Differential Forms with Applications to the Physical Sciences

ISBN-10: 0486661695

ISBN-13: 9780486661698

Edition: 1989

Authors: Harley Flanders
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Book details

List price: $14.95
Copyright year: 1989
Publisher: Dover Publications, Incorporated
Publication date: 12/1/1989
Binding: Paperback
Pages: 240
Size: 5.38" wide x 8.50" long x 0.50" tall
Weight: 0.550
Language: English

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 Poincar� 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, Amp�re'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
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