02574nam a22003017a 4500999001700000005001700017008004100034020001800075028012400093082001500217100001400232245006100246260004000307300004400347365000900391490004100400505027500441520108800716650001601804650001301820650004101833650005801874650012401932650002802056700001502084942000802099952016502107 c58627d5862720211220224356.0211130b ||||| |||| 00| 0 eng d a9781470437398 a:Variety Books Publishers & Distributors b:B-10 Street No 2 West Vinod Nagar Delhi 110092 c:IM2893d:25/11/2021  a515.64 KOT aKot, Mark aA First Course in the Calculus of Variationsc/ Mark Kot aNew Delhib:University Press c2014 ax, 298 pages : illustrations c; 22 cm. b1305 aStudent mathematical library, v. 72. a 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. aThis 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. aMathematics aAnalysis aCalculus of variations -- Textbooks. aCalculus of variations -- Study and teaching (Higher) aCalculus of variations and optimal control; optimization -- Instructional exposition (textbooks, tutorial papers, etc.) aCalculus of variations. aKot, Mark, cMDL 00102ddc4071aMDLbSNULd2021-11-30eVariety Books Publishers & Distributorsg1305.00l0o515.64 KOTpM314r2021-11-30 00:00:00w2021-11-30yMDLzFPDA Grant