Book description
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 engineers, as well as physicists and mathematicians.
- Provides a thorough explanation of how to apply differential equations to solve real-world engineering problems
- Helps researchers in mathematics, science, and engineering develop skills needed to implement mathematical techniques in their research
- Includes physical applications and methods used to solve practical problems to determine symmetry
Table of contents
- Cover image
- Title page
- Table of Contents
- Copyright
- Preface
- Chapter I. Exterior Algebra
-
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
- 2.8 Vector Fields. Tangent Bundle
- 2.9 Flows Over Manifolds
- 2.10 Lie Derivative
- 2.11 Distributions. The Frobenius Theorem
- II Exercises
- Chapter III. Lie Groups
- Chapter IV. Tensor Fields on Manifolds
-
Chapter V. Exterior Differential Forms
- 5.1 Scope of the Chapter
- 5.2 Exterior Differential Forms
- 5.3 Some Algebraic Properties
- 5.4 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
- Chapter VII. Linear Connections
-
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
- 8.7 Conservation Laws
- 8.8 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
- Chapter XI. Some Physical Applications
- References
- Index of Symbols
- Name Index
- Subject Index
Product information
- Title: Exterior Analysis
- Author(s):
- Release date: September 2013
- Publisher(s): Academic Press
- ISBN: 9780124159280
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