000			02859nmm a22002295i 4500
005			20230705150623.0
008			100715s2010 xxu| s |||| 0|eng d
020			_a9781441916211 _9978-1-4419-1621-1
082			_a515 _223
100			_aGhorpade, Sudhir R. _919688
245			_aA Course in Multivariable Calculus and Analysis _h[electronic resource] / _cby Sudhir R. Ghorpade, Balmohan V. Limaye.
250			_a1st ed. 2010.
260			_aNew York, NY : _bSpringer New York : _bImprint: Springer, _c2010.
300			_aXII, 477 p. 353 illus., 74 illus. in color. _bonline resource.
505			_aVectors and Functions -- Sequences, Continuity, and Limits -- Partial and Total Differentiation -- Applications of Partial Differentiation -- Multiple Integration -- Applications and Approximations of Multiple Integrals -- Double Series and Improper Double Integrals.
520			_aThis self-contained textbook gives a thorough exposition of multivariable calculus. It can be viewed as a sequel to the one-variable calculus text, A Course in Calculus and Real Analysis, published in the same series. The emphasis is on correlating general concepts and results of multivariable calculus with their counterparts in one-variable calculus. For example, when the general definition of the volume of a solid is given using triple integrals, the authors explain why the shell and washer methods of one-variable calculus for computing the volume of a solid of revolution must give the same answer. Further, the book includes genuine analogues of basic results in one-variable calculus, such as the mean value theorem and the fundamental theorem of calculus. This book is distinguished from others on the subject: it examines topics not typically covered, such as monotonicity, bimonotonicity, and convexity, together with their relation to partial differentiation, cubature rules for approximate evaluation of double integrals, and conditional as well as unconditional convergence of double series and improper double integrals. Moreover, the emphasis is on a geometric approach to such basic notions as local extremum and saddle point. Each chapter contains detailed proofs of relevant results, along with numerous examples and a wide collection of exercises of varying degrees of difficulty, making the book useful to undergraduate and graduate students alike. There is also an informative section of "Notes and Comments'' indicating some novel features of the treatment of topics in that chapter as well as references to relevant literature. The only prerequisite for this text is a course in one-variable calculus.
650			_aMathematical analysis. _919689
650			_aAnalysis. _919690
700			_aLimaye, Balmohan V. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut _919691
856			_uhttps://doi.org/10.1007/978-1-4419-1621-1
942			_cEBK
999			_c13553 _d13553