David Stapleton

As Professor of Mathematics and Statistics at the University of Central Oklahoma, I have taught courses in advanced calculus for applications, mathematical modeling, calculus of variations, tensors, numerical linear algebra, and other mathematical topics and have served three times as the Director of the Conference on Applied Mathematics. My research experience includes publishing articles through the AIAA, SIAM, IEEE/ION PLANS, Navigation, Foundations of Physics, Physics Communications, AJCM, STAIF, FAA, ICAO, and more. As a contractor, I have also worked projects for the FAA at the FAA Technical Center and the Mike Monroney Aeronautical Center as well as projects for the USAF at Cape Canaveral, Vandenberg AFB (now Vandenberg SFB), and Edwards AFB.

In my first textbook, Advanced Calculus for Mathematical Modeling in Engineering and Physics: With Discrete and Numerical Analogies, I have put forth with applications, my love for the mathematics behind many of the projects I have enjoyed working on that involve travel through air and space, and the mathematics that helps us to understand the equations of things big and small in nature. I am especially excited to show how calculus leads us to understand many of the equations of mathematical physics and to derive equations used in various branches of engineering. This text covers a broad spectrum of advanced calculus techniques, somewhat in the tradition of Francis Hildebrand’s classic text, Advanced Calculus for Applications. Following an introduction through elementary functional analysis to the state spaces of advanced calculus models, techniques are presented for solving ordinary and partial differential equations, analyzing special integrals for applications, solving optimization problems through the calculus of variations, evaluating complex line integrals, and understanding the elementary theory of tensors. Discrete analogies and numerical approximations using MATLAB/Octave programming supplement some of these subjects. The driving inspiration for this work has been the beauty of the way things work, and the amazing ability of mathematics to describe and predict what we observe around us and to aid in developing new technologies. I hope this presentation inspires an appreciation of the power of the language of calculus. As John von Neumann said, “The calculus was the first achievement of modern mathematics and it is difficult to overestimate its importance. I think it defines more unequivocally than anything else the inception of modern mathematics; and the system of mathematical analysis, which is its logical development, still constitutes the greatest technical advance in exact thinking.”

More recently I have provided the updates to generate the second edition of the textbook Numerical Linear Algebra with Applications: Using MATLAB and Octave, whose first edition by William Ford of the University of the Pacific was published in 2015. This text provides a practical understanding of modern computational techniques for the numerical solution of linear algebra problems and includes algorithm analysis, computational complexity, and numerical solution methods. There are six introductory chapters provided as background for those who haven’t taken theoretical linear algebra and the presentation includes a detailed explanation of the issues and methods for practical computing using MATLAB or Octave. Numerous applications to engineering and science appropriate for advanced undergraduate and beginning graduate students are explored en route. Appropriate for studies involving linear algebra in mathematics, computer science, engineering, and the physical sciences, this text puts forth practical computer methods and analysis for solving real world problems that are too big or complex to solve by hand.

With best wishes,

Dave