Mathematics of Variations and Artificial Intelligence

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.