9 Replies Latest reply: Feb 19, 2012 2:10 PM by A.Non RSS

    Explicit function definition

    ptc-4457992 Copper

      Hello,

       

      I am quite new to Mathcad. What I want to do is to define a function explicitly (i.e., as pairs of x - y or x - f(x) values), not analitically (through a formula). Does anyone know wether that is possible or not? I am using Mathcad 14 and I searched the user guide, provided examples and tutorials, but couldn't find anything related to this subject. I even tried to do that myself, by improvising, but without any success.

       

      Moreover, if it's possible to define a function explicitly, could one calculate definite integrals on it afterwards? (I know that is easy if the function is defined analitically).

       

      Best regards,

      Marius

        • Re: Explicit function definition
          MikeArmstrong Diamond

          Yes I believe it is possible, but I'm not sure exactly what your after.

           

          Could you provide an example and post the worksheet?

           

          Mike

            • Re: Explicit function definition
              ptc-4457992 Copper

              Hello!

              Thank you for your answer.  I don’t have a worksheet yet, but here is what I want to do (I simplified the problem a bit). I have the following (x  y) data set where y represents the value of the derivate function at point x:

              X                      Y

              0                       0

              0.2                    0.1987

              0.4                    0.3894  

              0.6                    0.5646   

              0.8                    0.7174

              1                       0.8415

              1.2                    0.932

              1.4                    0.9854

              1.5708              1

               

              What I want is to get the value of the function, by numerical integration, at these x points. I don’t need any curve fitting, interpolation function or any other kind of approximation. Could you give me some hints on how to solve this problem with Mathcad?

            • Re: Explicit function definition
              VladimirN. PTC Community Champion

              Hello!

               

              Provide a screenshot of what you want.

                • Re: Explicit function definition
                  ptc-4457992 Copper

                  Hello!

                  Thank you for your answer.  I don’t have a worksheet yet, but here is what I want to do (I simplified the problem a bit). I have the following (x  y) data set where y represents the value of the derivate function at point x:

                  X                      Y

                  0                       0

                  0.2                    0.1987

                  0.4                    0.3894  

                  0.6                    0.5646   

                  0.8                    0.7174

                  1                       0.8415

                  1.2                    0.932

                  1.4                    0.9854

                  1.5708              1

                   

                  What I want is to get the value of the function, by numerical integration, at these x points. I don’t need any curve fitting, interpolation function or any other kind of approximation. Could you give me some hints on how to solve this problem with Mathcad?

                • Re: Explicit function definition
                  FredKohlhepp Platinum

                  Given an x,y data set there are several ways to proceed; the choice depends on the data and what you want to do.  With a dense and complete data set you can use numerical integration techniques.  You can curve fit the data--find a function that approximates the data closely, and use the built-in integration schemes for manipulation.

                    • Re: Explicit function definition
                      ptc-4457992 Copper

                      Hello!

                      Thank you for your answer.  I don’t have a worksheet yet, but here is what I want to do (I simplified the problem a bit). I have the following (x  y) data set where y represents the value of the derivate function at point x:

                      X                      Y

                      0                       0

                      0.2                    0.1987

                      0.4                    0.3894  

                      0.6                    0.5646   

                      0.8                    0.7174

                      1                       0.8415

                      1.2                    0.932

                      1.4                    0.9854

                      1.5708              1

                       

                      What I want is to get the value of the function, by numerical integration, at these x points. I don’t need any curve fitting, interpolation function or any other kind of approximation. Could you give me some hints on how to solve this problem with Mathcad?

                    • Re: Explicit function definition
                      A.Non PTC Community Champion

                      You need to create an interpolating function. The most general solution is a cubic spline, but it's not always appropriate. Without seeing the data it's hard to say much more.

                        • Re: Explicit function definition
                          ptc-4457992 Copper

                          Hello!

                          Thank you for your answer.  I don’t have a worksheet yet, but here is what I want to do (I simplified the problem a bit). I have the following (x  y) data set where y represents the value of the derivate function at point x:

                          X                      Y

                          0                       0

                          0.2                    0.1987

                          0.4                    0.3894  

                          0.6                    0.5646   

                          0.8                    0.7174

                          1                       0.8415

                          1.2                    0.932

                          1.4                    0.9854

                          1.5708              1

                           

                          What I want is to get the value of the function, by numerical integration, at these x points. I don’t need any curve fitting, interpolation function or any other kind of approximation. Could you give me some hints on how to solve this problem with Mathcad?

                            • Re: Explicit function definition
                              A.Non PTC Community Champion

                              We don't need the same reply four times. It's just as easy to read one reply four times as it is to read four replies

                               

                              I don’t need any curve fitting, interpolation function or any other kind of approximation.

                              All numerical integration is approximate. The attached is a very general, and usually accurate, approach.