Foreword

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

Mathematica

(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

i

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

Mathematica

(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

i