an integral. More free lessons at: http://www.khanacademy.org/video?v=sw2p2

75) Periodic Definite Integral

2010 IIT JEE Paper 1 Problem 52 Periodic Definite Integral. The second term at about minute 14 should have a positive sign. Luckily, it doesn't effect the final answer! More free lessons at: http:/ ...

76) Simple Differential Equations

3 basic differential equations that can be solved by taking the antiderivatives of both sides.

77) Solid of Revolution (part 1)

Figuring out the volume of a function rotated about the x-axis. More free lessons at: http://www.khanacademy.org/video?v=R_aqS

78) Solid of Revolution (part 2)

The volume of y=sqrt(x) between x=0 and x=1 rotated around x-axis More free lessons at: http://www.khanacademy.org/video?v=iUzfs

79) Solid of Revolution (part 3)

Figuring out the equation for the volume of a sphere. More free lessons at: http://www.khanacademy.org/video?v=tqfU9

80) Solid of Revolution (part 4)

More volumes around the x-axis. More free lessons at: http://www.khanacademy.org/video?v=OtmjN

81) Solid of Revolution (part 5)

Use the "shell method" to rotate about the y-axis More free lessons at: http://www.khanacademy.org/video?v=NIdqk

82) Solid of Revolution (part 6)

Using the disk method around the y-axis. More free lessons at: http://www.khanacademy.org/video?v=F2psx

83) Solid of Revolution (part 7)

Taking the revolution around something other than one of the axes. More free lessons at: http://www.khanacademy.org/video?v=IZ8W-

84) Solid of Revolution (part 8)

The last part of the problem in part 7 More free lessons at: http://www.khanacademy.org/video?v=4Flj9

85) Sequences and Series (part 1)

Introduction to the arithmetic and geometric series

86) Sequences and series (part 2)

Finding the sum of an infinite geometric series.

87) Maclauren and Taylor Series Intuition

Approximating a function at 0 using a polynomial More free lessons at: http://www.khanacademy.org/video?v=epgwu

88) Cosine Taylor Series at 0 (Maclaurin)

Approximating f(x)=cos x using a Maclauren Series (special case of a Taylor series at x=0) More free lessons at: http://www.khanacademy.org/video?v=WWe7p

89) Sine Taylor Series at 0 (Maclaurin)

Sine Taylor Series at 0 (Maclaurin) More free lessons at: http://www.khanacademy.org/video?v=LlKvu

90) Taylor Series at 0 (Maclaurin) for e to the x

Taylor Series at 0 (Maclaurin) for e to the x More free lessons at: http://www.khanacademy.org/video?v=JYQqm

91) Euler's Formula and Euler's Identity

Rationale for Euler's Formula and Euler's Identity More free lessons at: http://www.khanacademy.org/video?v=mgNtP

92) Visualizing Taylor Series Approximations

Using Wolfram Alpha to approximate sin(x) More free lessons at: http://www.khanacademy.org/video?v=8dMLK

93) Generalized Taylor Series Approximation

Approximating a function around a non-zero x value More free lessons at: http://www.khanacademy.org/video?v=1LxhX

94) Visualizing Taylor Series for e^x

Visualizing Taylor Series for e^x More free lessons at: http://www.khanacademy.org/video?v=AFMXi

95) Polynomial approximation of functions (part 1)

Using a polynomial to approximate a function at f(0). More free lessons at: http://www.khanacademy.org/video?v=sy132

96) Polynomial approximation of functions (part 2)

Approximating a function with a polynomial by making the derivatives equal at f(0) (Maclauren Series) More free lessons at: http://www.khanacademy.org/video?v=3JG3q

97) Approximating functions with polynomials (part 3)

A glimpse of the mystery of the Universe as we approximate e^x with an infinite series. More free lessons at: http://www.khanacademy.org/video?v=XZDGr

98) Polynomial approximation of functions (part 4)

Approximating cos x with a Maclaurin series. More free lessons at: http://www.khanacademy.org/video?v=gcJeg

99) Polynomial approximations of functions (part 5)

MacLaurin representation of sin x More free lessons at: http://www.khanacademy.org/video?v=9AoDu

100) Polynomial approximation of functions (part 6)

A pattern emerges! More free lessons at: http://www.khanacademy.org/video?v=-gRNR