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An Introduction to Tensor Analysis
This is a short introduction to the topic of Tensor Analysis. A tensor is an entity which is represented in any coordinate system by an array of numbers called its components. The components change from coordinate system to coordinate in a systematic way described by rules. The arrays of numbers are...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Aalborg :
River Publishers,
2021.
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| Colección: | River Publishers Series in Mathematical and Engineering Sciences Ser.
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| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 100 | 1 | |a Koranga, Bipin Singh. | |
| 245 | 1 | 3 | |a An Introduction to Tensor Analysis |
| 260 | |a Aalborg : |b River Publishers, |c 2021. | ||
| 300 | |a 1 online resource (128 pages) | ||
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| 490 | 1 | |a River Publishers Series in Mathematical and Engineering Sciences Ser. | |
| 588 | 0 | |a Print version record. | |
| 505 | 0 | |a Intro -- AN INTRODUCTION TOTENSOR ANALYSIS -- Preface -- Syllabus -- Contents -- 1 Introduction -- 1.1 Symbols Multi-Suffix -- 1.2 Summation Convention -- References -- 2 Cartesian Tensor -- 2.1 Introduction -- 2.2 Transformation of Coordinates -- 2.3 Relations Between the Direction Cosines of Three Mutually Perpendicular Straight Lines -- 2.4 Transformation of Velocity Components -- 2.5 First-Order Tensors -- 2.6 Second-Order Tensors -- 2.7 Notation for Tensors -- 2.8 Algebraic Operations on Tensors -- 2.8.1 Sum and Difference of Tensors -- 2.8.2 Product of Tensors | |
| 505 | 8 | |a 2.9 Quotient Law of Tensors -- 2.10 Contraction Theorem -- 2.11 Symmetric and Skew-Symmetric Tensor -- 2.12 Alternate Tensor -- 2.13 Kronecker Tensor -- 2.14 Relation Between Alternate and Kronecker Tensors -- 2.15 Matrices and Tensors of First and Second Orders -- 2.16 Product of Two Matrices -- 2.17 Scalar and Vector Inner Product -- 2.17.1 Two Vectors -- 2.17.2 Scalar Product -- 2.17.3 Vector Product -- 2.18 Tensor Fields -- 2.18.1 Gradient of Tensor Field -- 2.18.2 Divergence of Vector Point Function -- 2.18.3 Curl of Vector Point Function -- 2.19 Tensorial Formulation of Gauss's Theorem | |
| 505 | 8 | |a 2.20 Tensorial Formulation of Stoke's Theorem -- 2.21 Exercise -- References -- 3 Tensor in Physics -- 3.1 Kinematics of Single Particle -- 3.1.1 Momentum -- 3.1.2 Acceleration -- 3.1.3 Force -- 3.2 Kinetic Energy and Potential Energy -- 3.3 Work Function and Potential Energy -- 3.4 Momentum and Angular Momentum -- 3.5 Moment of Inertia -- 3.6 Strain Tensor at Any Point -- 3.7 Stress Tensor at any Point P -- 3.7.1 Normal Stress -- 3.7.2 Simple Stress -- 3.7.3 Shearing Stress -- 3.8 Generalised Hooke's Law -- 3.9 Isotropic Tensor -- 3.10 Exercises -- References | |
| 505 | 8 | |a 4 Tensor in Analytic Solid Geometry -- 4.1 Vector as Directed Line Segments -- 4.2 Geometrical Interpretation of the Sum of two Vectors -- 4.3 Length and Angle between Two Vectors -- 4.4 Geometrical Interpretation of Scalar and Vector Products -- 4.4.1 Scalar Triple Product -- 4.4.2 Vector Triple Products -- 4.5 Tensor Formulation of Analytical Solid Geometry -- 4.5.1 Distance Between Two Points P(xi) and Q(yi) -- 4.5.2 Angle Between Two Lines with Direction Cosines -- 4.5.3 The Equation of Plane -- 4.5.4 Condition for Two Line Coplanar -- 4.6 Exercises -- References -- 5 General Tensor | |
| 505 | 8 | |a 5.1 Curvilinear Coordinates -- 5.2 Coordinate Transformation Equation -- 5.3 Contravariant and Covariant Tensor -- 5.4 Contravariant Vector or Contravariant Tensor of Order-One -- 5.5 Covariant Vector or Covariant Tensor of Order-One -- 5.6 Mixed Second-Order Tensor -- 5.7 General Tensor of Any Order -- 5.8 Metric Tensor -- 5.9 Associate Contravariant Metric Tensor -- 5.10 Associate Metric Tensor -- 5.11 Christoffel Symbols of the First and Second-Kind -- 5.12 Covariant Derivative of a Covariant Vector -- 5.13 Covariant Derivative of a Contravariant Vector -- 5.14 Exercises -- References | |
| 500 | |a 6 Tensor in Relativity. | ||
| 520 | |a This is a short introduction to the topic of Tensor Analysis. A tensor is an entity which is represented in any coordinate system by an array of numbers called its components. The components change from coordinate system to coordinate in a systematic way described by rules. The arrays of numbers are not the tensor; they are only the representation of the tensor in a particular coordinate system. The special properties of tensors are important for solving problems in Physics and Geometry. | ||
| 590 | |a ProQuest Ebook Central |b Ebook Central Academic Complete | ||
| 650 | 0 | |a Tensor algebra. | |
| 650 | 6 | |a Algèbre tensorielle. | |
| 650 | 7 | |a Tensor algebra |2 fast | |
| 700 | 1 | |a Padaliya, Sanjay Kumar. | |
| 758 | |i has work: |a INTRODUCTION TO TENSOR ANALYSIS (Text) |1 https://id.oclc.org/worldcat/entity/E39PD3pcJvTfr84kM6RYJwykMq |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
| 776 | 0 | 8 | |i Print version: |a Koranga, Bipin Singh. |t An Introduction to Tensor Analysis. |d Aalborg : River Publishers, ©2021 |z 9788770225816 |
| 830 | 0 | |a River Publishers Series in Mathematical and Engineering Sciences Ser. | |
| 856 | 4 | 0 | |u https://ebookcentral.uam.elogim.com/lib/uam-ebooks/detail.action?docID=6450277 |z Texto completo |
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