Book description
Exterior analysis uses differential forms (a mathematical technique) to analyze curves, surfaces, and structures. Exterior Analysis is a firstofitskind 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 realworld 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 HodgeDe 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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