(15c) General complex contour integration

[Brian Zilli]

The HP 15c Advanced Functions Handbook provides a program for evaluating a contour integral along a straight line segment in the complex plane and an example of its use.

In Section 1, we discuss the complex variable theory behind the example and use it to motivate the usefulness of a program for evaluating a contour integral along a general parameterized contour. In Section 2, we present such a program, and, in Section 3, we provide an example of its use. In Section 4, we present a program for approximating the derivative of a parameterized contour. Finally, in Section 5, we present a proof of a key assumption in the handbook example discussed in Section 1.


I hope this is interesting and useful to anyone interested in HP 15c programming and functions of a complex variable. Sections 1 and 5 should be useful to anyone seeking a deeper explanation of the complex variable theory underlying the "Contour Integrals" example on pp. 88-89 of the Advanced Functions Handbook.

[Werner]

Where is the 'like' button??
This sets a new benchmark for documentation quality..
Very interesting, very well explained, clearly formatted..
Thank you!
Cheers, Werner

[carey]

Brian,
Thank you for posting this!
This was precisely the example (along with its fluid dynamics application) in the Advanced Handbook that got me interested in the 15c many years ago.
I'm looking forward to working through your paper in detail.

[Brian Zilli]

Thank you all!

(11-08-2023 09:09 AM)carey Wrote:  This was precisely the example (along with its fluid dynamics application) in the Advanced Handbook that got me interested in the 15c many years ago.

I agree. I was of course impressed by the breadth of functions supported in Complex mode (especially since the 35s, released 25 years afterwards, did not have such robust support), but the fact that they could also be integrated on a pocket calculator originally released in 1982 is truly amazing.

It is just such a well-thought-out device.