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An Introduction to Tensor Analysis /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	An Introduction to Tensor Analysis /Sanjay Kumar Padaliya, Bipin Singh Koranga
作者:	Koranga, Bipin Singh.
其他作者:	Padaliya, Sanjay Kumar.
出版者:	Aalborg :River Publishers,2021.
面頁冊數:	xiii,112 pages ;24 cm.
附註:	6 Tensor in Relativity.
標題:	Tensor algebra.
ISBN:	9788770225809

An Introduction to Tensor Analysis /
Koranga, Bipin Singh.

An Introduction to Tensor Analysis /Sanjay Kumar Padaliya, Bipin Singh Koranga - Aalborg :River Publishers,2021. - xiii,112 pages ;24 cm. - River Publishers Series in Mathematical and Engineering Sciences Ser.. - River Publishers Series in Mathematical and Engineering Sciences Ser..

6 Tensor in Relativity.

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

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.

ISBN: 9788770225809Subjects--Topical Terms:

348467
Tensor algebra.

LC Class. No.: QA200 / .K673 2020

Dewey Class. No.: 515.724

An Introduction to Tensor Analysis /
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490 1 $a River Publishers Series in Mathematical and Engineering Sciences Ser.
500 $a 6 Tensor in Relativity.
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
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.
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650 # 0 $a Tensor algebra. $3 348467
650 # 6 $a Algèbre tensorielle. $3 916357
700 1 # $a Padaliya, Sanjay Kumar. $3 916258
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. $3 916259
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