Applied Differential Geometry

William L. Burke

doi:10.1017/CBO9781139171786

This is a self-contained introductory textbook on the calculus of differential forms and modern differential geometry. The intended audience is physicists, so the author emphasises applications and geometrical reasoning in order to give results and concepts a precise but intuitive meaning without getting bogged down in analysis. The large number of diagrams helps elucidate the fundamental ideas. Mathematical topics covered include differentiable manifolds, differential forms and twisted forms, the Hodge star operator, exterior differential systems and symplectic geometry. All of the mathematics is motivated and illustrated by useful physical examples.

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Applied Differential Geometry

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Contents

Frontmatter
pp i-vi

Contents
pp vii-x

Preface
pp xi-xiv

Glossary of notation
pp xv-xviii

Introduction
pp 1-10

I - Tensors in linear spaces
pp 11-50

II - Manifolds
pp 51-114

III - Transformations
pp 115-146

IV - The calculus of differential forms
pp 147-206

V - Applications of the exterior calculus
pp 207-270

VI - Classical electrodynamics
pp 271-304

VII - Dynamics of particles and fields
pp 305-346

VIII - Calculus on fiber bundles
pp 347-370

IX - Gravitation
pp 371-408

Bibliography
pp 409-410

Index
pp 411-414

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Applied Differential Geometry

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