Differential Forms with Applications to the Physical Sciences

Name: Differential Forms with Applications to the Physical Sciences
Price: 5.19 USD
Availability: InStock
ISBN: 9780486661698

ISBN-10: 0486661695

ISBN-13: 9780486661698

Edition: 1989

Authors: Harley Flanders

List price: $14.95

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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: 224
Size: 5.50" wide x 8.75" 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 Poincarï¿½ 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, Ampï¿½re'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