In this lecture, the focus is on studying functions of several variables and their derivatives. The challenge of visualizing functions of two variables is explored through graphing and contour plots. Contour plots are shown to be an elegant solution to the difficulty of drawing space pictures on a sheet of paper or a blackboard. The contour plot is essentially an xy plot with a bunch of curves representing the elevations on the graph. This method is compared to topographical maps and temperature maps, where the same concept is applied.
A lecture on level curves, partial derivatives, and tangent planes. The beginning of a study of functions of several variables.
Denis Auroux. 18.02 Multivariable Calculus, Fall 2007. (Massachusetts Institute of Technology: MIT OpenCourseWare). http://ocw.mit.edu (Accessed March 15, 2009). License: Creative Commons Attribution-Noncommercial-Share Alike.