Topics covered in the first two or three semesters of college calculus. Everything from limits to derivatives to integrals to vector calculus. Should understand the topics in the pre-calculus playlist first (the limit videos are in both playlists).
More intuition behind the chain rule and how it applies to implicit differentiation.
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 areas is to be a minimum; (b) a maximum? (Allow the possibility of no cut.).
Using a line integral to find the work done by a vector field example.
Showing that the line integral of a scalar field is independent of path direction.
Showing that, unlike line integrals of scalar fields, line integrals over vector fields are path direction dependent.
Showing that the line integral along closed curves of conservative vector fields is zero.
Example of taking a closed line integral of a conservative field.
Using path independence of a conservative vector field to solve a line integral.
Introduction to Parametrizing a Surface with Two Parameters.
Determining a Position Vector-Valued Function for a Parametrization of Two Parameters.