Chapter 2: Tensors
Lecture 3 (8/31)
The Indicial Notation
2A1. Summation Convention, Dummy indices
2A2. Free Indices
2A3. Kronecker Delta
2A4. Permutation Symbol
2A5. Operations with Indicial Notations
2B1 Tensor: A Linear Transformation
Lecture 4 (9/2)
Tensors
2B3 Components of a Transformed Vector
2B4 Sum of Tensors
2B7 Dyadic Product of Two Vectors
2B9 Identity Tensor and Tensor Inverse
2B10 Orthogonal tensor
2B11 Transformation Matrix Between Two Rectangular Cartesian Coordinate Systems
2B12 Transformation Laws of Cartesian Components of Vectors
Lecture 5 (9/9)
2B13 Transformation Laws of Cartesian Components of Tensors
2B14 Defining Tensors by Transformation Laws
2B15 Symmetric and Antisymmetric Tensors
2B16 The Dual Vector of an Antisymmetric Tensor
2B17 Eigenvalues and Eigenvectors of a Tensor
2B18 & 2B19 Principal Values and Principal Directions of Real Symmetric Tensors
2B20 Principal Scalar Invariants of a Tensor
Lecture 6 (9/14)
Part C Tensor Calculus
2C1 Tensor valued function of a Scalar
2C2 Scalar Field, Gradient of a Scalar Field
2C3 Vector Field, Gradient of a Vector Field
2C4 Divergence of a Vector Field and Divergence of a Tensor field