File : pdf, 451 KB, 47 pages
by R. Sharipov
TOC
CONTENTS.
CHAPT I. PRELIMINARY INFORMATION.
1. Geometrical and physical vectors.
2. Bound vectors and free vectors.
3. Euclidean space.
4. Bases and Cartesian coordinates.
5. What if we need to change a basis ? .
6. What happens to vectors when we change the basis ?
7. What is the novelty about vectors that we learned knowing transformation formula for their
coordinates ?
CHAPT II. TENSORS IN CARTESIAN COORDINATES.
8. Covectors.
9. Scalar product of vector and covector.
10. Linear operators.
11. Bilinear and quadratic forms.
12. General defnition of tensors.
13. Dot product and metric tensor.
14. Multiplication by numbers and addition.
15. Tensor product.
16. Contraction.
17. Raising and lowering indices.
18. Some special tensors and some useful formulas.
CHAPT III. TENSOR FIELDS. DIFFERENTIATION OF TENSORS.
19. Tensor fields in Cartesian coordinates.
20. Change of Cartesian coordinate system.
21. Differentiation of tensor fields.
22. Gradient, divergency, and rotor. Laplace and d’Alambert operators.
CHAPT IV. TENSOR FIELDS IN CURVILINEAR COORDINATES.
23. General idea of curvilinear coordinates.
24. Auxiliary Cartesian coordinate system.
25. Coordinate lines and the coordinate grid.
26. Moving frame of curvilinear coordinates.
27. Dynamics of moving frame.
28. Formula for Christophel symbols.
29. Tensor fields in curvilinear coordinates.
30. Differentiation of tensor fields in curvilinear coordinates.
31. Concordance of metric and connection.
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