TY - BOOK ID - 8284935 TI - A Course in Multivariable Calculus and Analysis AU - Ghorpade, Sudhir R. AU - Limaye, Balmohan V. PY - 2010 SN - 1441916202 9786613569172 1441916210 1280391251 PB - New York, NY : Springer New York : Imprint: Springer, DB - UniCat KW - Calculus -- Problems, exercises, etc. KW - Calculus. KW - Electronic books. -- local. KW - Functions of several complex variables -- Problems, exercises, etc. KW - Functions of several complex variables. KW - Calculus KW - Functions of several complex variables KW - Engineering & Applied Sciences KW - Mathematics KW - Applied Mathematics KW - Physical Sciences & Mathematics KW - Complex variables KW - Several complex variables, Functions of KW - Analysis (Mathematics) KW - Fluxions (Mathematics) KW - Infinitesimal calculus KW - Limits (Mathematics) KW - Mathematics. KW - Mathematical analysis. KW - Analysis (Mathematics). KW - Analysis. KW - 517.1 Mathematical analysis KW - Mathematical analysis KW - Math KW - Science KW - Functions of complex variables KW - Functions KW - Geometry, Infinitesimal KW - Global analysis (Mathematics). KW - Analysis, Global (Mathematics) KW - Differential topology KW - Geometry, Algebraic UR - https://www.unicat.be/uniCat?func=search&query=sysid:8284935 AB - This 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. ER -