UID:
almahu_9948026180002882
Format:
1 online resource (xii, 767 pages) :
,
illustrations
Edition:
1st edition
ISBN:
0-12-415928-1
Series Statement:
Gale eBooks
Content:
Exterior analysis uses differential forms (a mathematical technique) to analyze curves, surfaces, and structures. Exterior Analysis is a first-of-its-kind resource that uses applications of differential forms, offering a mathematical approach to solve problems in defining a precise measurement to ensure structural integrity. The book provides methods to study different types of equations and offers detailed explanations of fundamental theories and techniques to obtain concrete solutions to determine symmetry. It is a useful tool for structural, mechanical and electrical engine
Note:
Description based upon print version of record.
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Front Cover; Exterior Analysis: Using Applications of Differential Forms; Copyright Page; Table of Contents; Preface; Chapter I: Exterior Algebra; 1.1. Scope of the Chapter; 1.2. Linear Vector Spaces; 1.3. Multilinear Functionals; 1.4. Alternating k-Linear Functionals; 1.5. Exterior Algebra; 1.6. Rank of an Exterior Form; I. Exercises; Chapter II: Differentiable Manifolds; 2.1. Scope of the Chapter; 2.2. Differentiable Manifolds; 2.3. Differentiable Mappings; 2.4. Submanifolds; 2.5. Differentiable Curves; 2.6. Vectors. Tangent Spaces; 2.7. Differential of a Map Between Manifolds
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2.8. Vector Fields. Tangent Bundle2.9. Flows Over Manifolds; 2.10. Lie Derivative; 2.11. Distributions. the Frobenius Theorem; II. Exercises; Chapter III: Lie Groups; 3.1. Scope of the Chapter; 3.2. Lie Groups; 3.3. Lie Algebras; 3.4. Lie Group Homomorphisms; 3.5. One-Parameter Subgroups; 3.6. Adjoint Representation; 3.7. Lie Transformation Groups; III. Exercises; Chapter IV: Tensor Fields on Manifolds; 4.1. Scope of the Chapter; 4.2. Cotangent Bundle; 4.3. Tensor Fields; IV. Exercises; Chapter V: Exterior Differential Forms; 5.1. Scope of the Chapter; 5.2. Exterior Differential Forms
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5.3. Some Algebraic Properties5.4. Interior Product; 5.5. Bases Induced By the Volume Form; 5.6. Ideals of the Exterior Algebra Λ(M); 5.7. Exterior Forms Under Mappings; 5.8. Exterior Derivative; 5.9. Riemannian Manifolds. Hodge Dual; 5.10. Closed Ideals; 5.11. Lie Derivatives of Exterior Forms; 5.12. Isovector Fields of Ideals; 5.13. Exterior Systems and Their Solutions; 5.14. Forms Defined on a Lie Group; V. Exercises; Chapter VI: Homotopy Operator; 6.1. Scope of the Chapter; 6.2. Star-Shaped Regions; 6.3. Homotopy Operator; 6.4. Exact and Antiexact Forms; 6.5. Change of Centre
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6.6. Canonical Forms of 1-Forms, Closed 2- Forms6.7. An Exterior Differential Equation; 6.8. A System of Exterior Differential Equations; VI. Exercises; Chapter VII: Linear Connections; 7.1. Scope of the Chapter; 7.2. Connections on Manifolds; 7.3. Cartan Connection; 7.4. Levi-Civita Connection; 7.5. Differential Operators; VII. Exercises; Chapter VIII: Integration of Exterior Forms; 8.1. Scope of the Chapter; 8.2. Orientable Manifolds; 8.3. Integration of Forms in the Euclidean Space; 8.4. Simplices and Chains; 8.5. Integration of Forms on Manifolds; 8.6. The Stokes Theorem
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8.7. Conservation Laws8.8. The Cohomology of De Rham; 8.9. Harmonic Forms. Theory of Hodge-De Rham; 8.10. Poincare Duality; VIII. Exercises; Chapter IX: Partial Differential Equations; 9.1. Scope of the Chapter; 9.2. Ideals Formed By Differential Equations; 9.3. Isovector Fields of the Contact Ideal; 9.4. Isovector Fields of Balance Ideals; 9.5. Similarity Solutions; 9.6. The Method of Generalised Characteristics; 9.7. Horizontal Ideals and Their Solutions; 9.8. Equivalence Transformations; IX. Exercises; Chapter X: Calculus of Variations; 10.1. Scope of the Chapter
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10.2. Stationary Functionals
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English
Additional Edition:
ISBN 0-12-415902-8
Additional Edition:
ISBN 1-299-96300-5
Language:
English
