Differential forms with applications to the physical sciences / Harley Flanders

By:

Flanders, Harley, 1925-2013 [aut]

Resource type: Ressourcentyp: Buch (Online)Book (Online)Language: English Publisher: New York : Dover Publications, 1989Edition: Unabridged, corrected republicationDescription: 1 Online-RessourceISBN:

9780486139616

Subject(s):

Additional physical formats: 9780486661698 | 9781306351362 | Erscheint auch als: Differential forms with applications to the physical sciences. Druck-Ausgabe New York : Dover Publications, 1989. XV, 205 SMSC: MSC: *53-02 | 58-02 | 53A45 | 53B50 | 58A10RVK: RVK: SK 370LOC classification:

QA381

Online resources:

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Summary: 3.6. Converse of the Poincaré Lemma3.7. An Example; 3.8. Further Remarks; 3.9. Problems; IV -- Applications; 4.1. Moving Frames in E3; 4.2. Relation between Orthogonal and Skew-symmetric Matrices; 4.3. The 6-dimensional Frame Space; 4.4. The Laplacian, Orthogonal Coordinates; 4.5. Surfaces; 4.6. Maxwell's Field Equations; 4.7. Problems; V -- Manifolds and Integration; 5.1. Introduction; 5.2. Manifolds; 5.3. Tangent Vectors; 5.4. Differential Forms; 5.5. Euclidean Simplices; 5.6. Chains and Boundaries; 5.7. Integration of Forms; 5.8. Stokes' Theorem; 5.9. Periods and De Rham's Theorems.Summary: 5.10. Surfaces Some Examples; 5.11. Mappings of Chains; 5.12. Problems; VI -- Applications in Euclidean Space; 6.1. Volumes in En; 6.2. Winding Numbers, Degree of a Mapping; 6.3. The Hopf Invariant; 6.4. Linking Numbers, The Gauss Integral, Ampere's Law; VII -- Applications to Differential Equations; 7.1. Potential Theory; 7.2. The Heat Equation; 7.3. The Frobenius Integration Theorem; 7.4. Applications of the Frobenius Theorem; 7.5. Systems of Ordinary Equations; 7.6. The Third Lie Theorem; VIII -- Applications to Differential Geometry; 8.1. Surfaces (Continued); 8.2. Hypersurfaces.Summary: 8.3. Riemannian Geometry, Local Theory8.4. Riemannian Geometry, Harmonic Integrals; 8.5. Affine Connection; 8.6. Problems; IX -- Applications to Group Theory; 9.1. Lie Groups; 9.2. Examples of Lie Groups; 9.3. Matrix Groups; 9.4. Examples of Matrix Groups; 9.5. Bi-invariant Forms; 9.6. Problems; X -- Applications to Physics; 10.1. Phase and State Space; 10.2. Hamiltonian Systems; 10.3. Integral-invariants; 10.4. Brackets; 10.5. Contact Transformations; 10.6. Fluid Mechanics; 10.7. Problems; Bibliography; Glossary of Notation; Index.Summary: Title Page; Copyright Page; Dedication; Foreword; Preface to the Dover Edition; Preface to the First Edition; Table of Contents; I -- Introduction; 1.1. Exterior Differential Forms; 1.2. Comparison with Tensors; II -- Exterior Algebra; 2.1. The Space of p-Vectors; 2.2. Determinants; 2.3. Exterior Products; 2.4. Linear Transformations; 2.5. Inner Product Spaces; 2.6. Inner Products of p-Vectors; 2.7. The Star Operator; 2.8. Problems; III -- The Exterior Derivative; 3.1. Differential Forms; 3.2. Exterior Derivatives; 3.3. Mappings; 3.4. Change of Coordinates; 3.5. An Example from Mechanics.Summary: 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 theoryPPN: PPN: 1736619578Package identifier: Produktsigel: ZDB-4-NLEBK

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