LEADER 03460nam 22005175 450 001 9910254070503321 005 20230216100315.0 010 $a3-319-49314-0 024 7 $a10.1007/978-3-319-49314-5 035 $a(CKB)3710000001006490 035 $a(DE-He213)978-3-319-49314-5 035 $a(MiAaPQ)EBC6312308 035 $a(MiAaPQ)EBC5610742 035 $a(Au-PeEL)EBL5610742 035 $a(OCoLC)965145667 035 $a(PPN)197137784 035 $a(EXLCZ)993710000001006490 100 $a20161130d2016 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aCalculus and Analysis in Euclidean Space /$fby Jerry Shurman 205 $a1st ed. 2016. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2016. 215 $a1 online resource (XIII, 507 p. 182 illus., 59 illus. in color.) 225 1 $aUndergraduate Texts in Mathematics,$x2197-5604 300 $aIncludes index. 311 $a3-319-49312-4 327 $aPreface -- 1 Results from One-Variable Calculus -- Part I Multivariable Differential Calculus -- 2 Euclidean Space -- 3 Linear Mappings and Their Matrices -- 4 The Derivative -- 5 Inverse and Implicit Functions -- Part II Multivariable Integral Calculus -- 6 Integration -- 7 Approximation by Smooth Functions -- 8 Parameterized Curves -- 9 Integration of Differential Forms -- Index. 330 $aThe graceful role of analysis in underpinning calculus is often lost to their separation in the curriculum. This book entwines the two subjects, providing a conceptual approach to multivariable calculus closely supported by the structure and reasoning of analysis. The setting is Euclidean space, with the material on differentiation culminating in the inverse and implicit function theorems, and the material on integration culminating in the general fundamental theorem of integral calculus. More in-depth than most calculus books but less technical than a typical analysis introduction, Calculus and Analysis in Euclidean Space offers a rich blend of content to students outside the traditional mathematics major, while also providing transitional preparation for those who will continue on in the subject. The writing in this book aims to convey the intent of ideas early in discussion. The narrative proceeds through figures, formulas, and text, guiding the reader to do mathematics resourcefully by marshaling the skills of geometric intuition (the visual cortex being quickly instinctive) algebraic manipulation (symbol-patterns being precise and robust) incisive use of natural language (slogans that encapsulate central ideas enabling a large-scale grasp of the subject). Thinking in these ways renders mathematics coherent, inevitable, and fluid. The prerequisite is single-variable calculus, including familiarity with the foundational theorems and some experience with proofs. 410 0$aUndergraduate Texts in Mathematics,$x2197-5604 606 $aMathematical analysis 606 $aAnalysis 615 0$aMathematical analysis. 615 14$aAnalysis. 676 $a519.535 700 $aShurman$b Jerry$4aut$4http://id.loc.gov/vocabulary/relators/aut$0303262 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910254070503321 996 $aCalculus and analysis in euclidean space$91523205 997 $aUNINA