Generalized Trigonometric and Hyperbolic Functions

Book Preface

The major purpose of this book is to introduce and investigate various topics related to so-called generalized trigonometric and hyperbolic functions. The methodology and the associated analysis are essentially mine and in many cases are not connected mathematically with previous work on this subject. In general, our obtained results are derived and discussed using a “rigorous heuristic” style of mathematical analysis. However, in spite of what some might consider a limitation, this procedure allows very interesting results to follow. The background knowledge needed to study with profit and to understand the contents of the book consists of the reader having taken courses in elementary plane geometry, trigonometry, and a year of calculus.
Ronald Elbert Mickens received his BA degree in physics from Fisk University (1964) and a Ph.D. in theoretical physics from Vanderbilt University (1968). He held postdoctoral positions at the MIT Center for Theoretical Physics (1968–70), Vanderbilt University (1980–81), and the Joint Institute for Laboratory Astrophysics (1981–82). He was professor of physics at Fisk University from 1970 to 1981. Presently, he is the Distinguished Fuller E. Call-away Professor at Clark Atlanta University. His current research interests include nonlinear oscillations, asymptotic methods for difference and differential equations, numerical integration of differential equations, the mathematical modelling of periodic diseases, the history/sociology of African-Americans in science, and the relationship between mathematics and physics. As of 2016, he has published more than 335 peer-reviewed scientific/mathematical research articles; written and/or edited 17 books; published over 390 abstracts; and authored nearly 100 scientific bio-essays, book reviews, and commentaries. He serves on editorial boards of several research journals, including the Journal of Difference Equations and Applications and the International Journal of Evolution Equations. His scholarly writings have appeared in reference works such as African American Lives (Oxford University Press), American National Biography (Oxford University Press), and Biographical Encyclopedia of Scientists (Marshall Cavendish). His honors include fellowships from the Ford, Woodrow Wilson, and National Science Foundations, as well as election to Phi Beta Kappa (1964). During 1998–99, he was an American Physical Society (APS) Centennial speaker (as part of the activities to celebrate the 100th anniversary of the founding of the APS). He also served as a Distinguished National Lecturer for Sigma Xi, The Scientific Research Society for 2000–2002. His professional memberships include the American Association for the Advancement of Science, the APS (for which he is an elected Fellow), the History of Science Society, the Society for Mathematical Biology, and the American Mathematical Society.
In July 2014, “The Brauer–Mickens Distinguished Seminar Series,” in the Simon A. Levin Mathematical, Computational and Modeling Sciences Center (Arizona State University), was inaugurated to honor Ronald Mickens for his “stellar scholarly contributions to the mathematical, engineering, and natural sciences . . . and (his) overall service and mentorship to the applied mathematical sciences community.”