A first course in the calculus of variations
Material type: TextLanguage: English Series: Student Mathematical Library ; 72Publication details: Providence, Rhode Island American Mathematical Society (AMS) 2017Edition: Indian EditionDescription: x, 298 pISBN: 9781470437398 (PB)Subject(s): Calculus of variations | Calculus of variations and optimal control; optimization | MathematicsCurrent library | Home library | Call number | Materials specified | Copy number | Status | Date due | Barcode |
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IMSc Library | IMSc Library | 517.97 KOT (Browse shelf (Opens below)) | Available | 77182 | |||
IMSc Library | IMSc Library | 517.97 KOT (Browse shelf (Opens below)) | 1 | Available | 77165 |
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517.95 REN Introduction to partial differential equations | 517.95 VAS Partial differential equations | 517.97 KOT A first course in the calculus of variations | 517.97 KOT A first course in the calculus of variations | 517.98 BHA Notes on functional analysis | 517.98 HAA Functional Analysis | 517.98 HAA Functional Analysis |
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.
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