000			03704nam a22005415i 4500
001			978-0-8176-4473-4
003			DE-He213
005			20251006084435.0
007			cr nn 008mamaa
008			100301s2006 xxu| s |||| 0|eng d
020			_a9780817644734
020			_a99780817644734
024	7		_a10.1007/0-8176-4473-3 _2doi
082	0	4	_a516 _223
100	1		_aAndreescu, Titu. _eauthor.
245	1	0	_aGeometric Problems on Maxima and Minima _h[electronic resource] / _cby Titu Andreescu, Oleg Mushkarov, Luchezar Stoyanov.
264		1	_aBoston, MA : _bBirkhäuser Boston, _c2006.
300			_aX, 264 p., 262 illus. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
505	0		_aMethods for Finding Geometric Extrema -- Selected Types of Geometric Extremum Problems -- Miscellaneous -- Hints and Solutions to the Exercises.
520			_aQuestions of maxima and minima have great practical significance, with applications to physics, engineering, and economics; they have also given rise to theoretical advances, notably in calculus and optimization. Indeed, while most texts view the study of extrema within the context of calculus, this carefully constructed problem book takes a uniquely intuitive approach to the subject: it presents hundreds of extreme-value problems, examples, and solutions primarily through Euclidean geometry. Key features and topics: * Comprehensive selection of problems, including Greek geometry and optics, Newtonian mechanics, isoperimetric problems, and recently solved problems such as Malfatti's problem * Unified approach to the subject, with emphasis on geometric, algebraic, analytic, and combinatorial reasoning * Presentation and application of classical inequalities, including Cauchy--Schwarz and Minkowski's Inequality; basic results in calculus, such as the Intermediate Value Theorem; and emphasis on simple but useful geometric concepts, including transformations, convexity, and symmetry * Clear solutions to the problems, often accompanied by figures * Hundreds of exercises of varying difficulty, from straightforward to Olympiad-caliber Written by a team of established mathematicians and professors, this work draws on the authors' experience in the classroom and as Olympiad coaches. By exposing readers to a wealth of creative problem-solving approaches, the text communicates not only geometry but also algebra, calculus, and topology. Ideal for use at the junior and senior undergraduate level, as well as in enrichment programs and Olympiad training for advanced high school students, this book's breadth and depth will appeal to a wide audience, from secondary school teachers and pupils to graduate students, professional mathematicians, and puzzle enthusiasts.
650		0	_aMATHEMATICS.
650		0	_aALGEBRA.
650		0	_aGLOBAL ANALYSIS (MATHEMATICS).
650		0	_aCOMBINATORICS.
650		0	_aGEOMETRY.
650		0	_aMATHEMATICAL OPTIMIZATION.
650		0	_aTOPOLOGY.
650	1	4	_aMATHEMATICS.
650	2	4	_aGEOMETRY.
650	2	4	_aOPTIMIZATION.
650	2	4	_aALGEBRA.
650	2	4	_aANALYSIS.
650	2	4	_aCOMBINATORICS.
650	2	4	_aTOPOLOGY.
700	1		_aMushkarov, Oleg. _eauthor.
700	1		_aStoyanov, Luchezar. _eauthor.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9780817635176
856	4	0	_uhttp://dx.doi.org/10.1007/0-8176-4473-3 _zVer el texto completo en las instalaciones del CICY
912			_aZDB-2-SMA
942			_2ddc _cER
999			_c59660 _d59660