towards the end. Thus, on the one hand, it is by no means necessar
for a reader of this book to have been exposed to real analysis; an
yet, on the other hand, such prior exposure cannot help but increas
the book’s accessibility.
Students taking a first course on this topic typically have divers
backgrounds among engineering, mathematics and the natural or so
cial sciences. The range of potential applications is correspondingl
broad: the calculus of variations and optimal control theory hav
been widely used in numerous ways in, e.g., biology [27, 35, 58],
criminology [18], economics [10, 26], engineering [3, 49], finance [9
management science [12, 57], and physics [45, 63] from a variet
of perspectives, so that the needs of students are too extensive t
be universally accommodated. Yet one can still identify a solid cor
of material to serve as a foundation for future graduate studies, re
gardless of academic discipline, or whether those studies are applie
or theoretical. It is this core of material that I seek to expoun
as lucidly as possible, and in such a way that the book is suitabl
not only as an undergraduate text, but also for self-study. In othe
words, this book is primarily a mathematics text, albeit one aime
across disciplines. Nevertheless, I incorporate applications—cance
chemotherapy in Lecture 20, navigational control in Lecture 22 an
renewable resource harvesting in Lecture 24—to round out the theme
developed in the earlier lectures.
Arnold Arthurs introduced me to the calculus of variations i
1973-74, and these lectures are based on numerous sources consulte
at various times over the 35 years that have since elapsed; sometime
with regard to teaching at FSU; sometimes with regard to my own re
search contributions to the literature on optimal control theory; an
only recently with regard to this book. It is hard now to judge th
relative extents to which I have relied on various authors. Neverthe
less, I have relied most heavily on—in alphabetical order—Akhieze
[1], Bryson & Ho [8], Clark [10], Clegg [11], Gelfand & Fomin [16
Hadley & Kemp [19], Hestenes [20], Hocking [22], Lee & Marku
[33], Leitmann [34], Pars [47], Pinch [50] and Pontryagin et al. [51
and other authors are cited in the bibliography. I am grateful to a
of them, and to each in a measure proportional to my indebtedness
numbers in square brackets denote references in the bibliography (p. 245
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