Differential Geometry of Curves and Surfaces (Undergraduate - download pdf or read online

By Kristopher Tapp

Newly up to date for Kindle, it is a textbook on differential geometry well-suited to numerous classes in this subject. For readers looking an undemanding textual content, the must haves are minimum and contain lots of examples and intermediate steps inside of proofs, whereas delivering a call for participation to extra excursive purposes and complicated issues. For readers sure for graduate college in math or physics, it is a transparent, concise, rigorous improvement of the subject together with the deep international theorems. For the advantage of all readers, the writer employs numerous thoughts to render the tricky summary principles herein extra comprehensible and engaging.
Over three hundred colour illustrations carry the maths to existence, immediately clarifying recommendations in ways in which grayscale couldn't. Green-boxed definitions and purple-boxed theorems aid to visually manage the mathematical content material. colour is even used in the textual content to focus on logical relationships.
Applications abound! The examine of conformal and equiareal capabilities is grounded in its software to cartography. Evolutes, involutes and cycloids are brought via Christiaan Huygens' attention-grabbing tale: in trying to resolve the recognized longitude challenge with a mathematically-improved pendulum clock, he invented arithmetic that will 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 device known as a planimeter. Foucault’s Pendulum is helping one visualize a parallel vector box alongside a range of the earth. Even greater, 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 fashionable physics, that's past the scope of this ebook. The GPS in any motor vehicle wouldn’t paintings with no basic relativity, formalized in the course of the language of differential geometry. all through this booklet, functions, metaphors and visualizations are instruments that inspire and make clear the rigorous mathematical content material, yet by no means change it. 

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Differential Geometry of Curves and Surfaces (Undergraduate Texts in Mathematics) by Kristopher Tapp


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