Community Tip - You can subscribe to a forum, label or individual post and receive email notifications when someone posts a new topic or reply. Learn more! X
Two memories from my years in graduate school are behind the title of this posting. First, a steak dinner was a special treat for my wife and me during that time. The problem example for this blog A Stefan Problem in Cylindrical Coordinates demonstrates Mathcad's ability to solve those special, unique problems that are difficult or insolvable without a program like Mathcad.
The second memory is of being taught how to obtain symbolic solutions to partial differential equations in Advanced Transport Phenomena class. The solutions to several problems involved Bessel functions. Having worked for several years in industry before returning to a university, I asked the professor - why spend the time getting a symbolic solution when what was actually needed was a numerical result? I added that obtaining a numerical result from evaluation of the Bessel functions was probably as time consuming as a obtaining a numerical solution of the partial differential equations. His answer was that symbolic solutions were preferred for publication. That answer offered me no incentive and I lost interest in symbolic solutions at that time.
Mathcad has changed my attitude toward symbolic solutions, but only because, when they are paired with numerical methods, the combination is more powerful than the separate parts. Just as steak and potatoes are a great paring, so too are symbolic and numerical methods. I increasingly use symbolic methods to solve for variables in nonlinear equations or to obtain derivatives and integrals of functions. The melt radius worksheet uses symbolic methods up to the final numerical solution of the ODE's developed by the symbolic analysis.
For me, this combination of symbolic-numerical methods is a paradigm shift in problem solving. I believe it increases my creativity by allowing me to think more about problem structure as opposed to the details of numerical solutions. The "tight" integration between symbolic and numerical methods in Mathcad makes it easy to combine the methods.
So which is steak and which are potatoes? Numerical methods are still the basic "food"...the potatoes. However, in spite of my earlier aversion to symbolic methods, I now consider them worthy of special status...steak. However, this is the kind of steak that I can't "cook" myself. Thankfully, Mathcad can do the "cooking" for me!
Next: Raw is Better (no, it's not another food blog, it's about model validation)