Project NExT CAS Panel Session University of Wisconsin, Madison July 30, 2008 Mathematica in the Military: Using CAS tools at the United States Military Academy Edward W. Swim Assistant Professor & Davies Fellow Department of Mathematical Sciences United States Military Academy West Point NY

USMA Core Math Mathematical Modeling and Introduction to Calculus: Modeling with Continuous Functions, Discrete Dynamical Systems, Matrix Algebra, Systems of Difference Equations, and Instantaneous Change Calculus I: Single Variable Derivatives, Vector Functions, Multivariable Functions and their Derivatives, and Modeling with Ordinary Differential Equations Calculus II: Single Variable Integration, Integration of Vector Functions, Multivariable Integration, and Ordinary Differential Equations Probability and Statistics: Probability, Distribution Functions, Least Squares, Random Variables, Estimation, Hypothesis Testing, Linear Regression

Board Problems Find the local minimum, maximum, and saddle points of the following functions:

Example Problem A 2km×2km portion of a lakebed is modeled by the function Build a 3D Plot and a Contour Plot of the lakebed. Estimate the depth of the lake at its lowest point. Find the coordinates for this point. Use the second derivative test to classify this critical point.

Example Problem The water table begins at the highest point of this surface on the boundary y = -1. What are the coordinates of this point? Is the critical point you found at the bottom of the lake an absolute minimum? Verify your answer.

USMA Dept. of Math. Sci. Technology Goals Use software to visualize and analyze mathematical functions. Use a computer algebra system to solve linear and nonlinear equations and systems of equations. Evaluate derivatives and integrals using a computer algebra system. Leverage technology to solve complex problems.