Differential Geometry of Curves and Surfaces

Nonfiction, Science & Nature, Mathematics, Geometry
Cover of the book Differential Geometry of Curves and Surfaces by Kristopher Tapp, Springer International Publishing
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Kristopher Tapp ISBN: 9783319397993
Publisher: Springer International Publishing Publication: September 30, 2016
Imprint: Springer Language: English
Author: Kristopher Tapp
ISBN: 9783319397993
Publisher: Springer International Publishing
Publication: September 30, 2016
Imprint: Springer
Language: English

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. 

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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. 

More books from Springer International Publishing

Cover of the book Ministering Spiritually to Families by Kristopher Tapp
Cover of the book The Speaking Self: Language Lore and English Usage by Kristopher Tapp
Cover of the book Semantics, Pragmatics and Meaning Revisited by Kristopher Tapp
Cover of the book Mathematics and Methodology for Economics by Kristopher Tapp
Cover of the book Numerical Ecology with R by Kristopher Tapp
Cover of the book Rare Genitourinary Tumors by Kristopher Tapp
Cover of the book Inclusive Robotics for a Better Society by Kristopher Tapp
Cover of the book Literary Translation and Cultural Mediators in 'Peripheral' Cultures by Kristopher Tapp
Cover of the book Advances in Artificial Intelligence and Soft Computing by Kristopher Tapp
Cover of the book Cyber Security by Kristopher Tapp
Cover of the book Pre-carboniferous Evolution of the San Rafael Block, Argentina by Kristopher Tapp
Cover of the book A Primer on Quantum Fluids by Kristopher Tapp
Cover of the book Excitation Spectra of Square Lattice Antiferromagnets by Kristopher Tapp
Cover of the book Theoretical Physics 2 by Kristopher Tapp
Cover of the book Cardiac Regeneration by Kristopher Tapp
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy