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Calculus - Khan Academy

Calculus - Khan Academy

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

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

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Lessons hide description

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

Introduction to the intuition behind limits

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

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

Introduction to the Epsilon Delta Definition of a Limit.

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

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

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

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 ...

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

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

Part 4 of derivatives. Introduction to the chain rule.

Examples using the Chain Rule

Even more examples using the chain rule.

More examples of taking derivatives

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

Taking the derivative when y is defined implicitly.

A hairier implicit differentiation problem.

2 more implicit differentiation examples

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

Implicit differentiation example that involves the tangent function

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

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

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

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

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

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

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

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

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

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

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

More graphing with calculus.

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

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.

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 ...

Minimizing the cost of material for an open rectangular box.

Using derivatives to solve rate-of-change problems

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

The classic falling ladder problem

An introduction to indefinite integration of polynomials.

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

Integration by doing the chain rule in reverse.

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

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

Another example using integration by parts.

Finding the antiderivative using u-substitution.

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.

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

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

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

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

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

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

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

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

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:/ ...

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

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

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

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

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

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

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

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

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

Introduction to the arithmetic and geometric series

Finding the sum of an infinite geometric series.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

 

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