Week

Topics

1

Base vectors, cartesian coordinates, summation convention,range, Kronecker delta and permutation symbols.


Study Materials: To review vector knowledge in the undergraduate lessons

2

Scalar and vecctor product, scalar triple producti vector triple product, reciprocal base vectors.


Study Materials: To review vector knowledge in the undergraduate lessons

3

Covariant and contravariant components of a vector and Euclidean metric tensor.


Study Materials: To review integral knowledge in the undergraduate lessons

4

Vector functions, differentiation, GreenGauss ande Stokes integral theorems


Study Materials: To review matrix knowledge in the undergraduate lessons

5

Fundamental concepts for matrix algebra, matrix polynomials and CayleyHamilton theorem


Study Materials: Fundamental books for Linear Algebra

6

Theory of invariants and integrity basis


Study Materials: Research and reading for concerning subjects

7

Introduction to the curvilinear coordinates


Study Materials: Research and reading for concerning subjects

8

Vectors and tensors in curvilinear coordinates


Study Materials: Research and reading for concerning subjects

9

Physical components of vectors and tensors


Study Materials: Research and reading for concerning subjects

10

Tensor calculus, Covariant and contravariant partial derivatives


Study Materials: Research and reading for concerning subjects

11

Divergance, Curl and laplacian operators in curvilinear coordinates


Study Materials: Research and reading for concerning subjects

12

Differential operators in cylindrical and spherical coordinates


Study Materials: Research and reading for concerning subjects

13

GreenGauss and Stokes theorems in curvilinear coordinates


Study Materials: Research and reading for concerning subjects

14

Riemann_Christoffel curvature tensor and Bianchi identities


Study Materials: Research and reading for concerning subjects

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