A First Course in the Calculus of Variations
Kot, Mark
A First Course in the Calculus of Variations / Mark Kot - New Delhi :University Press 2014 - x, 298 pages : illustrations ; 22 cm. - Student mathematical library, v. 72. .
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.
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.
9781470437398
Variety Books Publishers & Distributors :B-10 Street No 2 West Vinod Nagar Delhi 110092
Mathematics
Analysis
Calculus of variations -- Textbooks.
Calculus of variations -- Study and teaching (Higher)
Calculus of variations and optimal control; optimization -- Instructional exposition (textbooks, tutorial papers, etc.)
Calculus of variations.
515.64 KOT
A First Course in the Calculus of Variations / Mark Kot - New Delhi :University Press 2014 - x, 298 pages : illustrations ; 22 cm. - Student mathematical library, v. 72. .
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.
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.
9781470437398
Variety Books Publishers & Distributors :B-10 Street No 2 West Vinod Nagar Delhi 110092
Mathematics
Analysis
Calculus of variations -- Textbooks.
Calculus of variations -- Study and teaching (Higher)
Calculus of variations and optimal control; optimization -- Instructional exposition (textbooks, tutorial papers, etc.)
Calculus of variations.
515.64 KOT
