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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. Clairautâ€™s Theorem is presented as a conservation law for angular momentum. Greenâ€™s Theorem makes possible a drafting tool called a planimeter. Foucaultâ€™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 wouldnâ€™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.

- Series:
**Undergraduate Texts in Mathematics** - Author:
**Kristopher Tapp (auth.)** - Year:
**2016** - Publisher:
**Springer International Publishing** - Language:
**English** - ISBN:
**978-3-319-39798-6,978-3-319-39799-3**

- File size:
**14 529 537** - Format:
**pdf**

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This introduction to the conformal differential geometry of surfaces and submanifolds covers those aspects of the geometry of surfaces that only refer to an angle measurement, but not to a length measurement. Different methods (models) are presented for a...

This elementary account of the differential geometry of curves and surfaces in space deals with curvature and torsion, involutes and evolutes, curves on a surface, curvature of surfaces, and developable and ruled surfaces. The examples feature many specia...

Curves and surfaces are objects that everyone can see, and many of the questions that can be asked about them are natural and easily understood. Differential geometry is concerned with the precise mathematical formulation of some of these questions, and w...

Differential geometry is an actively developing area of modern mathematics. This volume presents a classical approach to the general topics of the geometry of curves, including the theory of curves in n-dimensional Euclidean space. The author investigates...

Differential geometry is the study of the curvature and calculus of curves and surfaces. A New Approach to Differential Geometry using Clifford's Geometric Algebra simplifies the discussion to an accessible level of differential geometry by introducing Cl...

This volume presents the cutting-edge contributions to the Seventh International Workshop on Complex Structures and Vector Fields, which was organized as a continuation of the high successful preceding workshops on similar research. The volume includes wo...

The present book aims to give a fairly comprehensive account of the fundamentals of differential manifolds and differential geometry. The size of the book influenced where to stop, and there would be enough material for a second volume (this is not a thre...

This book is based on a series of lectures delivered over the years by the author at the University Pierre et Marie Curie in Paris, at the University of Stuttgart, and at City University of Hong Kong. Its two-fold aim is to provide a thorough introduction...

Affine differential geometry has undergone a period of revival and rapid progress in the past decade. This book is a self-contained and systematic account of affine differential geometry from a contemporary view. It covers not only the classical theory, b...

The law is a mandate and a mirror; it both commands and reflects. It should not come as a shock that scientists and physicians often prefer the mirror at times when society seems to be demanding a mandate. This may be especially true in the rapidly advanc...

It has been both a pleasure and an honor to edit this book. The pleasure has been in interacting with the gifted authors who wrote the chapters for this volume and the honor has been in knowing that the book is dedicated to a great man and a brilliant psy...

Contemporary behavior therapy encompasses diverse conceptual positions, clinical and applied problems, and intervention techniques. Behavior therapy has spread to several disciplines to provide substantive concepts and procedures as well as methodological...

"The old order changeth, yielding place to new. " When Tennyson wrote this, he was unfamiliar with the pace of modem science else he would have said the new is displaced by the newer. When Gilbert and I gathered the papers for the first edition of this ov...

This volume of the Proceedings of the congress ISAAC '97 collects the conÂ tributions of the four sections 1. Function theoretic and functional analytic methods for pde, 2. Applications of function theory of several complex variables to pde, 3. Integral e...

Although the monograph Progress in Optimization I: Contributions from AusÂ tralasia grew from the idea of publishing a proceedings of the Fourth OptimizaÂ tion Day, held in July 1997 at the Royal Melbourne Institute of Technology, the focus soon changed t...

This book presents a selection of papers presented to the Second InterÂ national Symposium on Semi-Markov Models: Theory and Applications held in Compiegne (France) in December 1998. This international meeting had the same aim as the first one held in Bru...

101 17. The company job balance sheet 101 18. The personnel and jobs structure 119 19. Work in homogeneous groups 125 20. Incorporation of Galois lattices 130 21. The selection of teams for associated tasks 134 22. A brief reference to costs 138 23. Probl...

This book reports on a set of new techniques for resolving current issues in networked control systems. The main focus is on strategies for event-based control, for both centralized and decentralized architectures. The first part of the book addresses the...