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ISBN 10: 1541013638
ISBN 13: 9781541013636
Author: Dr Taha Sochi
1.1 Historical Overview of Development & Use of Tensor Calculus
1.2 General Conventions
1.3 General Mathematical Background
1.3.1 Coordinate Systems
1.3.2 Vector Algebra and Calculus
1.3.3 Matrix Algebra
1.4 Exercises
Tensors
2.1 General Background about Tensors
2.2 General Terms and Concepts
2.3 General Rules
2.4 Examples of Tensors of Different Ranks
2.5 Applications of Tensors
2.6 Types of Tensor
2.6.1 Covariant and Contravariant Tensors
2.6.2 True and Pseudo Tensors
2.6.3 Absolute and Relative Tensors
2.6.4 Isotropic and Anisotropic Tensors
2.6.5 Symmetric and Anti-symmetric Tensors
2.7 Exercises
Tensor Operations
3.1 Addition and Subtraction
3.2 Multiplication of Tensor by Scalar
3.3 Tensor Multiplication
3.4 Contraction
3.5 Inner Product
3.6 Permutation
3.7 Tensor Test: Quotient Rule
3.8 Exercises
4.1 Kronecker delta
4.2 Permutation epsilon
4.3 Useful Identities Involving δ and/or ε
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Tags: Dr Taha Sochi, Calculus, Simple