Mathematics of Variations and Artificial Intelligence: Linear Mathematics. Multivariable Optimization and Nonlinear Programming (De Gruyter Textbook)

This book has been written primarily as a graduate textbook for the foundational materials in three topics. While the traditional Advanced Engineering Mathematics (AEM) pedagogy is to bundle all the eight or so major topics into textbooks that often contain over a thousand pages, it has recently become clear that this approach does not work well for students.

The unique feature of this book is the presentation of a modern contribution to the AEM curriculum, as evidenced by the carefully selected state-of-the-art versions of the classical AEM topics of variational methods, as well as the inclusion of the more recent trend of applying AI in AEM. The modern introduction of physics-informed neural networks and Fourier neural operators represents a potential paradigm shift in the way that engineers obtain design data. This book will help actualize that for graduate students and practicing engineers alike. The author is not aware of any existing AEM textbooks that can promise the proposed features in their entirety.

In addition to engineering students, students majoring in Mathematics, Applied Mathematics, Theoretical Physics and Computer Science should also find this book to be of immense value to them.

Foluso Ladeinde earned several degrees from Cornell University, including the Ph.D. from The Sibley School of Mechanical and Aerospace Engineering. He is a tenured faculty member in the Department of Mechanical Engineering at Stony Brook University, where he teaches courses in aerospace propulsion, numerical methods, applied mathematics, and theoretical fluid dynamics.  He is the founding Chairman and was the Department Head (2015-2019) of the ABET-accredited Department of Mechanical Engineering, State University of New York, Incheon, South Korea. He was a Summer Faculty Fellow for ten years at the United States Air Force at Wright-Patterson AFB, Dayton, Ohio. Dr. Ladeinde’s research uses advanced computational science and applied mathematics to investigate theoretical fluid dynamics, fluid flow turbulence theory, two-phase flows and heat transfer, supersonic combustion, and, more recently, atmospheric cloud microphysics.  His work has been funded by the United States National Science Foundation (NSF), the United States Air Force (USAF), the United States Navy (USN), the Air Force Office of Scientific Research (AFOSR), the Defense Advanced Research Projects Agency (DARPA), the National Aeronautics and Space Administration (NASA), and commercial industry, including The Boeing Aerospace Corporation. He served two terms on the External Review Board of the NASA Center for Aerospace Research at North Carolina A&T University, Greensboro, North Carolina. Dr. Ladeinde has served as an Associate Editor (2009-2013) of the AIAA Journal, the flagship journal of the American Institute of Aeronautics and Astronautics (AIAA), an Associate Editor (2015-2025) of The ASCE Journal of Aerospace Engineering, and a Guest Editor of the Physics of Fluids (2020-2021). He is an Associate Fellow of AIAA, a Fellow of the American Society of Mechanical Engineers (ASME), a Life Member of the American Physical Society (APS), and a member of the Society of Industrial and Applied Mathematics (SIAM) and The Combustion Institute. He has published over 250 papers in archival journals and peer-reviewed conference proceedings. Dr. Ladeinde is the auhtor of the 606-page book “Applications of Complex Variables: Asymptotics and Integral Transfroms,“ published by De Gruyter.