calculus khanacademy

Calculus - Khan Academy

Calculus - Khan Academy

reported by (19 courses)
2,718 click
HTML code

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.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to KhanAcademy’s Differential Calculus channel:
Subscribe to KhanAcademy:

Lessons hide description

Why we study differential calculus More free lessons at:

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 right now: ...

Watch the next lesson: ...

Sal walking through the derivative intuition module made by Ben Eater Practice this lesson yourself on right now: ...

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 right now: ...

Introduction to L'Hôpital's Rule Practice this lesson yourself on right now: ...

L'Hôpital's Rule Example 1 Practice this lesson yourself on right now: ...

L'Hôpital's Rule Example 2 Practice this lesson yourself on right now: ...

L'Hôpital's Rule Example 3 Practice this lesson yourself on right now: ...

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 right now: ...

Practice this lesson yourself on right now: ...

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:

Another example of finding an anti-derivative using trigonometric substitution More free lessons at:

Example using trig substitution (and trig identities) to solve an integral. More free lessons at:

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:

The volume of y=sqrt(x) between x=0 and x=1 rotated around x-axis More free lessons at:

Figuring out the equation for the volume of a sphere. More free lessons at:

More volumes around the x-axis. More free lessons at:

Use the "shell method" to rotate about the y-axis More free lessons at:

Using the disk method around the y-axis. More free lessons at:

Taking the revolution around something other than one of the axes. More free lessons at:

The last part of the problem in part 7 More free lessons at:

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:

Approximating f(x)=cos x using a Maclauren Series (special case of a Taylor series at x=0) More free lessons at:

Sine Taylor Series at 0 (Maclaurin) More free lessons at:

Taylor Series at 0 (Maclaurin) for e to the x More free lessons at:

Rationale for Euler's Formula and Euler's Identity More free lessons at:

Using Wolfram Alpha to approximate sin(x) More free lessons at:

Approximating a function around a non-zero x value More free lessons at:

Visualizing Taylor Series for e^x More free lessons at:

Using a polynomial to approximate a function at f(0). More free lessons at:

Approximating a function with a polynomial by making the derivatives equal at f(0) (Maclauren Series) More free lessons at:

A glimpse of the mystery of the Universe as we approximate e^x with an infinite series. More free lessons at:

Approximating cos x with a Maclaurin series. More free lessons at:

MacLaurin representation of sin x More free lessons at:

A pattern emerges! More free lessons at:


School Secondary School 521 views

Chemistry and Macromolecules 10 lessons

Chemistry for high school Biology. Biochemistry and the macromolecules - carbohydrates, lipids, proteins, and nucleic acids.

School Secondary School 395 views

DNA & RNA 7 lessons

DNA and RNA videos for high school Biology

School Graduate School 1678 views

Linear Algebra - Khan Academy 142 lessons

Matrices, vectors, vector spaces, transformations. Covers all topics in a first year college linear algebra course. This is an advanced course normally taken by science or engineering majors after tak

School Graduate School 2614 views

Biology - Khan Academy 61 lessons

Covers topics seen in a first year college or high school biology course.

School Graduate School 1637 views

Arithmetic - Khan Academy 38 lessons

Start here if you have very little background in math fundamentals (or just want to make sure you do). Arithmetic on Khan Academy: So you're ready to have some arithmetic fun? You've come to the ri

School Graduate School 2564 views

Algebra - Khan Academy 96 lessons

Algebra I on Khan Academy: Algebra is the language through which we describe patterns. Think of it as a shorthand, of sorts. As opposed to having to do something over and over again, algebra gives you

School Graduate School 2435 views

Probability and Statistics - Khan Academy 41 lessons

Probability and statistics on Khan Academy: We dare you to go through a day in which you never consider or use probability. Did you check the weather forecast? Busted! Did you decide to go through the

School School 454 views

Cell Biology : Anatomy and Physiology Lectures 5 lessons

For the complete series as well as over 200 A&P videos, lecture notes, and interactive quizzes, please visit us at Almost all anatomy and physiology course have the student learn ho

University Mathematics 909 views

Math 1A/1B. Pre-Calculus: Polynomials and Rational Functions - UCI 17 lessons

This open course provides the student with review of intermediate algebra, geometry, and trigonometry. It is designed for those want to be successful in an introductory college calculus course, but wo

Web Stats

Community: 21,157 users
Active courses: 1,160
Lessons: 27,686
Data: 83 GB
Online: 8 users

News about new courses