Foreword This set of lectures forms a gentle introduction to both the classical theory of the calculus of variations and the more modern develop- ments of optimal control theory from the perspective of an applied mathematician. It focuses on understanding concepts and how to ap- ply them, as opposed to rigorous proofs of existence and uniqueness theorems and so it serves as a prelude to more advanced texts in much the same way that calculus serves as a prelude to real anal- ysis. The prerequisites are correspondingly modest: the standard calculus sequence, a first course on ordinary differential equations, some facility with a mathematical software package, such as Maple, Mathematica (which I used to draw all of the figures in this book) or MATLAB—nowadays, almost invariably implied by the first two prerequisites—and that intangible quantity, a degree of mathemati- cal maturity. Here at Florida State University, the senior-level course from which this book emerged requires either a first course on par- tial differential equations—through which most students qualify—or a course on analysis or advanced calculus, and either counts as suﬃ- cient evidence of mathematical maturity. These few prerequisites are an adequate basis on which to build a sound working knowledge of the subject. To be sure, there ultimately arise issues that cannot be addressed without the tools of functional analysis but these are in- tentionally beyond the scope of this book, though touched on briefly ix

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