 # Representation theory

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Representation theory
```CONTENTS
26.21
26.22
26.23
26.24
Absolute derivatives along curves
Geodesics
Exercises
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
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
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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