Curated Video
What is Calculus in Math? Simple Explanation with Examples
Calculus is a branch of mathematics that deals with very small changes. Calculus consists of two main segments—differential calculus and integral calculus. Differential calculus primarily deals with the rate of change of things, while...
Institute for New Economic Thinking
John Smithin: Forging Fresh Tools from the Past
Professor Smithin argues that new economic thinking is not only about new thinking but also about recovering past knowledge from past crises. He talks about the policy response from the 2008 crisis compared to the 1930s. Most crucially,...
Institute for New Economic Thinking
Eric Weinstein: Economic Thinking In A Fallible World
By Marshall Auerback The philosopher Karl Popper argued that we cannot know empirical truths with absolute certainty. According to Popper, even scientific laws can't be verified beyond a shadow of a doubt. They can only be falsified by...
Institute for New Economic Thinking
Eric Weinstein: What Math and Physics Can Do for New Economic Thinking
Welcome to our video series called "New Economic Thinking." The series will feature dozens of conversations with leading economists on the most important issues facing economics and the global economy today. This episode features...
Math Fortress
Differential Equations: Implicit Solutions (Level 1 of 3)
This video introduces the basic concepts associated with solutions of ordinary differential equations. This video goes over implicit solutions of differential equations. The concept of a formal solution is also presented.
Khan Academy
Limit Examples (Part 1), Limits, Differential Calculus
One example is finding the limit as x approaches -1 of (2x+2)/(x+1), solved by simplifying the expression and then explored intuitively by looking at the left and right-hand limits. The second example of finding the limit as x approaches...
Curated OER
Introduction to Rate-of-Change Problems
Sal solves an example for finding the rate of change of the height of water in a cone at a specific point when it is being filled at a given rate. In this video, Sal reviews the volume of a cone and the chain rule and then, uses these to...
Curated OER
Maxima Minima Slope Intuition
Before solving any problems, Sal gives an overview of what happens to the slope, first derivative, and second derivative at local maxima and minima to give the viewer a more intuitive feel for these types of problems.
Curated OER
Optimization Example 4
Sal does another optimization example, this time, minimizing the total cost of an open rectangular box. In this problem, the volume can be defined in terms of a single variable and given a cost model, he builds a cost equation. He finds...
Curated OER
Graphing with Calculus
In a problem where you are not given the original function, but rather only three known points on the graph and a few additional pieces of information about when the first and second derivatives are positive or negative, Sal shows how...
Curated OER
Optimization with Calculus 3
Using what one learned about finding the minimum and maximum of functions, the optimization problem to find two numbers whose product is -16 and whose sum of squares is a minimum is solved. Sal starts by writing the equations and...
Khan Academy
Proof: lim (sin x)/x
By looking at the expression (sin x)/x that is not defined at the limit value of 0, Sal uses the squeeze theorem to show that the function can be bound between two other functions that are defined at the limit value, so the limit can...
Khan Academy
Proof: d/dx(x^n)
Using the binomial theorem and definition of a limit, Sal shows a proof that the derivative of xn equals nxn-1.
Khan Academy
Proof: d/dx(sqrt(x)) Taking Derivatives Differential Calculus
Using the definition of a limit, Sal proves that the derivative of x or x1/2 equals _ x-1/2.
Khan Academy
Proof: d/dx(ln x)=1/x
Using the definition of a limit, various properties of logarithms, and a definition of e, Sal shows the proof of the derivative of ln x = 1/x. Note: The video titled "Proof of Derivatives of Ln(x) and e^x,Ó has a more straightforward...
Khan Academy
Proof: d/dx(e^x) = e6x
Using the derivative of ln x, the chain rule, and the definition of a limit, Sal shows proof that the derivative of ex = ex. Note: The video titled "Proof of Derivatives of Ln(x) and e^x,Ó clearly explains this proof.
Khan Academy
Introduction to Limits, Limits, Differential Calculus
Sal begins his explanation of limits with a few basic examples and takes a more intuitive point of view before looking at a formal mathematical definition in later videos. He starts by introducing the notation for limits and describes...
Khan Academy
Equation of a Tangent Line, Taking Derivatives, Differential Calculus
Using a specific example, Sal shows how to find the equation of a tangent line to a given function at a specific point. Specifically, he solves the problem of finding the tangent line to the function f(x) = xex at x = 1. This problem...
Khan Academy
Power Rule Introduction (Old) Taking derivatives, Differential Calculus
This video covers the differential notation dy/dx and generalizes the rule for finding the derivative of any polynomial. It also extends the notion of the derivatives covered in the Khan Academy videos, "Calculus Derivatives 2Ó and...
Khan Academy
Calculus: Derivatives 2
Sal continues where he left off with the last video, "Derivatives 1, Ó by looking at the equation y = x^2 and examining the slope of the second line at a specific point, and again defining the limit as x approaches zero to get the slope...
Khan Academy
The derivative of f(x)=x^2 for any x Taking derivatives, Differential Calculus
By defining the formal definition of a derivative, f(x), Sal can find the general form of the derivate function for the example f(x) = x2. He continues to stress the importance of an intuitive understanding of derivative functions.
Khan Academy
Calculus: Derivatives 2 (New HD Version)
Sal continues where he left off with the last video, "Derivatives 1, Ó by looking at the equation y = x2 and examining the slope of the second line at a specific point. He continues defining the limit as x approaches zero to get the...
Khan Academy
Calculus: Derivatives 1
Sal defines the term derivative by taking the listener on a well-organized tour of the slope. First, he reviews the concept of the slope of a line from algebra, then extends this idea to look at the slope of the curve by first examining...