LEADER 03974nam 22005175 450 001 9910254087803321 005 20200701152322.0 010 $a3-319-39799-0 024 7 $a10.1007/978-3-319-39799-3 035 $a(CKB)3710000000872812 035 $a(DE-He213)978-3-319-39799-3 035 $a(MiAaPQ)EBC6313221 035 $a(MiAaPQ)EBC5588393 035 $a(Au-PeEL)EBL5588393 035 $a(OCoLC)960727402 035 $a(PPN)195510178 035 $a(EXLCZ)993710000000872812 100 $a20160914d2016 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aDifferential Geometry of Curves and Surfaces /$fby Kristopher Tapp 205 $a1st ed. 2016. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2016. 215 $a1 online resource (VIII, 366 p. 186 illus. in color.) 225 1 $aUndergraduate Texts in Mathematics,$x0172-6056 300 $aIncludes index. 311 $a3-319-39798-2 327 $aIntroduction -- Curves -- Additional topics in curves -- Surfaces -- The curvature of a surface -- Geodesics -- The Gauss?Bonnet theorem -- Appendix A: The topology of subsets of Rn -- Recommended excursions -- Index. 330 $aThis is a textbook on differential geometry well-suited to a variety of courses on this topic. For readers seeking an elementary text, the prerequisites are minimal and include plenty of examples and intermediate steps within proofs, while providing an invitation to more excursive applications and advanced topics. For readers bound for graduate school in math or physics, this is a clear, concise, rigorous development of the topic including the deep global theorems. For the benefit of all readers, the author employs various techniques to render the difficult abstract ideas herein more understandable and engaging. Over 300 color illustrations bring the mathematics to life, instantly clarifying concepts in ways that grayscale could not. Green-boxed definitions and purple-boxed theorems help to visually organize the mathematical content. Color is even used within the text to highlight logical relationships. Applications abound! The study of conformal and equiareal functions is grounded in its application to cartography. Evolutes, involutes and cycloids are introduced through Christiaan Huygens' fascinating story: in attempting to solve the famous longitude problem with a mathematically-improved pendulum clock, he invented mathematics that would later be applied to optics and gears. Clairaut?s Theorem is presented as a conservation law for angular momentum. Green?s Theorem makes possible a drafting tool called a planimeter. Foucault?s Pendulum helps one visualize a parallel vector field along a latitude of the earth. Even better, a south-pointing chariot helps one visualize a parallel vector field along any curve in any surface. In truth, the most profound application of differential geometry is to modern physics, which is beyond the scope of this book. The GPS in any car wouldn?t work without general relativity, formalized through the language of differential geometry. Throughout this book, applications, metaphors and visualizations are tools that motivate and clarify the rigorous mathematical content, but never replace it. . 410 0$aUndergraduate Texts in Mathematics,$x0172-6056 606 $aDifferential geometry 606 $aDifferential Geometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M21022 615 0$aDifferential geometry. 615 14$aDifferential Geometry. 676 $a516.36 700 $aTapp$b Kristopher$4aut$4http://id.loc.gov/vocabulary/relators/aut$0755882 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910254087803321 996 $aDifferential geometry of curves and surfaces$91523267 997 $aUNINA