math prelim for tensors
Post on 10-Dec-2015
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Tensors & other Mathematical preliminaries
-Nilanjan Mitra nilanjan@civil.iitkgp.ernet.in
www.facweb.iitkgp.ernet.in/~nilanjan
Cartesian coordinate frame: Positively oriented orthonormal basis
{e1, e2, e3}
Basis vectors obey
Inner product:
Cross product:
2
Relationship between Kronecker delta and permutation/alternating/LEVI-CIVITA symbol
Prove :
3
Tensor Product:
Prove :
4
Tensor
5
Look-back on inner, cross & tensor product of vectors (viewpoint of mapping)
6
Tensor Algebra
7
Tensor Algebra
Spherical and Deviatoric part of a Tensor
Inner product of a Tensor
8
9
Determinant & cofactor of a Tensor
10
11
Eigenvalue and eigenvectors
12
13
14
15
Differentiation of functions of a scalar
16
Differentiation of functions of a scalar
17
Differentiation of functions of fields
18
Divergence, Curl and Laplacian
19
Differentiation of functions of fields
20
21
22
23
24
26
Integral theorems
27
28
29
30
31
32
33
34
35
36
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