{"product_id":"9783030013998","title":"Undergraduate Texts in Mathematics","description":"\u003ch1\u003eUndergraduate Texts in Mathematics\u003c\/h1\u003e \u003ch2\u003eGhorpade, Sudhir R.; Limaye, Balmohan V.\u003c\/h2\u003e \u003cp\u003e\u003c\/p\u003e\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\u003eThis 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.\u003cp\u003e\u003c\/p\u003e\u003cp\u003eIn 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’ \u003ci\u003eA Course in Multivariable Calculus\u003c\/i\u003e is an ideal companion volume, offering a natural extension of the approach developed here to the multivariable setting.\u003cbr\u003e\u003c\/p\u003e\u003cp\u003e\u003cb\u003eFrom reviews:\u003cbr\u003e\u003c\/b\u003e\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 \u003cb\u003eN.J. Wildberger, Aust. Math. Soc. Gaz.\u003c\/b\u003e\u003c\/p\u003e \u003ch3\u003eDetails\u003c\/h3\u003e \u003cp\u003ePublished by: Springer\u003c\/p\u003e \u003cp\u003ePublication Date: 2018-11-27\u003c\/p\u003e \u003cp\u003eFormat: Hardcover\u003c\/p\u003e \u003cp\u003eISBN-13: 9783030013998\u003c\/p\u003e \u003cp\u003eDOI: 10.1007\/978-3-030-01400-1\u003c\/p\u003e \u003cp\u003eDimensions: 235cm x155cm\u003c\/p\u003e \u003cp\u003ePages: 538\u003c\/p\u003e ","brand":"Springer International Publishing","offers":[{"title":"Default Title","offer_id":44521617031308,"sku":"9783030013998","price":71.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9783030013998.jpg?v=1775712629","url":"https:\/\/fh90cf-fv.myshopify.com\/products\/9783030013998","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}