03100nmm a2200301 u 4500001001200000003002700012005001700039007002400056008004100080020001800121100002100139245009400160250001700254260005600271300005400327505006900381653002600450653003300476710003400509041001900543989003600562490003900598856007200637082001100709520099400720520016201714520092201876EB001230441EBX0100000000000000087374400000000000000.0cr|||||||||||||||||||||161005 ||| eng a97833193979931 aTapp, Kristopher00aDifferential Geometry of Curves and SurfaceshElektronische Ressourcecby Kristopher Tapp a1st ed. 2016 aChambSpringer International Publishingc2016, 2016 aVIII, 366 p. 186 illus. in colorbonline resource0 aThe topology of subsets of Rn -- Recommended excursions -- Index aDifferential Geometry aGlobal differential geometry2 aSpringerLink (Online service)07aeng2ISO 639-2 bSpringeraSpringer eBooks 2005-0 aUndergraduate Texts in Mathematics uhttps://doi.org/10.1007/978-3-319-39799-3?nosfx=yxVerlag3Volltext0 a516.36 aApplications 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. aThroughout this book, applications, metaphors and visualizations are tools that motivate and clarify the rigorous mathematical content, but never replace it. 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.