Modelling with Ordinary Differential Equations

Alfio Borzì, born 1965 in Catania (Italy), is the professor and chair of Scientific Computing at the Institute for Mathematics of the University of Würzburg, Germany. He studied Mathematics and Physics in Catania and Trieste where he received his PhD in Mathematics from Scuola Internazionale Superiore di Studi Avanzati (SISSA). He served as Research Officer at the University of Oxford (UK) and as Assistant Professor at the University of Graz (Austria) where he completed his habilitation and was appointed as Associate Professor. Since 2011 he has been Professor of Scientific Computing at the University of Würzburg. Alfio Borzi is the author of 4 mathematics books and numerous articles in journals. The main topics of his research and teaching activities are modelling and numerical analysis, numerical optimisation and machine learning, optimal control theory and scientific computing. He is member of the editorial board for SIAM Review and of the book series Advances in Mechanics and Mathematics (AMMA).

“Alfio Borzì's Modelling with Ordinary Differential Equations is a remarkably comprehensive text that succeeds in something rare: it covers the classical foundations of ODE theory with precision and rigour, while consistently opening windows to advanced and genuinely original applications that are hard to find in comparable textbooks. The opening chapter on the modelling process already sets the tone — it is superb and immediately conveys the spirit that carries the entire book. The treatment of compartment models and the master equation, Hamiltonian systems, and — further along — the excursions into special relativity and quantum mechanics are captivating and showcase the author's ability to connect apparently distant topics through the unifying language of ODEs. Indeed, a recurring strength of this book is that the final two or three subsections of most chapters present fascinating perspectives that one does not easily encounter elsewhere. Chapter 9 on the calculus of variations is particularly original and engaging; the chapter on optimal control provides the Pontryagin Maximum Principle with a proof in admirably compact form — something I have long been looking for. The final chapter on neural networks and ODEs brings the subject into a very timely and modern context. Overall, this book is an extraordinary resource and a true Fundgrube (treasure trove) for anyone interested in the many facets of ODE modelling. If I were to use it as a course textbook, I would need at least two semesters with four hours of lectures and two hours of tutorials each — which speaks for itself. Warmly recommended.”—Professor Volker Schulz, Universität Trier"Expertly written, organized and presented, Modelling with Ordinary Differential Equations: A Comprehensive Approach is an ideal textbook for college and university Numerical Analysis & Scientific Computing curriculums. [. . . ] unreservedly recommended as a critically important addition to academic library collections"—Midwest Book Review

• 1. Introduction 2. Elementary solution methods for simple ODEs 3. Theory of ordinary differential equations 4. Systems of ordinary differential equations 5. Higher-order ordinary differential equations 6. Mechanics and second-order ODEs 7. Numerical solution of ODE problems 8. Stability of ODE systems 9. ODEs and the calculus of variations 10. Optimal control of ODE models 11. Inverse problems with ODE models 12. Differential games 13. Stochastic differential equations 14. Neural networks and ODE problems