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