Exterior Analysis
Using Applications of Differential Forms
- 1st Edition - August 29, 2013
- Imprint: Academic Press
- Author: Erdogan Suhubi
- Language: English
- Hardback ISBN:9 7 8 - 0 - 1 2 - 4 1 5 9 0 2 - 0
- eBook ISBN:9 7 8 - 0 - 1 2 - 4 1 5 9 2 8 - 0
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 appl… Read more
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Request a sales quoteExterior 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
Physical Scientists, Engineers, Applied Mathematicians
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
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
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
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
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
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
6.6 Canonical Forms of 1-Forms, Closed 2- Forms
6.7 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
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
10.1 Scope of the Chapter
10.2 Stationary Functionals
10.3 Euler-Lagrange Equations
10.4 Noetherian Vector Fields
10.5 Variational Problem for a General Action Functional
X Exercises
Chapter XI. Some Physical Applications
11.1 Scope of the Chapter
11.2 Conservative Mechanics
11.3 Poisson Bracket of 1-Forms and Smooth Functions
11.4 Canonical Transformations
11.5 Non-Conservative Mechanics
11.6 Electromagnetism
11.7 Thermodynamics
XI Exercises
References
Index of Symbols
Name Index
Subject Index
- Edition: 1
- Published: August 29, 2013
- No. of pages (Hardback): 779
- No. of pages (eBook): 779
- Imprint: Academic Press
- Language: English
- Hardback ISBN: 9780124159020
- eBook ISBN: 9780124159280
ES
Erdogan Suhubi
Affiliations and expertise
Yeditepe University, Department of Mathematics, Kayisdagi, TurkeyRead Exterior Analysis on ScienceDirect