Download e-book for kindle: Differential Geometry of Curves and Surfaces (Undergraduate by Kristopher Tapp

By Kristopher Tapp

ISBN-10: 3319397982

ISBN-13: 9783319397986

Newly up-to-date for Kindle, this can be a textbook on differential geometry well-suited to various classes in this subject. For readers looking an undemanding textual content, the necessities are minimum and comprise lots of examples and intermediate steps inside proofs, whereas delivering a call for participation to extra excursive purposes and complicated subject matters. For readers certain for graduate institution in math or physics, this can be a transparent, concise, rigorous improvement of the subject together with the deep international theorems. For the good thing about all readers, the writer employs a number of thoughts to render the tricky summary rules herein extra comprehensible and engaging.

Over three hundred colour illustrations deliver the maths to existence, immediately clarifying strategies in ways in which grayscale couldn't. Green-boxed definitions and purple-boxed theorems aid to visually arrange the mathematical content material. colour is even used in the textual content to spotlight logical relationships.

Applications abound! The research of conformal and equiareal features is grounded in its program to cartography. Evolutes, involutes and cycloids are brought via Christiaan Huygens' attention-grabbing tale: in trying to remedy the well-known longitude challenge with a mathematically-improved pendulum clock, he invented arithmetic that may later be utilized to optics and gears. Clairaut’s Theorem is gifted as a conservation legislation for angular momentum. Green’s Theorem makes attainable a drafting instrument known as a planimeter. Foucault’s Pendulum is helping one visualize a parallel vector box alongside a range of the earth. Even larger, a south-pointing chariot is helping one visualize a parallel vector box alongside any curve in any surface.

In fact, the main profound program of differential geometry is to trendy physics, that's past the scope of this e-book. The GPS in any vehicle wouldn’t paintings with out normal relativity, formalized in the course of the language of differential geometry. all through this publication, purposes, metaphors and visualizations are instruments that encourage and make clear the rigorous mathematical content material, yet by no means substitute it.

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