Theoretical Physics

1. Introduction.- 2. Newtonian Mechanics.- 2.1 Space and Time in Classical Mechanics.- 2.2 Newton's Laws.- 2.3 A Few Important Force Laws.- 2.4 The Energy of a Particle in a Force Field.- 2.4.1 Line Integrals.- 2.4.2 Work and Energy.- 2.5 Several Interacting Particles.- 2.6 Momentum and Momentum Conservation.- 2.7 Angular Momentum.- 2.8 The Two-Body Problem.- 2.9 The Kepler Problem.- 2.10 Scattering.- 2.10.1 Relative Motion in the Scattering Process.- 2.10.2 The Center of Mass System and the Laboratory System.- 2.11 The Scattering Cross-Section.- 2.12 The Virial Theorem.- 2.13 Mechanical Similarity.- 2.14 Some General Observations About the Many-Body Problem.- Problems.- 3. Lagrangian Methods in Classical Mechanics.- 3.1 A Sketch of the Problem and Its Solution in the Case of a Pendulum.- 3.2 The Lagrangian Method of the First Type.- 3.3 The Lagrangian Method of the Second Type.- 3.4 The Conservation of Energy in Motions Which are Limited by Constraints.- 3.5 Non-holonomic Constraints.- 3.6 Invariants and Conservation Laws.- 3.7 The Hamiltonian.- 3.7.1 Lagrange's Equations and Hamilton's Equations.- 3.7.2 Aside on the Further Development of Theoretical Mechanics and the Theory of Dynamical Systems.- 3.8 The Hamiltonian Principle of Stationary Action.- 3.8.1 Functionals and Functional Derivatives.- 3.8.2 Hamilton's Principle.- 3.8.3 Hamilton's Principle for Systems with Holonomic Constraints.- Problems.- 4. Rigid Bodies.- 4.1 The Kinematics of the Rigid Body.- 4.2 The Inertia Tensor and the Kinetic Energy of a Rigid Body.- 4.2.1 Definition and Elementary Properties of the Inertia Tensor.- 4.2.2 Calculation of Inertia Tensors.- 4.3 The Angular Momentum of a Rigid Body, Euler's Equations.- 4.4 The Equations of Motion for the Eulerian Angles.- Problems.- 5. Motion in a Noninertial System of Reference.- 5.1 Fictitious Forces in Noninertial Systems.- 5.2 Foucault's Pendulum.- 6. Linear Oscillations.- 6.1 Linear Approximations About a Point of Equilibrium.- 6.2 A Few General Remarks About Linear Differential Equations.- 6.3 Homogeneous Linear Systems with One Degree of Freedom and Constant Coefficients.- 6.4 Homogeneous Linear Systems with n Degrees of Freedom and Constant Coefficients.- 6.4.1 Normal Modes and Eigenfrequencies.- 6.4.2 Examples of the Calculation of Normal Modes.- 6.5 The Response of Linear Systems to External Forces.- 6.5.1 External Oscillating Forces.- 6.5.2 Superposition of External Harmonic Forces.- 6.5.3 Periodic External Forces.- 6.5.4 Arbitrary External Forces.- Problems.- 7. Classical Statistical Mechanics.- 7.1 Thermodynamic Systems and Distribution Functions.- 7.2 Entropy.- 7.3 Temperature, Pressure, and Chemical Potential.- 7.3.1 Systems with Exchange of Energy.- 7.3.2 Systems with an Exchange of Volume.- 7.3.3 Systems with Exchanges of Energy and Particles.- 7.4 The Gibbs Equation and the Forms of Energy Exchange.- 7.5 The Canonical Ensemble and the Free Energy.- 7.6 Thermodynamic Potentials.- 7.7 Material Constants.- 7.8 Changes of State.- 7.8.1 Reversible and Irreversible Processes.- 7.8.2 Adiabatic and Non-adiabatic Processes.- 7.8.3 The Joule-Thomson Process.- 7.9 The Transformation of Heat into Work, the Carnot Efficiency.- 7.10 The Laws of Thermodynamics.- 7.11 The Phenomenological Basis of Thermodynamics.- 7.11.1 Thermodynamics and Statistical Mechanics.- 7.11.2 The First Law of Thermodynamics.- 7.11.3 The Second and Third Laws.- 7.11.4 The Thermal and Caloric Equations of State.- 7.12 Equilibrium and Stability Conditions.- 7.12.1 Equilibrium and Stability in Exchange Processes.- 7.12.2 Equilibrium, Stability and Thermodynamic Potentials.- Problems.- 8. Applications of Thermodynamics.- 8.1 Phase Transformations and Phase Diagrams.- 8.2 The Latent Heat of Phase Transitions.- 8.3 Solutions.- 8.4 Henry's Law, Osmosis.- 8.4.1 Henry's Law.- 8.4.2 Osmosis.- 8.5 Phase Transitions in Solutions.- 8.5.1 Case (2): Miscibility in Only One Phase.- 8.5.2 Case (3): Miscibility in Two Phases.- Problem.- 9. Elements of Fluid Mechanics.- 9.1 A Few Introductory Remarks About Fluid Mechanics.- 9.2 The General Balance Equation.- 9.3 Particular Balance Equations.- 9.4 Entropy Production, Generalized Forces, and Fluids.- 9.5 The Differential Equations of Fluid Mechanics.- 9.6 A Few Elementary Applications of the Navier-Stokes Equations.- Problem.- 10. The Most Important Linear Partial Differential Equations of Physics.- 10.1 General Considerations.- 10.1.1 Types of Linear Partial Differential Equations, the Formulation of Boundary and Initial Value Problems.- 10.1.2 Initial Value Problems in ?D.- 10.1.3 Inhomogeneous Equations and Green's Functions.- 10.2 Solutions of the Wave Equation.- 10.3 Boundary Value Problems.- 10.3.1 Initial Observations.- 10.3.2 Examples of Boundary Value Problems.- 10.3.3 The General Treatment of Boundary Value Problems.- 10.4 The Helmholtz Equation in Spherical Coordinates, Spherical Harmonics, and Bessel Functions.- 10.4.1 Separation of Variables.- 10.4.2 The Angular Equations, Spherical Harmonics.- 10.4.3 The Radial Equation, Bessel Functions.- 10.4.4 Solutions of the Helmholtz Equation.- 10.4.5 Supplementary Considerations.- Problems.- 11. Electrostatics.- 11.1 The Basic Equations of Electrostatics and Their First Consequences.- 11.1.1 Coulomb's Law and the Electric Field.- 11.1.2 Electrostatic Potential and the Poisson Equation.- 11.1.3 Examples and Important Properties of Electrostatic Fields.- 11.2 Boundary Value Problems in Electrostatics, Green's Functions.- 11.2.1 Dirichlet and Neumann Green's Functions.- 11.2.2 Supplementary Remarks on Boundary Value Problems in Electrostatics.- 11.3 The Calculation of Green's Functions, the Method of Images.- 11.4 The Calculation of Green's Functions, Expansion in Spherical Harmonics.- 11.5 Localized Charge Distributions, the Multipole Expansion.- 11.6 Electrostatic Potential Energy.- Problems.- 12. Moving Charges, Magnetostatics.- 12.1 The Biot-Savart Law, the Fundamental Equations of Magnetostatics.- 12.1.1 Electric Current Density and Magnetic Fields.- 12.1.2 The Vector Potential and Ampere's Law.- 12.1.3 The SI-System of Units in Electrodynamics.- 12.2 Localized Current Distributions.- 12.2.1 The Magnetic Dipole Moment.- 12.2.2 Force, Potential, and Torque in a Magnetic Field.- 13. Time Dependent Electromagnetic Fields.- 13.1 Maxwell's Equations.- 13.2 Potentials and Gauge Transformations.- 13.3 Electromagnetic Waves in a Vacuum, the Polarization of Transverse Waves.- 13.4 Electromagnetic Waves, the Influence of Sources.- 13.5 The Energy of the Electromagnetic Field.- 13.5.1 Balance of Energy and the Poynting Vector.- 13.5.2 The Energy Flux of the Radiation Field.- 13.5.3 The Energy of the Electric Field.- 13.5.4 The Energy of the Magnetic Field.- 13.5.5 Self-Energy and Interaction Energy.- 13.6 The Momentum of the Electromagnetic Field.- 14. Elements of the Electrodynamics of Continuous Media.- 14.1 The Macroscopic Maxwell Equations.- 14.1.1 Microscopic and Macroscopic Fields.- 14.1.2 The Average Charge Density and Electric Displacement.- 14.1.3 The Average Current Density and the Magnetic Field Strength.- 14.2 Electrostatic Fields in Continuous Media.- 14.3 Magnetostatic Fields in Continuous Media.- 14.4 Plane Waves in Matter, Wave Packets.- 14.4.1 The Frequency Dependence of Susceptibility.- 14.4.2 Wave Packets, Phase and Group Velocity.- 14.5 Reflection and Refraction at Plane Boundary Surfaces.- 14.5.1 Boundary Conditions, the Laws of Reflection and Refraction.- 14.5.2 Fresnel's Equations.- 14.5.3 Special Effects of Reflection and Refraction.- Appendices.- A. The ?-Function.- B. Conic Sections.- C. Tensors.- D. Fourier Series and Fourier Integrals.- D.1 Fourier Series.- D.2 Fourier Integrals and Fourier Transforms.- E. Distributions and Green's Functions.- E.1 Distributions.- E.2 Green's Functions.- F. Vector Analysis and Curvilinear Coordinates.- F.1 Vector Fields and Scalar Fields.- F.2 Line, Surface, and Volume Integrals.- F.3 Stokes's Theorem.- F.4 Gauss's Theorem.- F.5 Applications of the Integral Theorems.- F.6 Curvilinear Coordinates.- Problems.- References.