Differential Geometry of Curves and Surfaces (Undergraduate by Kristopher Tapp

By Kristopher Tapp

Newly up to date for Kindle, this can be a textbook on differential geometry well-suited to quite a few classes in this subject. For readers looking an hassle-free textual content, the must haves are minimum and contain lots of examples and intermediate steps inside proofs, whereas offering a call for participation to extra excursive purposes and complex themes. For readers sure for graduate institution in math or physics, this can be a transparent, concise, rigorous improvement of the subject together with the deep worldwide theorems. For the good thing about all readers, the writer employs a variety of options to render the tough summary principles herein extra comprehensible and engaging.

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

Applications abound! The learn of conformal and equiareal services is grounded in its program to cartography. Evolutes, involutes and cycloids are brought via Christiaan Huygens' attention-grabbing tale: in trying to resolve the well-known longitude challenge with a mathematically-improved pendulum clock, he invented arithmetic that might later be utilized to optics and gears. Clairaut’s Theorem is gifted as a conservation legislations for angular momentum. Green’s Theorem makes attainable a drafting software known as a planimeter. Foucault’s Pendulum is helping one visualize a parallel vector box alongside a range of the earth. Even higher, 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 is past the scope of this publication. The GPS in any automobile wouldn’t paintings with out basic relativity, formalized in the course of the language of differential geometry. all through this e-book, purposes, metaphors and visualizations are instruments that inspire and make clear the rigorous mathematical content material, yet by no means exchange it.

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