{"product_id":"a-course-in-calculus-and-real-analysis-von-sudhir-r-ghorpade-und-balmohan-v-limaye","title":"A Course in Calculus and Real Analysis","description":"\n                                \n                \u003cp\u003eOffering a unified exposition of calculus and classical real analysis, this textbook presents a meticulous introduction to single‐variable calculus. Throughout, the exposition makes a distinction between the intrinsic geometric definition of a notion and its analytic characterization, establishing firm foundations for topics often encountered earlier without proof. Each chapter contains numerous examples and a large selection of exercises, as well as a “Notes and Comments” section, which highlights distinctive features of the exposition and provides additional references to relevant literature.\u003c\/p\u003e\n                                This second edition contains substantial revisions and additions, including several simplified proofs, new sections, and new and revised figures and exercises. A new chapter discusses sequences and series of real‐valued functions of a real variable, and their continuous counterpart: improper integrals depending on a parameter. Two new appendices cover a construction of the real numbers using Cauchy sequences, and a self‐contained proof of the Fundamental Theorem of Algebra.\n                \n                \u003cp\u003e\u003c\/p\u003e\n                                \n                \u003cp\u003e\n                                        In addition to the usual prerequisites for a first course in single‐variable calculus, the reader should possess some mathematical maturity and an ability to understand and appreciate proofs. This textbook can be used for a rigorous undergraduate course in calculus, or as a supplement to a later course in real analysis. The authors’ \n                    \n                    \u003ci\u003eA Course in Multivariable Calculus\u003c\/i\u003e\n                                         is an ideal companion volume, offering a natural extension of the approach developed here to the multivariable setting.\n                    \n                    \u003cbr\u003e\n                                    \n                \u003c\/p\u003e\n                                \n                \u003cp\u003e\n                                        \n                    \u003cb\u003e\n                                                From reviews:\n                        \n                        \u003cbr\u003e\n                                            \n                    \u003c\/b\u003e\n                                        \n                    \u003ci\u003e[The first edition is] a rigorous, well-presented and original introduction to the core of undergraduate mathematics — first-year calculus. It develops this subject carefully from a foundation of high-school algebra, with interesting improvements and insights rarely found in other books. […] This book is a tour de force, and a necessary addition to the library of anyone involved in teaching calculus, or studying it seriously.\u003c\/i\u003e\n                                         \n                    \n                    \u003cb\u003eN.J. Wildberger, Aust. Math. Soc. Gaz.\u003c\/b\u003e\n                                    \n                \u003c\/p\u003e\n                            \n            \u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9783030013998\"\u003e\u003ch3\u003e\u003c\/h3\u003e\u003c\/div\u003e\u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9783030827410\"\u003e\u003ch3\u003e\u003c\/h3\u003e\u003c\/div\u003e","brand":"Autorenwelt Shop","offers":[{"title":"Hardcover - 9783030013998","offer_id":57859122659653,"sku":"9783030013998","price":74.89,"currency_code":"EUR","in_stock":true},{"title":"Softcover - 9783030827410","offer_id":57910043083077,"sku":"9783030827410","price":53.49,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0940\/0622\/files\/c8bf358a-dfec-40f4-9bf5-ce9132553a07.jpg?v=1778905156","url":"https:\/\/shop.autorenwelt.de\/products\/a-course-in-calculus-and-real-analysis-von-sudhir-r-ghorpade-und-balmohan-v-limaye","provider":"Autorenwelt Shop","version":"1.0","type":"link"}