Dan, here are some more reasons:
Mathcad Enhances the STEM Curriculum at Every Educational Level
A STEM professional typically has studied algebra and trigonometry, the calculus sequence, and differential equations. Engineering and math students might also study linear (matrix) algebra; a more advanced course in differential equations (ordinary and partial); probability and statistics (possibly including Design of Experiments). A course in advanced calculus for applications might survey some or all of the post-calculus areas mentioned.
Pick up a textbook on any of these math subjects, and Mathcad works well as a supplement. Mathcad can literally make the equations and graphs in the book "come alive." Plus, Mathcad has programming, the value of which cannot be overestimated.
Mathcad Facilitates "Classical" Symbolic Math
Mathcad actually facilitates two kinds of math: symbolics and numerics. In symbolics, one simplifies and/or solves equations and systems of equations. The solutions are expressed with symbols, and not numbers per se. In numerics, one assigns numerical values to the symbols up front, and wants the results to have numerical values. Mathcad experts tend to favor one or the other: symbolics or numerics. I associate symbolics with "classical" mathematics. Classical mathematics is what is typically taught in schools, colleges and universities these days. Success leads to neat, though possibly quite complicated solutions: expansions in terms of circular or special functions, Fourier analysis, etc.
Mathcad Empowers Numerics-Based Research
There are areas of STEM that do not admit "tidy" analytical solutions, areas that suggest problems which we can only investigate and solve using computers and numerics. One such area is nonlinear systems. Research in nonlinear systems typically involves setting up and solving systems of nonlinear differential equations. Here are just two examples.
The Newtonian N-body Problem for N >= 3. Even for N = 3 (three gravitating Newtonian particles), no purely analytical solution to the associated system of eighteen first-order, ordinary differential equations is possible. But we can investigate the numerical behavior with Mathcad. Mathcad's powerful numerical integrators make this kind of nonlinear math relatively easy to investigate.
Chemical Kinetics. Do a Google search for YouTube videos on the Belousov-Zhabotinsky (BZ) reaction, a chemical reaction in which the quantities of reactants and products actually oscillate as the reaction proceeds. This leads, for example, to solutions that change color, back and forth over spectrum of colors, as the concentrations of the chemical species oscillate. Want to know more about chemical kinetics? PlanetPTC has a forum on this! Viktor Korobov and Valery Ochkov will be publishing in spring 2011 a book that uses Mathcad to quantify, for example, what happens in a BZ reaction.
To sum up: any high school student who is so fortunate as to be taught Mathcad by STEM professionals (the ones whom we know as high school science and math teachers!) will be well-positioned for success in his or her college and post-academic STEM career.
