- Chapter 1 -- components of a tensor in a given basis, contravariant and covariant vectors/tensors, tensor notation and transformation laws, curvilinear coordinates, tensor operations (addition, scalar multiplication, outer/inner product, contraction), the Einstein summation convention, the Kronecker delta, and worked exercises 1.2--1.13.
- Chapter 2 -- matrices as tensor notation, matrix multiplication, the identity and inverse matrix, the transpose, orthogonal matrices, the permutation symbol, the determinant and its Laplace expansion, the scalar product and vector norm, the angle between two vectors, the cross product in \(\mathbb{R}^3\), and inverting a matrix.
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