TY  - BOOK
AU  - Kot, Mark
AU  - Kot, Mark,
TI  - A First Course in the Calculus of Variations
T2  - Student mathematical library, v. 72
SN  - 9781470437398
U1  - 515.64 KOT 
PY  - 2014///
CY  - New Delhi
PB  - :University Press 
KW  - Mathematics
KW  - Analysis
KW  - Calculus of variations -- Textbooks
KW  - Calculus of variations -- Study and teaching (Higher)
KW  - Calculus of variations and optimal control; optimization -- Instructional exposition (textbooks, tutorial papers, etc.)
KW  - Calculus of variations
N1  - 	Introduction --
The first variation --
Cases and examples --
Basic generalizations --
Constraints --
The second variation --
Review and preview --
The homogeneous problem --
Variable-endpoint conditions --
Broken extremals --
Strong variations --
Sufficient conditions
N2  - This book is intended for a first course in the calculus of variations, at the senior or beginning graduate level. The reader will learn methods for finding functions that maximize or minimize integrals. The text lays out important necessary and sufficient conditions for extrema in historical order, and it illustrates these conditions with numerous worked-out examples from mechanics, optics, geometry, and other fields. The exposition starts with simple integrals containing a single independent variable, a single dependent variable, and a single derivative, subject to weak variations, but steadily moves on to more advanced topics, including multivariate problems, constrained extrema, homogeneous problems, problems with variable endpoints, broken extremals, strong variations, and sufficiency conditions. Numerous line drawings clarify the mathematics. Each chapter ends with recommended readings that introduce the student to the relevant scientific literature and with exercises that consolidate understanding. Mark Kot teaches at the University of Washington, Seattle. WA
ER  -