From Newton to Mandelbrot: A primer in theoretical physics

Cover......Page __sk_0000.djvu
Copyright......Page __sk_0002.djvu
Contents......Page __sk_0005.djvu
Preface......Page __sk_0003.djvu
1.1.1 Basic Concepts of Mechanics and Kinematics......Page __sk_0009.djvu
1.1.2 Newton's Law of Motion......Page __sk_0011.djvu
1.1.3 Simple Applications of Newton's Law......Page __sk_0013.djvu
1.1.4 Hannonic Oscillator in One Dimension......Page __sk_0020.djvu
1.2 Mechanics of Point Mass Systems......Page __sk_0023.djvu
1.2.1 The Ten Laws of Conservation......Page __sk_0024.djvu
1.2.2 The Two-body Problem......Page __sk_0025.djvu
1.2.3 Constraining Forces and d'Alembert's Principle......Page __sk_0026.djvu
1.3.1 The Lagrange Function......Page __sk_0030.djvu
1.3.2 The Hamilton Function......Page __sk_0032.djvu
1.3.3 Hannonic Approximation for Small Oscillations......Page __sk_0034.djvu
1.4 Mechanics of Rigid Bodies......Page __sk_0038.djvu
1.4.1 Kinematics and Inertia Tensor......Page __sk_0039.djvu
1.4.2 Equations of Motion......Page __sk_0043.djvu
1.5.1 Basic Concepts......Page __sk_0048.djvu
1.5.2 Stress, Strain and Hooke's Law......Page __sk_0052.djvu
1.5.3 Waves in Isotropic Continua......Page __sk_0054.djvu
1.5.4 Hydrodynamics......Page __sk_0056.djvu
2.1.1 Steady Electric and Magnetic Fields......Page __sk_0063.djvu
2.1.2 Maxwell's Equations and Vector Potential......Page __sk_0067.djvu
2.1.3 Energy Density of the Field......Page __sk_0069.djvu
2.1.4 Electromagnetic Waves......Page __sk_0070.djvu
2.1.5 Fourier Transfonnation......Page __sk_0071.djvu
2.1.6 Inhomogeneous Wave Equation......Page __sk_0072.djvu
2.1.7 Applications......Page __sk_0073.djvu
2.2.1 Maxwell's Equations in Matter......Page __sk_0077.djvu
2.2.2 Properties of Matter......Page __sk_0078.djvu
2.2.3 Wave Equation in Matter......Page __sk_0080.djvu
2.2.4 Electrostatics at Surfaces......Page __sk_0081.djvu
2.3.1 Lorentz Transfonnation......Page __sk_0084.djvu
2.3.2 Relativistic Electrodynamics......Page __sk_0087.djvu
2.3.3 Energy, Mass and Momentum......Page __sk_0089.djvu
3.1.1 Introduction......Page __sk_0091.djvu
3.1.2 Mathematical Foundations......Page __sk_0092.djvu
3.1.3 Basic Axioms of Quantum Theory......Page __sk_0093.djvu
3.1.4 Operators......Page __sk_0096.djvu
3.1.5 Heisenberg's Uncertainty Principle......Page __sk_0097.djvu
3.2.1 The Basic Equation......Page __sk_0098.djvu
3.2.2 Penetration......Page __sk_0100.djvu
3.2.3 Tunnel Effect......Page __sk_0101.djvu
3.2.4 Quasi-classical WKB Approximation......Page __sk_0102.djvu
3.2.5 Free and Bound States in the Potential Well......Page __sk_0103.djvu
3.2.6 Hannonic Oscillators......Page __sk_0104.djvu
3.3.1 Angular Momentum Operator......Page __sk_0107.djvu
3.3.2 Eigenfunctions of L² and L_z......Page __sk_0108.djvu
3.3.3 Hydrogen Atom......Page __sk_0109.djvu
3.3.4 Atomic Structure and the Periodic System......Page __sk_0112.djvu
3.3.5 Indistinguishability......Page __sk_0113.djvu
3.3.6 Exchange Reactions and Homopolar Binding......Page __sk_0114.djvu
3.4.1 Steady Perturbation Theory......Page __sk_0117.djvu
3.4.2 Unsteady Perturbation Theory......Page __sk_0118.djvu
3.4.3 Scattering and Born's First Approximation......Page __sk_0120.djvu
4.1.1 Canonical Distribution......Page __sk_0123.djvu
4.1.2 Entropy, Axioms and Free Energy......Page __sk_0126.djvu
4.2.1 Energy and Other Thennodynamic Potentials......Page __sk_0129.djvu
4.2.2 Thennodynamic Relations......Page __sk_0131.djvu
4.2.3 Alternatives to the Canonical Probability Distribution......Page __sk_0133.djvu
4.2.4 Efficiency and the Carnot Cycle......Page __sk_0135.djvu
4.2.5 Phase Equilibrium and the Clausius-Clapeyron Equation......Page __sk_0136.djvu
4.2.6 Mass Action Law for Gases......Page __sk_0139.djvu
4.2.7 The Laws of Henry, Raoult and van't Hoff......Page __sk_0140.djvu
4.2.8 Joule-Thomson Effect......Page __sk_0142.djvu
4.3.1 Fenni and Bose Distributions......Page __sk_0143.djvu
4.3.2 Classical Limiting Case: ßµ -> -inf......Page __sk_0145.djvu
4.3.3 Classical Equidistribution Law......Page __sk_0147.djvu
4.3.4 Ideal Fenni-gas at Low Temperatures: ßµ -> +inf......Page __sk_0148.djvu
4.3.5 Ideal Bose-gas at Low Temperatures: ßµ -> 0......Page __sk_0149.djvu
4.3.6 Vibrations......Page __sk_0152.djvu
4.3.7 Virial Expansion for Real Gases......Page __sk_0153.djvu
4.3.8 Van der Waals' Equation......Page __sk_0154.djvu
4.3.9 Magnetism of Localised Spins......Page __sk_0156.djvu
4.3.10 Scaling Theory......Page __sk_0160.djvu
5. Fractals in Theoretical Physics......Page __sk_0179.djvu
5.1 Non-random Fractals......Page __sk_0180.djvu
5.2 Random Fractals: The Unbiased Random Walk......Page __sk_0182.djvu
5.3.2 Higher Dimensions......Page __sk_0184.djvu
5.3.3 Additional Lengths that Scale with sqrt(t)......Page __sk_0185.djvu
5.5 Fractal Dimension of the Unbiased Random Walk......Page __sk_0186.djvu
5.6.1 Biased Random Walk......Page __sk_0187.djvu
5.6.2 Scaling of the Characteristic Length......Page __sk_0188.djvu
5.7 Functional Equations and Scaling: Two Variables......Page __sk_0189.djvu
5.8 Fractals and the Critical Dimension......Page __sk_0191.djvu
5.9 Fractal Aggregates......Page __sk_0196.djvu
5.10 Fractals in Nature......Page __sk_0199.djvu
A.l Mechanics, Electricity and Magnetism......Page __sk_0205.djvu
A.2 Quantum Mechanics and Statistical Physics......Page __sk_0209.djvu
Further Reading......Page __sk_0212.djvu
Name and Subject Index......Page __sk_0213.djvu