# Calculus - Khan Academy

Topics covered in the first two or three semesters of college calculus. Everything from limits to derivatives to integrals to vector calculus.

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## Lessons hide description |
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## 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)) |

## 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. |

## 25) Derivatives (part 9)## More examples of taking derivatives |

## 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". |

## 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 |

## 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 |

## 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 |

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