Advanced problem solving in PTC Mathcad… Wizardry or a journey of discovery?

It’s fair to say that most people very rarely make use of the full breadth of capabilities that are provided with most modern software packages. There is just so much capability packed into software applications today which offer capabilities to so many user specific requirements. The same is probably true of some users of PTC Mathcad. The reasons may often be a combination of limiting factors such as time pressures at work, lack of training etc.

So if you are new to PTC Mathcad you may well have some questions about the extent to which you should invest your effort and time in attempting a solution to your problem with PTC Mathcad. Should I use PTC Mathcad for this task? Is it the right tool? Can PTC Mathcad solve my complex engineering problem? Can it handle large data sets? Often the answers to these questions can come from experience, consulting colleagues or just trial and error.

As engineers we often find ourselves working with different software applications each having its unique advantage to help with the task at hand. In my experience I find some of the most interesting solutions are those that are able to combine the distinct capabilities of each tool. At the end of the day we want to use the tool that gets us a solution to the problem quicker, easier and at the lowest cost with a caveat that there may be other factors thrown into the mix to consider as well.

So what are the capabilities of PTC Mathcad that will allow you to develop solutions to complex problems?

  • Comprehensive set of mathematical operators; allow you to define and calculate mathematical equations that have built-in numerical routines, such as integrals or derivatives.
  • Programming Syntax; allows you to define functions, allows for repetitive calculations, and simulate behaviour of your function/model over time.
  • Solve Blocks; solve numerical systems, differential equations.
  • Function library; choice of more than 700 functions that allow you to solve problems in various fields of engineering and science.
  • Custom functions; extends the set of functions to include those developed in other languages and incorporate those functions into the PTC Mathcad environment
  • Symbolic solver; solve problems analytically and use them to enhance your solutions
  • Embedded Excel Component; provides a useful capability that allows you to make use of the good things that Excel offers within the PTC Mathcad environment.

Often these capabilities in isolation only form part of any solution. Yet by combining these capabilities together we create a truly powerful set of capabilities that enhance that ability to solve challenging problems. Let’s take the example of Jacobian elliptic functions which are not defined in PTC Mathcad.










The fact that these functions are not defined in PTC Mathcad should not necessarily be treated as a red light to quit using PTC Mathcad and pick up another tool. The capabilities in PTC Mathcad make it fairly straightforward for us to define these 3 functions and to make use of them. Notice that in defining these functions we call on another function that we have formulated quite elegantly by making use of a solve block. The solve block numerically solves the equation by changing the value of θ for any given value of u and k until the constraint is met.










Furthermore the function theta(u,k) calls yet another function F(θ,k) that has been defined using PTC Mathcad’s integral operator. This function defines an elliptic integral of the first kind.







This example illustrates how all of this comes together nicely to present an elegant yet powerful way to solve problems that require functions that may not be defined in PTC Mathcad. The 2D plots are a useful way of comparing the results and checking them for correctness and validity.



















If you are on that journey of discovery, what you can be sure of is that there is a wealth of information out there to help you get started. This is often the quickest road to self-learning and understanding the capabilities and true potential of PTC Mathcad. Make use of the free worksheets and some additional collections on a huge range of topics  you can purchase here.

To get an even better idea of PTC Mathcad’s capabilities, you can go to our dedicated page focused on solving advanced engineering mathematics – watch an overview video of Solving advanced engineering mathematics with PTC Mathcad.

Don’t have PTC Mathcad? Try it out for free with PTC Mathcad Express.





1] Abramowitz, M. and Stegun, I. A.. “Jacobian Elliptic Functions and Theta Functions.” Chapter 16: Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 10th printing. New York: Dover, pp. 569-586, 1972.

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