000 03794nam a22005055i 4500
001 978-0-387-36425-4
003 DE-He213
005 20161121231026.0
007 cr nn 008mamaa
008 100301s2006 xxu| s |||| 0|eng d
020 _a9780387364254
_9978-0-387-36425-4
024 7 _a10.1007/0-387-36425-0
_2doi
050 4 _aQA299.6-433
072 7 _aPBK
_2bicssc
072 7 _aMAT034000
_2bisacsh
082 0 4 _a515
_223
100 1 _aGhorpade, Sudhir R.
_eauthor.
245 1 2 _aA Course in Calculus and Real Analysis
_h[electronic resource] /
_cby Sudhir R. Ghorpade, Balmohan V. Limaye.
264 1 _aNew York, NY :
_bSpringer New York,
_c2006.
300 _aX, 432 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_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 _aMathematical analysis.
650 0 _aAnalysis (Mathematics).
650 0 _aFunctions of real variables.
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
912 _aZDB-2-SMA
950 _aMathematics and Statistics (Springer-11649)
999 _c507488
_d507488