Dynamics from Newton to Dirac

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1  Classical Mechanics
1.1  Newton's Proposition LXXI	3
1.2  Did Newton Answer Halley’s Question?	7
1.3  On Derivations of Kepler’s Laws	21
1.4  Centripetal and Centrifugal Forces	30
1.5  Inertial Forces and D'Alembert's Principle	40
1.6  Inverse-Square Forces and Orthogonal Polynomials	46
1.7  The Bulging Earth	52
1.8  Intrinsic Wobble of Spinning Objects	58
1.9  Newtonian Precession of Mercury’s Perihelion	60
1.10  Lagrangian and Hamiltonian Mechanics	68
1.11  The Virial Theorem	74
1.12  Noether's Theorem	80
2  Waves
2.1  Huygens’ Principle	86
2.2  Phase, Group, and Signal Velocity	96
2.3  Aberration of Force and Waves	103
2.4  Propagation of Pressure and Waves	109
2.5  On Diffraction	122
2.6  Interference or Refraction?	140
3  Thermodynamics
3.1  The Speed of Sound	148
3.2  Energy, Entropy, Enthalpy	154
3.3  Reversibility and Entropy	158
3.4  True, Equivalent, and Calibrated Airspeeds	165
3.5  Potential Flow and D'Alembert's Paradox	168
3.6  Reasoning with Reversibility	174
3.7  The Ergodic Hypothesis and Equipartition of Energy	180
3.8  Analytic Functions, The Magnus Effect, and Wings	189
4  Electrodynamics
4.1  The Curl of the Curl	204
4.2  Retarded and Advanced Potential	209
4.3  The Electric Potential of a Moving Charge	213
4.4  The Electric and Magnetic Fields of a Moving Charge	219
4.5  Lorentz Boosts and the Electromagnetic Field	225
4.6  Maxwell and Second-Degree Commutation	228
4.7  Electromagnetic Energy, One Way or Another	231
4.8  Transformation of Electromagnetic Amplitude	237
4.9  Magnetic Dipoles	240
4.10  Does an Accelerating Charge Radiate?	254
5  Quantum Theory
5.1  The Necessity of the Quantum	265
5.2  On the Origins of Quantum Mechanics	271
5.3  Magnetism and Earnshaw's Theorem	280
5.4  Hermitian Matrices	287
5.5  On Matrix Mechanics	292
5.6  Quantum Oscillator and Delannoy Numbers	309
5.7  Bras, Kets, and Matrices	319
5.8  The Hydrogen Atom	328
5.9  Higher-Order Wave Equations and Matter Waves	338
5.10  Dirac's Belt	343
5.11  Fourier Transforms and Uncertainty	353
5.12  Quantum Entanglement and Bell's Theorem	358
5.13  The Dirac Equation	373
5.14  On the Higgs Mechanism	391