You have a basic understanding of what a limit is. Now, in this tutorial, we can explore situation where we take the limit as x approaches negative or positive infinity (and situations where the limit itself could be unbounded).
This video looks at Limits at positive and negative infinity.
This video looks at Limits to define continuity.
This video looks at Limits with two horizontal asymptotes.
This 13-minute video lesson looks at a concrete example using a line integral.
This 13-minute video lesson examines a line integral over a closed path (part 1).
This 10-minute video lesson provides part 2 of the example of taking a line integral over a closed path.
This series of videos focusing on calculus covers line integral of scalar and vector-valued functions, Green's Theorem and 2-D Divergence Teorem.
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.
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).
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.
This 17-minute video lesson shows how to use line integrals to find the work done on a particle moving through a vector field.
This 13-minute video looks at approximating a function at 0 using a polynomial.
If over the last hour on the highway, you averaged 60 miles per hour, then you must have been going exactly 60 miles per hour at some point. This is the gist of the mean value theorem (which generalizes the idea for any continuous, differentiable function).
This 17-minute video lesson looks at the iIntuition behind the Mean Value Theorem. [Calculus playlist: Lesson 55 of 156]
This 17-minute video lesson looks at the iIntuition behind the Mean Value Theorem. [Calculus playlist: Lesson 55 of 156]
Can calculus be used to figure out when a function takes on a local or global maximum value? Absolutely. Not only that, but derivatives and second derivatives can also help us understand the shape of the function (whether they are concave upward or downward). If you have a basic conceptual understanding of derivatives, then you can start applying that knowledge here to identify critical points, extrema, inflections points and even to graph functions.
This video looks at minimizing combined area.
Using calculus to solve optimization problems.
This video looks at minimizing the cost of a storage container.