Melvin Royer

Associate Professor; Chair, Division of Mathematics and Computer Information Sciences

Melvin Royer headshot

M.S.; Ph.D.



 OHSN 170-R


Math and Computer Information Sciences




 Curriculum Vitae


Dr. Royer joined IWU in 2001. He has taught mathematics at community and technical colleges as well as at the university level and occasionally does volunteer English teaching in Asia. His professional interests include mathematical analysis, dynamical systems, applied mathematics, and post-secondary mathematics education. He and his wife, Barb, enjoy travel, music, church activities, and reading.


Dynamical Systems: Useful Beauty 
My favorite research topic is dynamical systems. Consider a sequence starting with first term x(0)=0.6 and with successive terms given by x(n+1)=ax(n)*(1-x(n)). If a=2.8, the sequence values soon approach a number around 0.64. If a=3.2, the sequence values eventually oscillate between numbers approximately 0.51 and 0.80. Finally, if a=3.6, the sequence values never have a clear pattern at all.

It is not at all obvious why small changes to the value of a result in such different sequences. The incredible structures of some fractals, such as the Mandelbrot Set, are due to very different sequence behaviors resulting from slightly different dynamical systems. I see the beauty of such fractals as a creation of God in the same way He can be seen in the patterns of a sunset or a mountain view. But dynamical systems are not just beautiful. They are frequently used to model biological populations, including of germs and cancer cells. By adjusting values in these mathematical models, scientists can help predict ways to effectively control the spread of diseases.


  • Ph.D.
    1997, Purdue University
  • M.S.
    1989, Purdue University
  • B.S.
    1988, Purdue University
Indiana Wesleyan University
4201 S. Washington St.
Marion, IN 46953