Differential Geometry of Curves and Surfaces (Undergraduate Texts in Mathematics)
Tapp, Kristopher
ISBN 10: 3319397982 ISBN 13: 9783319397986
Verlag: Springer (edition 1st ed. 2016), 2016
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It's a preowned item in good condition and includes all the pages. It may have some general signs of wear and tear, such as markings, highlighting, slight damage to the cover, minimal wear to the binding, etc., but they will not affect the overall reading experience. Bestandsnummer des Verkäufers 3319397982-11-1
Inhaltsangabe:
This 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.
Über die Autorin bzw. den Autor:
Kristopher Tapp is Professor of Mathematics at Saint Joseph's University. He has been awarded two National Science Foundation research grants to support research in differential geometry, and several teaching awards. He is the author of Symmetry: A Mathematical Exploration (Springer, 2012) and over twenty research papers featured in top journals.
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Titel: Differential Geometry of Curves and Surfaces...
Verlag: Springer (edition 1st ed. 2016)
Erscheinungsdatum: 2016
Einband: Hardcover
Zustand: Good
Auflage: 1st ed. 2016.
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Differential Geometry of Curves and Surfaces (Undergraduate Texts in Mathematics)
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Differential Geometry of Curves and Surfaces (eng)
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DIFFERENTIAL GEOMETRY OF CURVES & SURFAC
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Differential Geometry of Curves and Surfaces
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Differential Geometry of Curves and Surfaces
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ISBN 10: 3319397982
ISBN 13: 9783319397986
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Buch. Zustand: Neu. Druck auf Anfrage Neuware - Printed after ordering - This 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. Artikel-Nr. 9783319397986
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Differential Geometry of Curves and Surfaces
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ISBN 10: 3319397982
ISBN 13: 9783319397986
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Differential Geometry of Curves and Surfaces (Undergraduate Texts in Mathematics)
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Differential Geometry of Curves and Surfaces
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ISBN 10: 3319397982
ISBN 13: 9783319397986
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Zustand: New. Can be used as a textbook in elementary and more advanced courses in differential geometryFocuses on applications of differential geometry, lending simplicity to more difficult and abstract conceptsFeatures f. Artikel-Nr. 121215623
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