This book is about the growing intersection of data-driven methods, applied
optimization, and the classical fields of engineering mathematics and mathematical physics. We have been developing this material over a number of
years, primarily to educate our advanced undergrad and beginning graduate
students from engineering and physical science departments. Typically, such
students have backgrounds in linear algebra, differential equations, and scientific computing, with engineers often having some exposure to control theory
and/or partial differential equations. However, most undergraduate curricula
in engineering and science fields have little or no exposure to data methods
and/or optimization. Likewise, computer scientists and statisticians have little
exposure to dynamical systems and control. Our goal is to provide a broad entry point to applied data science for both of these groups of students. We have
chosen the methods discussed in this book for their 1) relevance, 2) simplicity,
and 3) generality, and we have attempted to present a range of topics, from
basic introductory material up to research-level techniques.