Davide La Torre

Matteo Rocca

Giovanni P. Crespi

Second-order Mollified Derivatives and Optimization

Adam Riccoboni

Herb Kunze

Manuel Ruiz Galán

The fields of Artificial Intelligence (AI) and Machine Learning (ML) have grown dramatically in recent years, with an increasingly impressive spectrum of successful applications. This book represents a key reference for anybody interested in the intersection between mathematics and AI/ML and provides an overview of the current research streams. Engineering Mathematics and Artificial Intelligence: Foundations, Methods, and Applications discusses the theory behind ML and shows how mathematics can be used in AI. The book illustrates how to improve existing algorithms by using advanced mathematics and offers cutting-edge AI technologies. The book goes on to discuss how ML can support mathematical modeling and how to simulate data by using artificial neural networks. Future integration between ML and complex mathematical techniques is also highlighted within the book. This book is written for researchers, practitioners, engineers, and AI consultants.

Foundations, Methods, and Applications

Engineering Mathematics and Artificial Intelligence

Franklin Mendivil

Edward R. Vrscay

The idea of modeling the behaviour of phenomena at multiple scales has become a useful tool in both pure and applied mathematics. Fractal-based techniques lie at the heart of this area, as fractals are inherently multiscale objects; they very often describe nonlinear phenomena better than traditional mathematical models. In many cases they have been used for solving inverse problems arising in models described by systems of differential equations and dynamical systems. "Fractal-Based Methods in Analysis" draws together, for the first time in book form, methods and results from almost twenty years of research in this topic, including new viewpoints and results in many of the chapters. For each topic the theoretical framework is carefully explained using examples and applications. The second chapter on basic iterated function systems theory is designed to be used as the basis for a course and includes many exercises. This chapter, along with the three background appendices on topological and metric spaces, measure theory, and basic results from set-valued analysis, make the book suitable for self-study or as a source book for a graduate course. The other chapters illustrate many extensions and applications of fractal-based methods to different areas. This book is intended for graduate students and researchers in applied mathematics, engineering and social sciences. Herb Kunze is a professor of mathematics at the University of Guelph in Ontario. Davide La Torre is an associate professor of mathematics in the Department of Economics, Management and Quantitative Methods of the University of Milan. Franklin Mendivil is a professor of mathematics at Acadia University in Nova Scotia. Edward Vrscay is a professor in the department of Applied Mathematics at the University of Waterloo in Ontario. The major focus of their research is on fractals and the applications of fractals.

Fractal-Based Methods in Analysis

Davide La Torre

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