Advanced Calculus for Mathematical Modeling in Engineering and Physics With Discrete and Numerical Analogies

Advanced Calculus for Mathematical Modeling in Engineering and Physics: With Discrete and Numerical Analogies introduces the principles and methods of advanced calculus for mathematical modeling through a balance of theory and application using a state space approach with elementary functional analysis. This framework facilitates a deeper understanding of the nature of mathematical models, and of the behavior of their solutions. The work provides a variety of advanced calculus models for mathematical, physical science, and engineering audiences, with discussions on how calculus-based models and their discrete analogies are generated. This valuable textbook offers scientific computations driven by Octave/MATLAB script.

1. Calculus Models in State Spaces 2. Ordinary Differential Equations and Recurrence Relations 3. Systems Of Differential Equations and Discrete Analogies 4. Integration For Advanced Calculus Models 5. Partial Differential Equations and Applications 6. Calculus Of Variations 7. Calculus With Complex Numbers 8. Introduction to Tensors

David Stapleton received his BS from the University of California, Santa Barbara and MS from the University of California, San Diego, before earning his PhD from University of Arizona in 1990. Now a Professor at University of Central Oklahoma, Dr. Stapleton has taught courses in advanced calculus for applications, mathematical modeling, calculus of variations, tensors, numerical linear algebra, and other mathematical topics and has served three times as the Director of the Conference on Applied Mathematics. He has published articles in various journals and proceedings of the AIAA, SIAM, IEEE/ION PLANS, Navigation, Foundations of Physics, Physics Communications, AJCM, STAIF, FAA, ICAO, and more. He has also worked as a contractor to the FAA at the FAA Technical Center and Mike Monroney Aeronautical Center and also has experience as a contractor to the USAF at Cape Canaveral, Vandenberg AFB (now Vandenberg SFB), and Edwards AFB.

• Adopts a state space/functional analysis approach to advanced calculus-based models to provide a better understanding of the development of models and the behaviors of their solutions
• Uniquely includes discrete analogies to calculus-based models, as well as the derivation of many advanced calculus models of physics and engineering– instead of only seeking solutions to the models
• Offers online teaching support for qualified instructors (for selected solutions) and study materials for students (MATLAB/Octave scripts)