# Lagrange Multipliers

## Web Based Material

The method of Lagrange multipliers is a geometric method based on gradient vector fields and their relationship to level curves. The following web pages show how Maple can be used to gain a solid insight into the geometry of the method.

http://mathlab.cit.cornell.edu/local_maple/mvc/week_7/lagm.1.html
The geometry of Lagrange multipliers is explored in the context of the optimization problem on an elipse.
http://www.geom.umn.edu/education/UMTYMP/CalcIII/1994/StudentLabs/Lagrange/Lagrange.html
Applications of Lagrange multipliers to find extrema on the world famous Pringle surface, the most efficient way to build a silo and a snowcone.
http://www.geom.umn.edu./~thurman/calcIII/Lab13/welcome.html
Using maple to explore the geometry between Lagrange Multipliers.
http://www.math.ucdavis.edu/~hom/calculus/Lagrangef/overview.html
This site provides a quick overview of the method, a problem list and provides hints on how to solve the problems. If you need more practice at using Lagrange multipliers go here.
http://www.cba.uh.edu/~pricha/internet/ic1_opt.htm#constraints
Basic revision of minimisation and maximisation in one-dimension.
http://student-www.uchicago.edu/~sbjensen/Tutorials/Lagrange.html
"Lagrange multipliers are a pretty spiffy technique in multivariable calculus, and yet a great many people don't have any clear idea what they are or when they're useful. With luck, this overview will help to make the concept and application a bit clearer."

### Web Based Material - Computational Pages

http://www.math.umd.edu/~jmr/241/lagrange.htm.
"In this notebook, we will examine the problem of finding the extreme values of a function on a bounded region." (MATLAB)
http://archives.math.utk.edu/topics/multivariableCalculus.html.
Collection of MATLAB links dealing with Multivariable Calculus.

## Lecture Notes

My lecture notes are available here.