000			03713nam a22004575i 4500
001			978-0-387-36425-4
003			DE-He213
005			20250710083956.0
007			cr nn 008mamaa
008			100301s2006 xxu| s |||| 0|eng d
020			_a9780387364254 _a99780387364254
024	7		_a10.1007/0-387-36425-0 _2doi
082	0	4	_a515 _223
100	1		_aGhorpade, Sudhir R. _eauthor.
245	1	2	_aA Course in Calculus and Real Analysis _h[recurso electrónico] / _cby Sudhir R. Ghorpade, Balmohan V. Limaye.
264		1	_aNew York, NY : _bSpringer New York, _c2006.
300			_aX, 432 p. 71 illus. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_arecurso en línea _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aUndergraduate Texts in Mathematics, _x0172-6056
505	0		_aNumbers and Functions -- Sequences -- Continuity and Limits -- Differentiation -- Applications of Differentiation -- Integration -- Elementary Transcendental Functions -- Applications and Approximations of Riemann Integrals -- Infinite Series and Improper Integrals.
520			_aThis book provides a self-contained and rigorous introduction to calculus of functions of one variable. The presentation and sequencing of topics emphasizes the structural development of calculus. At the same time, due importance is given to computational techniques and applications. The authors have strived to make a distinction between the intrinsic definition of a geometric notion and its analytic characterization. Throughout the book, the authors highlight the fact that calculus provides a firm foundation to several concepts and results that are generally encountered in high school and accepted on faith. For example, one can find here a proof of the classical result that the ratio of the circumference of a circle to its diameter is the same for all circles. Also, this book helps students get a clear understanding of the concept of an angle and the definitions of the logarithmic, exponential and trigonometric functions together with a proof of the fact that these are not algebraic functions. A number of topics that may have been inadequately covered in calculus courses and glossed over in real analysis courses are treated here in considerable detail. As such, this book provides a unified exposition of calculus and real analysis. The only prerequisites for reading this book are topics that are normally covered in high school; however, the reader is expected to possess some mathematical maturity and an ability to understand and appreciate proofs. This book can be used as a textbook for a serious undergraduate course in calculus, while parts of the book can be used for advanced undergraduate and graduate courses in real analysis. Each chapter contains several examples and a large selection of exercises, as well as "Notes and Comments" describing salient features of the exposition, related developments and references to relevant literature.
650		0	_aMATHEMATICS.
650		0	_aGLOBAL ANALYSIS (MATHEMATICS).
650		0	_aSEQUENCES (MATHEMATICS).
650	1	4	_aMATHEMATICS.
650	2	4	_aANALYSIS.
650	2	4	_aREAL FUNCTIONS.
650	2	4	_aSEQUENCES, SERIES, SUMMABILITY.
700	1		_aLimaye, Balmohan V. _eauthor.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9780387305301
830		0	_aUndergraduate Texts in Mathematics, _x0172-6056
856	4	0	_uhttp://dx.doi.org/10.1007/0-387-36425-0 _zVer el texto completo en las instalaciones del CICY
912			_aZDB-2-SMA
942			_2ddc _cER
999			_c57497 _d57497