| Introduction |
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1 | (2) |
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3 | (16) |
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3 | (1) |
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Finite groups of order n ≤ 8 |
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4 | (3) |
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7 | (1) |
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8 | (7) |
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8 | (3) |
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11 | (1) |
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11 | (3) |
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Other functions and representations of quaternions |
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14 | (1) |
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Classical vector calculus |
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15 | (2) |
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Scalar product and vector product |
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15 | (1) |
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Triple scalar and double vector products |
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16 | (1) |
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17 | (2) |
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Rotation groups SO (4) and SO (3) |
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19 | (18) |
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Orthogonal groups O(4) and SO(4) |
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19 | (3) |
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Orthogonal groups O(3) and SO(3) |
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22 | (2) |
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24 | (4) |
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Double cyclic groups Cn (order N = 2n) |
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24 | (1) |
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Double dihedral groups Dn (N = 4n) |
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24 | (1) |
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Double tetrahedral group (N = 24) |
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25 | (1) |
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Double octahedral group (N = 48) |
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26 | (1) |
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Double icosahedral group (N = 120) |
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27 | (1) |
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Infinitesimal transformations of SO(4) |
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28 | (4) |
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Symmetries and invariants: Kepler's problem |
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32 | (2) |
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34 | (3) |
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37 | (20) |
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Algebra of complex quaternions H(C) |
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37 | (1) |
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Lorentz groups O(1,3) and SO(1,3) |
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38 | (3) |
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38 | (1) |
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38 | (1) |
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Groups O(1,3) and SO(1,3) |
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39 | (2) |
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Orthochronous, proper Lorentz group |
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41 | (3) |
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41 | (2) |
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Infinitesimal transformations of SO(1,3) |
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43 | (1) |
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Four-vectors and multivectors in H(C) |
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44 | (3) |
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Relativistic kinematics via H(C) |
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47 | (3) |
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Special Lorentz transformation |
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47 | (1) |
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General pure Lorentz transformation |
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48 | (1) |
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Composition of velocities |
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48 | (2) |
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50 | (2) |
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Group of conformal transformations |
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52 | (2) |
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54 | (3) |
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57 | (18) |
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57 | (2) |
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57 | (1) |
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Clifford algebra H H over R |
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58 | (1) |
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Multivector calculus within H H |
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59 | (5) |
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Exterior and interior products with a vector |
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59 | (2) |
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Products of two multivectors |
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61 | (1) |
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62 | (2) |
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Classical vector calculus |
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64 | (1) |
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64 | (5) |
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64 | (2) |
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66 | (3) |
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69 | (3) |
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69 | (1) |
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Infinitesimal elements of curves, surfaces and hypersurfaces |
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69 | (2) |
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71 | (1) |
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72 | (3) |
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75 | (16) |
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Pseudo-orthogonal groups O(1, 3) and SO(1, 3) |
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75 | (3) |
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75 | (1) |
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Symmetry with respect to a hyperplane |
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75 | (2) |
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Pseudo-orthogonal groups O(1, 3) and SO(1, 3) |
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77 | (1) |
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Proper orthochronous Lorentz group |
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78 | (4) |
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78 | (1) |
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Pure Lorentz transformation |
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79 | (2) |
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General Lorentz transformation |
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81 | (1) |
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Group of conformal transformations |
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82 | (3) |
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82 | (1) |
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Properties of conformal transformations |
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83 | (1) |
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Transformation of multivectors |
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84 | (1) |
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85 | (3) |
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85 | (1) |
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Unitary and symplectic unitary groups |
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86 | (2) |
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88 | (3) |
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91 | (14) |
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91 | (3) |
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Special Lorentz transformation |
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91 | (1) |
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92 | (2) |
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General Lorentz transformation |
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94 | (1) |
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94 | (5) |
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94 | (3) |
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97 | (2) |
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Relativistic dynamics of a point mass |
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99 | (4) |
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99 | (1) |
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100 | (3) |
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103 | (2) |
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Classical electromagnetism |
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105 | (22) |
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Electromagnetic quantities |
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105 | (5) |
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Four-current density and four-potential |
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105 | (2) |
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Electromagnetic field bivector |
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107 | (3) |
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110 | (8) |
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110 | (5) |
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115 | (1) |
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116 | (2) |
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118 | (3) |
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Electromagnetic waves in vacuum |
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118 | (1) |
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Electromagnetic waves in a conductor |
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119 | (1) |
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Electromagnetic waves in a perfect medium |
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120 | (1) |
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121 | (4) |
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121 | (2) |
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123 | (1) |
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Aberration of distant stars |
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124 | (1) |
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125 | (2) |
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127 | (8) |
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127 | (1) |
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128 | (1) |
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129 | (1) |
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130 | (5) |
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130 | (3) |
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133 | (2) |
| Conclusion |
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135 | (2) |
| Solutions |
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137 | (16) |
| Formulary: multivector products within H(C) |
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153 | (4) |
| Formulary: multivector products within H H (over R) |
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157 | (4) |
| Formulary: four-nabla operator within H H (over R) |
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161 | (2) |
| Work-sheet: H(C) (Mathematica) |
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163 | (2) |
| Work-sheet H H over (Mathematica) |
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165 | (2) |
| Work-sheet: matrices M2(H) (Mathematica) |
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167 | (2) |
| Clifford algebras: isomorphisms |
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169 | (2) |
| Clifford algebras: synoptic table |
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171 | (2) |
| Bibliography |
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173 | (4) |
| Index |
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177 | |
Lisainfo e-raamatute kohta