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Differentiable Manifolds: A Theoritical Physics Approach

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This textbook explores the theory behind differentiable manifolds and investigates various physics applications along the way. Basic concepts, such as differentiable manifolds, differentiable mappings, tangent vectors, vector fields, and differential forms, are briefly introduced in the first three chapters. Chapter 4 gives a concise introduction to differential geometry needed in subsequent chapters. Chapters 5 and 6 provide interesting applications to connections and Riemannian manifolds. Lie groups and Hamiltonian mechanics are closely examined in the last two chapters. Included throughout the book are a collection of exercises of varying degrees of difficulty.

Differentiable Manifolds is intended for graduate students and researchers interested in a theoretical physics approach to the subject. Prerequisites include multivariable calculus, linear algebra, differential equations, and a basic knowledge of analytical mechanics.

Author: Torres del Castillo Gerardo
Publisher: BIRKHAUSER
Pages: 275
ISBN: 9780817682705
Cover: Hardback
Edition Number: 1
Release Year: 2012

Gerardo Torres del Castillo has published two books previously, both in Birkhauser's Progress in Mathematical Physics series: 3-D Spinors, Spin-Weighted Functions and their Applications, and Spinors in Four-Dimensional Spaces.

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