Differential Forms with Applications to the Physical Sciences

By: HARLEY FLANDERS

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Paperback | 1 December 1989

At a Glance

Paperback
224 Pages

Edition Type
New edition

Dimensions(cm)
20.9 x 13.6 x 2.1

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A graduate-level text utilizing exterior differential forms in the analysis of a variety of mathematical problems in the physical and engineering sciences. "To the reader who wishes to obtain a bird's-eye view of the theory of differential forms with applications to other branches of pure mathematics, applied mathematic and physics, I can recommend no better book." - T. J. Willmore, London Mathematical Society Journal. This excellent text introduces the use of exterior differential forms as a powerful tool in the analysis of a variety of mathematical problems in the physical and engineering sciences. Requiring familiarity with several variable calculus and some knowledge of linear algebra and set theory, it is directed primarily to engineers and physical scientists, but it has also been used successfully to introduce modern differential geometry to students in mathematics. Chapter I introduces exterior differential forms and their comparisons with tensors. The next three chapters take up exterior algebra, the exterior derivative and their applications. Chapter V discusses manifolds and integration, and Chapter VI covers applications in Euclidean space. The last three chapters explore applications to differential equations, differential geometry, and group theory. "The book is very readable, indeed, enjoyable - and, although addressed to engineers and scientists, should be not at all inaccessible to or inappropriate for... first year graduate students and bright undergraduates." - F. E. J. Linton, Wesleyan University, American Mathematical Monthly.

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You Can Find This Book In

Non-Fiction Mathematics Applied Mathematics Calculus & Mathematical Analysis Differential Calculus & Equations

Foreword
Preface to the Dover Edition
Preface to the First Edition
Introduction
Exterior Differential Forms
Comparison with Tensors
Exterior algebra
The Space of p-vectors
Determinants
Exterior Products
Linear Transformations
Inner Product Spaces
Inner Products of p-vectors
The Star Operator
Problems
The Exterior Derivative
Differential Forms
Exterior Derivative
Mappings
Change of coordinates
An Example from Mechanics
Converse of the Poincaré Lemma
An Example
Further Remarks
Problems
Applications
Moving Frames in E superscript 3
Relation between Orthogonal and Skew-symmetric Matrices
The 6-dimensional Frame Space
The Laplacian, Orthogonal Coordinates
Surfaces
Maxwell's Field Equations
Problems
Manifolds and Integration
Introduction
Manifolds
Tangent Vectors
Differential Forms
Euclidean Simplices
Chains and Boundaries
Integration of Forms
Stokes' Theorem
Periods and De Rham's Theorems
Surfaces; Some Examples
Mappings of Chains
Problems
Applications in Euclidean Space
Volumes in E superscript n
Winding Numbers, Degree of a Mapping
The Hopf Invariant
Linking Numbers, the Gauss Integral, Ampère's Law
Applications to Different Equations
Potential Theory
The Heat Equation
The Frobenius Integration Theorem
Applications of the Frobenius Theorem
Systems of Ordinary Equations
The Third Lie Theorem
Applications to Differential Geometry
Surfaces (Continued)
Hypersurfaces
Riemannian Geometry, Local Theory
Riemannian Geometry, Harmonic Integrals
Affine Connection
Problems
Applications to Group Theory
Lie Groups
Examples of Lie Groups
Matrix Groups
Examples of Matrix Groups
Bi-invariant Forms
Problems X. Applications to Physics
Phase and State Space
Hamiltonian Systems
Integral-invariants
Brackets
Contact Transformations
Fluid Mechanics
Problems Bibliography
Glossary of Notation
Index
Table of Contents provided by Publisher. All Rights Reserved.

Differential Forms with Applications to the Physical Sciences

At a Glance

Paperback

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