This video looks at Falling ladder related rates.
This video looks at Finding slope of tangent line with implicit differentiation.
You get the general idea that taking a definite integral of a function is related to evaluating the antiderivative, but where did this connection come from. This tutorial focuses on the fundamental theorem of calculus which ties the ideas of integration and differentiation together. We'll explain what it is, give a proof and then show examples of taking derivatives of integrals where the Fundamental Theorem is directly applicable.
This 7-minute video lessonn looks at approximating a function around a non-zero x value
This video looks at Generalizing what we did in the last video for f(x) to get the "formula" for using the disc method around the x-axis.
This video looks at Generalizing a left Riemann sum with equally spaced rectangles.
This video looks at Looking at the example from the last video in a more generalized way.
This 10-minute video lesson provides an introduction to the gradient.
This 11-minute video lesson examines intuition of the gradient of a scalar field (temperature in a room) in 3 dimensions.
This 21-minute video lesson looks at Graphing functions using derivatives.
This 11-minute video lesson uses Green's Theorem to solve a line integral of a vector field.
This 7-minute video lesson provides Another example of applying Green's Theorem.
This 14-minute video lesson provides part 1 of the proof of Green's Theorem.
This 19-minute video lesson provides part 2 of the proof of Green's Theorem.
This video looks at seeing that Green's Theorem is just a special case of stokes' Theorem.
This video looks at identifying minima and maxima for x^3 - 12x - 5.
This video looks at the implicit derivative of e^(xy^2) = x - y.
This video looks at the implicit derivative of y = cos(5x - 3y).
This video looks at the implicit derivative of (x^2+y^2)^3 = 5x^2y^2.
This video looks at the implicit derivative of (x-y)^2 = x + y + 1.