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Calculus - Double and Triple Integrals: Triple Integrals
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This is about as many integrals we can use before our brains explode. Now we can sum variable quantities in three-dimensions (what is the mass of a 3-D wacky object that has variable mass)!

Subject:
Calculus
Mathematics
Material Type:
Lecture
Provider:
Khan Academy
Provider Set:
Khan Academy
Author:
Salman Khan
Date Added:
08/13/2020
Calculus: Indefinite and Definite Integrals
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This series of videos focusing on calculus covers indefinite integral as anti-derivative, definite integral as area under a curve, integration by parts, u-substitution, trig substitution.

Subject:
Calculus
Mathematics
Material Type:
Lecture
Provider:
Khan Academy
Provider Set:
Khan Academy
Date Added:
08/13/2020
Calculus: Limits
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This series of videos focusing on calculus covers limit introduction, squeeze theorem, and epsilon-delta definition of limits.

Subject:
Calculus
Mathematics
Material Type:
Lecture
Provider:
Khan Academy
Provider Set:
Khan Academy
Date Added:
08/13/2020
Calculus - Limits: Limits
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Limits are the core tool that we build upon for calculus. Many times, a function can be undefined at a point, but we can think about what the function "approaches" as it gets closer and closer to that point (this is the "limit"). Other times, the function may be defined at a point, but it may approach a different limit. There are many, many times where the function value is the same as the limit at a point. Either way, this is a powerful tool as we start thinking about slope of a tangent line to a curve.

Subject:
Calculus
Mathematics
Material Type:
Lecture
Provider:
Khan Academy
Provider Set:
Khan Academy
Date Added:
08/13/2020
Calculus - Limits: Old Limits Tutorial
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This tutorial covers much of the same material as the "Limits" tutorial, but does it with Sal's original "old school" videos. The sound, resolution or handwriting isn't as good, but some people find them more charming.

Subject:
Calculus
Mathematics
Material Type:
Lecture
Provider:
Khan Academy
Provider Set:
Khan Academy
Date Added:
08/13/2020
Calculus - Line Integrals and Green's Theorem: Green's Theorem
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CC BY-NC-SA
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It is sometimes easier to take a double integral (a particular double integral as we'll see) over a region and sometimes easier to take a line integral around the boundary. Green's theorem draws the connection between the two so we can go back and forth. This tutorial proves Green's theorem and then gives a few examples of using it. If you can take line integrals through vector fields, you're ready for Mr. Green.

Subject:
Calculus
Mathematics
Material Type:
Lecture
Provider:
Khan Academy
Provider Set:
Khan Academy
Author:
Salman Khan
Date Added:
08/13/2020
Calculus - Line Integrals and Green's Theorem: Line Integrals For Scalar Functions
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With traditional integrals, our "path" was straight and linear (most of the time, we traversed the x-axis). Now we can explore taking integrals over any line or curve (called line integrals).

Subject:
Calculus
Mathematics
Material Type:
Lecture
Provider:
Khan Academy
Provider Set:
Khan Academy
Author:
Salman Khan
Date Added:
08/13/2020
Calculus - Line Integrals and Green's Theorem: Line Integrals In Vector Fields
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CC BY-NC-SA
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You've done some work with line integral with scalar functions and you know something about parameterizing position-vector valued functions. In that case, welcome! You are now ready to explore a core tool math and physics: the line integral for vector fields. Need to know the work done as a mass is moved through a gravitational field. No sweat with line integrals.

Subject:
Calculus
Mathematics
Material Type:
Lecture
Provider:
Khan Academy
Provider Set:
Khan Academy
Author:
Salman Khan
Date Added:
08/13/2020
Calculus - Partial Derivatives, Gradient, Divergence, Curl: Partial Derivatives
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Let's jump out of that boring (okay, it wasn't THAT boring) 2-D world into the exciting 3-D world that we all live and breath in. Instead of functions of x that can be visualized as lines, we can have functions of x and y that can be visualized as surfaces. But does the idea of a derivative still make sense? Of course it does! As long as you specify what direction you're going in. Welcome to the world of partial derivatives!

Subject:
Calculus
Mathematics
Material Type:
Lecture
Provider:
Khan Academy
Provider Set:
Khan Academy
Author:
Salman Khan
Date Added:
08/13/2020
Calculus - Sequences, Series and Function Approximation: Maclaurin and Taylor Series
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CC BY-NC-SA
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In this tutorial, we will learn to approximate differentiable functions with polynomials. Beyond just being super cool, this can be useful for approximating functions so that they are easier to calculate, differentiate or integrate. So whether you will have to write simulations or become a bond trader (bond traders use polynomial approximation to estimate changes in bond prices given interest rate changes and vice versa), this tutorial could be fun. If that isn't motivation enough, we also come up with one of the most epic and powerful conclusions in all of mathematics in this tutorial: Euler's identity.

Subject:
Calculus
Mathematics
Material Type:
Lecture
Provider:
Khan Academy
Provider Set:
Khan Academy
Author:
Salman Khan
Date Added:
08/13/2020
Calculus - Surface Integrals and Stokes' Theorem: Parameterizing a Surface
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CC BY-NC-SA
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You can parameterize a line with a position vector valued function and understand what a differential means in that context already. This tutorial will take things further by parametrizing surfaces (2 parameters baby!) and have us thinking about partial differentials.

Subject:
Calculus
Mathematics
Material Type:
Lecture
Provider:
Khan Academy
Provider Set:
Khan Academy
Author:
Salman Khan
Date Added:
08/13/2020