Differential Geometry of Manifolds

From the coauthor of Differential Geometry of Curves and Surfaces, this companion book presents the extension of differential geometry from curves and surfaces to manifolds in general. It provides a broad introduction to the field of differentiable and Riemannian manifolds, tying together the classical and modern formulations. The three appendices provide background information on point set topology, calculus of variations, and multilinear algebra—topics that may not have been covered in the prerequisite courses of multivariable calculus and linear algebra.

Differential Geometry of Manifolds takes a practical approach, containing extensive exercises and focusing on applications of differential geometry in physics, including the Hamiltonian formulation of dynamics (with a view toward symplectic manifolds), the tensorial formulation of electromagnetism, some string theory, and some fundamental concepts in general relativity.

1101428636
Differential Geometry of Manifolds

From the coauthor of Differential Geometry of Curves and Surfaces, this companion book presents the extension of differential geometry from curves and surfaces to manifolds in general. It provides a broad introduction to the field of differentiable and Riemannian manifolds, tying together the classical and modern formulations. The three appendices provide background information on point set topology, calculus of variations, and multilinear algebra—topics that may not have been covered in the prerequisite courses of multivariable calculus and linear algebra.

Differential Geometry of Manifolds takes a practical approach, containing extensive exercises and focusing on applications of differential geometry in physics, including the Hamiltonian formulation of dynamics (with a view toward symplectic manifolds), the tensorial formulation of electromagnetism, some string theory, and some fundamental concepts in general relativity.

57.95 In Stock
Differential Geometry of Manifolds

Differential Geometry of Manifolds

by Stephen T. Lovett
Differential Geometry of Manifolds

Differential Geometry of Manifolds

by Stephen T. Lovett

eBook

$57.95 

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Overview

From the coauthor of Differential Geometry of Curves and Surfaces, this companion book presents the extension of differential geometry from curves and surfaces to manifolds in general. It provides a broad introduction to the field of differentiable and Riemannian manifolds, tying together the classical and modern formulations. The three appendices provide background information on point set topology, calculus of variations, and multilinear algebra—topics that may not have been covered in the prerequisite courses of multivariable calculus and linear algebra.

Differential Geometry of Manifolds takes a practical approach, containing extensive exercises and focusing on applications of differential geometry in physics, including the Hamiltonian formulation of dynamics (with a view toward symplectic manifolds), the tensorial formulation of electromagnetism, some string theory, and some fundamental concepts in general relativity.


Product Details

ISBN-13: 9781439865460
Publisher: CRC Press
Publication date: 06/11/2010
Sold by: Barnes & Noble
Format: eBook
Pages: 440
File size: 17 MB
Note: This product may take a few minutes to download.

About the Author

Stephen Lovett is an associate professor of mathematics at Wheaton College in Illinois. Lovett has also taught at Eastern Nazarene College and has taught introductory courses on differential geometry for many years. Lovett has traveled extensively and has given many talks over the past several years on differential and algebraic geometry, as well as cryptography.

Table of Contents

Analysis of Multivariable Functions
Functions from Rn to Rm
Continuity, Limits, and Differentiability
Differentiation Rules: Functions of Class Cr
Inverse and Implicit Function Theorems
Coordinates, Frames, and Tensor Notation
Curvilinear Coordinates
Moving Frames in Physics
Moving Frames and Matrix Functions
Tensor Notation
Differentiable Manifolds
Definitions and Examples
Differentiable Maps between Manifolds
Tangent Spaces and Differentials
Immersions, Submersions, and Submanifolds
Chapter Summary
Analysis on Manifolds
Vector Bundles on Manifolds
Vector Fields on Manifolds
Differential Forms
Integration on Manifolds
Stokes’ Theorem
Introduction to Riemannian Geometry
Riemannian Metrics
Connections and Covariant Differentiation
Vector Fields Along Curves: Geodesics
The Curvature Tensor
Applications of Manifolds to Physics
Hamiltonian Mechanics
Electromagnetism
Geometric Concepts in String Theory
A Brief Introduction to General Relativity
Point Set Topology
Introduction
Metric Spaces
Topological Spaces
Proof of the Regular Jordan Curve Theorem
Simplicial Complexes and Triangulations
Euler Characteristic
Calculus of Variations
Formulation of Several Problems
The Euler-Lagrange Equation
Several Dependent Variables
Isoperimetric Problems and Lagrange Multipliers
Multilinear Algebra
Direct Sums
Bilinear and Quadratic Forms
The Hom Space and the Dual Space
The Tensor Product
Symmetric Product and Alternating Product
The Wedge Product and Analytic Geometry

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