000			01930nam a22002297a 4500
008			230510b |||||||| |||| 00| 0 eng d
020			_a9781470437398 (PB)
041			_aeng
080			_a517.97 _bKOT
100			_aKot, Mark
245			_aA first course in the calculus of variations
250			_aIndian Edition
260			_aProvidence, Rhode Island _bAmerican Mathematical Society (AMS) _c2017
300			_ax, 298 p
490			_aStudent Mathematical Library _v72
505			_aIntroduction 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
520			_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.
650			_aCalculus of variations
650			_aCalculus of variations and optimal control; optimization
690			_aMathematics
942			_cBK
999			_c59893 _d59893