Tensors

CONTENTS
24.9
24.10
24.11
24.12
24.13
24.14
24.15
Cauchy’s theorem
Cauchy’s integral formula
Taylor and Laurent series
Residue theorem
Definite integrals using contour integration
Exercises
Hints and answers
849
851
853
858
861
867
870
25
25.1
25.2
25.3
25.4
25.5
25.6
25.7
25.8
Applications of complex variables
Complex potentials
Applications of conformal transformations
Location of zeros
Summation of series
Inverse Laplace transform
Stokes’ equation and Airy integrals
WKB methods
Approximations to integrals
871
871
876
879
882
884
888
895
905
Level lines and saddle points; steepest descents; stationary phase
25.9 Exercises
25.10 Hints and answers
920
925
26
26.1
26.2
26.3
26.4
26.5
26.6
26.7
26.8
26.9
26.10
26.11
26.12
26.13
26.14
26.15
26.16
26.17
26.18
26.19
26.20
927
928
929
930
932
935
938
939
941
944
946
949
950
954
955
957
960
963
965
968
971
Tensors
Some notation
Change of basis
Cartesian tensors
First- and zero-order Cartesian tensors
Second- and higher-order Cartesian tensors
The algebra of tensors
The quotient law
The tensors δij and ijk
Isotropic tensors
Improper rotations and pseudotensors
Dual tensors
Physical applications of tensors
Integral theorems for tensors
Non-Cartesian coordinates
The metric tensor
General coordinate transformations and tensors
Relative tensors
Derivatives of basis vectors and Christoffel symbols
Covariant differentiation
Vector operators in tensor form
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