 # Representation theory

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Representation theory
```CONTENTS
26.21
26.22
26.23
26.24
Absolute derivatives along curves
Geodesics
Exercises
Hints and answers
975
976
977
982
27
27.1
Numerical methods
Algebraic and transcendental equations
984
985
Rearrangement of the equation; linear interpolation; binary chopping;
Newton–Raphson method
27.2
27.3
Convergence of iteration schemes
Simultaneous linear equations
992
994
Gaussian elimination; Gauss–Seidel iteration; tridiagonal matrices
27.4
Numerical integration
1000
Trapezium rule; Simpson’s rule; Gaussian integration; Monte Carlo methods
27.5
27.6
Finite diﬀerences
Diﬀerential equations
1019
1020
Diﬀerence equations; Taylor series solutions; prediction and correction;
Runge–Kutta methods; isoclines
27.7
27.8
27.9
27.10
Higher-order equations
Partial diﬀerential equations
Exercises
Hints and answers
1028
1030
1033
1039
28
28.1
Group theory
Groups
1041
1041
Deﬁnition of a group; examples of groups
28.2
28.3
28.4
28.5
28.6
28.7
Finite groups
Non-Abelian groups
Permutation groups
Mappings between groups
Subgroups
Subdividing a group
1049
1052
1056
1059
1061
1063
Equivalence relations and classes; congruence and cosets; conjugates and
classes
28.8
28.9
Exercises
Hints and answers
1070
1074
29
29.1
29.2
29.3
29.4
29.5
Representation theory
Dipole moments of molecules
Choosing an appropriate formalism
Equivalent representations
Reducibility of a representation
The orthogonality theorem for irreducible representations
1076
1077
1078
1084
1086
1090
xv
```
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