Introductory University Physics — Contents Advanced Resources AD 03 · 58 chapters + 2 appendices

Introductory University Physics— From Mechanics to Special Relativity: University Physics for Precocious High-School Students —

This book is a teaching resource that gathers into a single volume the foundations of the physics studied in the first few years at a university of science and engineering. It is based on the eight volumes of Yasuhide Mochizuki's handwritten notebooks, “Physics Notes” (mechanics, waves, mechanics of materials, thermodynamics, electromagnetism, analytical mechanics, statistical mechanics, and special relativity). The laws, definitions, derivations, worked calculations, and figures of the original notes are included without omitting a single one, and, so that even a precocious high-school student who wants to understand university physics can read the book, we have supplied explanations of how new symbols are read, the steps between lines of equations, and concrete examples and figures. Content that is not written in the original notes but is indispensable to a textbook (fracture mechanics, full-fledged statistical mechanics, Minkowski spacetime and four-vectors, and so on) has been added in chapters of its own.

Each section contains worked examples in which no intermediate steps are omitted, and each chapter ends with exercises. The mathematics you need can be filled in through links to the relevant sections of the companion volume “University Mathematics” (AD 02). We have placed importance on showing how the results you memorized as formulas in high school physics (the equations for motion with constant acceleration, the period of simple harmonic motion, the Doppler effect, the equation of state of gases, Coulomb's law, and so on) are derived once calculus is used, and how they are connected with one another. The worked examples draw many of their subjects from materials science, such as metals, ceramics, and semiconductors. Quantum mechanics is not treated (it is covered in the companion volume “Quantum Mechanics (AD 04, in Japanese)”). The parts on statistical mechanics and special relativity also serve as preparation for moving on to quantum mechanics, condensed matter physics, and particle physics.

How to read this book
  • Part I (Mechanics) is the foundation for everything. First read Chapters 1 through 10 in order.
  • Part II (Waves), Part III (Mechanics of Materials and Fracture Mechanics), Part IV (Thermodynamics), and Part V (Electromagnetism) may be read, after Part I, starting with whichever part interests you. The last chapter of Part V (electromagnetic waves) is connected with the treatment of light in Part II.
  • Part VI (Analytical Mechanics) presupposes Part I, Part VII (Statistical Mechanics) presupposes Parts IV and VI, and Part VIII (Special Relativity) presupposes Parts I and V.
  • Physical constants, units, and symbols can be looked up in Appendix B. Solutions to the exercises are in Appendix A.
Part I Mechanics
  1. Chapter 1Description of Motion — Position, Velocity, Acceleration, and Vectors The Particle Model; Position Vector, Displacement, Velocity, and Acceleration; SI Base Units, Derived Units, and Dimensional Analysis; Motion with Constant Acceleration in One Dimension — Deriving the Three High-School Physics Formulas; Free Fall and Vertical Upward Throw; $x$-$t$ Graphs and $v$-$t$ Graphs — Slope and Area; A Preview of Inner and Cross Products — Where They Appear in Mechanics
  2. Chapter 2Newton's Laws of Motion — Momentum and Angular Momentum Newton's First Law and Inertial Frames; Newton's Second Law — The Equation of Motion, Momentum, and Impulse; Newton's Third Law — Action and Reaction, Internal Forces and External Forces; Conservation of Momentum — From Two-Body to $N$-Body Systems; Torque and Angular Momentum; Advanced Topic: The Coefficient of Restitution and One-Dimensional Collisions
  3. Chapter 3Description of Curvilinear Motion — Polar Coordinates and Tangential and Normal Acceleration Transformation to Plane Polar Coordinates; Basis Vectors of the Polar Coordinate System — The Rotation Matrix; The Unit Tangent Vector and Velocity; The Unit Normal Vector and the Tangential and Normal Components of Acceleration; The Formula for the Radius of Curvature and Examples
  4. Chapter 4Work and Energy The Definition of Work — The Inner Product of Force and Displacement; Work and Kinetic Energy — The Work–Energy Theorem; Work along a Curve — An Example with Friction; Conservative Forces and Potential Energy; Conservation of Mechanical Energy; Power and Potential Energy Curves
  5. Chapter 5Projectile Motion and Circular Motion — Air Resistance and Centripetal Acceleration Projectile Motion without Air Resistance — Trajectory, Highest Point, and Horizontal Range; Projectile Motion with Air Resistance — Resistance Proportional to Velocity and Terminal Velocity; Advanced Topic: Resistance Proportional to the Square of the Velocity and the Terminal Velocity of Fast Objects; Uniform Circular Motion and Centripetal Acceleration
  6. Chapter 6Motion in Polar Coordinates and Conic Sections Velocity in Polar Coordinates; Acceleration in Polar Coordinates — The Physical Meaning of Each Term; Conic Sections in Polar Coordinates — Classification by Eccentricity
  7. Chapter 7Simple Harmonic, Damped, and Forced Oscillations The Mass–Spring System and the General Solution of Simple Harmonic Motion; Energy of Simple Harmonic Motion and the Simple Pendulum; Damped Oscillations — The Three Cases in the Presence of Resistance; Forced Oscillations and Resonance
  8. Chapter 8Central Forces and Planetary Motion — Kepler's Laws and the Earth Tunnel Central Forces and Conservation of Angular Momentum — Constant Areal Velocity (Kepler's Second Law); Proof of Kepler's First Law; Kepler's Third Law — Period and Semi-Major Axis; Gravitational Potential Energy, the Effective Potential, and Escape Velocity; Gravity inside a Uniform Sphere (the Shell Theorem) and the Earth Tunnel
  9. Chapter 9Moving Reference Frames and Fictitious Forces — Centrifugal and Coriolis Forces Inertial and Non-Inertial Frames — Fictitious Forces in a Translationally Accelerating Frame; Time Derivatives in a Rotating Coordinate System; Centrifugal and Coriolis Forces; The Rotation of the Earth and Everyday Phenomena; Correspondence with the Acceleration in Polar Coordinates
  10. Chapter 10Systems of Particles and Rigid Bodies — Center of Mass, Moment of Inertia, and the Rotational Equation of Motion The Center of Mass of a System of Particles and Its Equation of Motion; Motion of Extended Bodies — Two Equations for Handling Rigid Bodies; The Definition of the Moment of Inertia; Moment of Inertia of a Rod — About an End and about the Center of Mass; Moment of Inertia of a Sphere (I) — Calculation in Spherical Coordinates; Moment of Inertia of a Sphere (II) — An Alternative Solution by Stacking Thin Disks; The Parallel-Axis and Perpendicular-Axis Theorems and Moments of Inertia of Typical Shapes; Angular Momentum of a Rigid Body, the Rotational Equation of Motion, and Rotational Kinetic Energy; Rolling without Slipping — A Sphere and a Cylinder Rolling Down an Incline; The Physical Pendulum
Part II Waves
  1. Chapter 11Basic Properties of Waves — The Equation of a Wave, Interference, Standing Waves, and Diffraction Review of Simple Harmonic Motion — The Starting Point for Understanding Waves; The Wave Equation — The Mathematics of a Waveform Traveling without Distortion; What Is a Wave? — Transverse and Longitudinal Waves and the Derivation of the Wave Function; Phase Velocity and the Direction of Propagation; Wave Energy and Wave Intensity; Interference of Waves — In Phase and in Antiphase; Standing Waves; Huygens's Principle and the Laws of Reflection and Refraction; Diffraction of Waves
  2. Chapter 12Sound Waves — The Doppler Effect, Beats, Resonance, and Vibrations of Strings The Speed of Sound and the Doppler Effect; Shock Waves — When the Source Exceeds the Speed of Sound; The Oblique Doppler Effect and Beats; Resonance and Standing Waves in an Air Column; Why Reflection Occurs at an Open End; Resonance of Strings and the Speed of Waves on a String; Resonance of a String Driven by a Tuning Fork
  3. Chapter 13Fundamentals of Light Waves — Measuring the Speed of Light and the Refractive Index Comparison of Light Waves and Sound Waves; Polarization and Malus's Law; The Absolute Refractive Index; Differences in Dispersion between Sound Waves and Light Waves; Is the Speed of Light Finite? — Rømer's Astronomical Discovery (1676); Measuring the Speed of Light (1) — Fizeau's Experiment; Measuring the Speed of Light (2) — The Rotating-Mirror Method (Foucault)
  4. Chapter 14Reflection and Refraction of Light — Phase Changes, Fermat's Principle, and Total Internal Reflection Fixed-End and Free-End Reflection — Derivation from Boundary Conditions; Reflection and Transmission Conditions for Strings of Different Linear Densities; The Physical Meaning of the Reflection Conditions — From Strings to Light; The Laws of Reflection and Refraction; Fermat's Principle — The Optical Path Length Takes a Minimum (Stationary) Value; Light as an Electromagnetic Wave and the Dispersion of Light; Total Internal Reflection — The Critical Angle and Optical Fibers
  5. Chapter 15Lenses and Image Formation Lenses, Focal Points, and the Sign Convention; Derivation of the Lens Equation for a Convex Lens; Derivation of the Lens Equation for a Concave Lens; Image Formation by Multiple Lenses — Sequential Imaging and Lenses in Contact; Applications of Lenses — The Magnifying Glass, the Camera, and the Microscope
  6. Chapter 16Interference of Light and the Diffraction Grating — Young's Experiment, Thin Films, and Newton's Rings Optical Path Length (Optical Distance); Young's Double-Slit Experiment; The Diffraction Grating; Interference of Light by Thin Films; Interference in a Wedge-Shaped Air Layer; Newton's Rings; Advanced Topic: Applications of Interference — Antireflection Coatings, Interference Filters, and X-Ray Diffraction
  7. Chapter 17Superposition of Waves and Fourier Analysis — Wave Packets and Group Velocity The Principle of Superposition and d'Alembert's General Solution; Fourier Series of Periodic Waves — The Square Wave and the Sawtooth Wave; Normal Modes of Strings and Air Columns — Separation of Variables and the Fourier Basis; Beats — The Simplest Wave Packet; Wave Packets, Group Velocity, and Dispersion Relations; The Fourier Transform and the Width of a Wave Packet — $\Delta x\,\Delta k\gtrsim1$
Part III Mechanics of Materials and Fracture Mechanics
  1. Chapter 18Fundamentals of Mechanics of Materials — Loads, Stress, and Strain Basic Assumptions of Mechanics of Materials and Internal Forces; Classification of Loads; The Definition of Stress; Longitudinal Strain, Transverse Strain, and Poisson's Ratio; Shear Strain and Volumetric Strain
  2. Chapter 19Hooke's Law, Elastic Moduli, and Material Testing Hooke's Law; Young's Modulus, Shear Modulus, and Bulk Modulus; Advanced Topic: Relations among the Elastic Constants — Why Are There Only Two Independent Elastic Constants?; Material Testing; Advanced Topic: Details of the Stress–Strain Diagram and True Stress and True Strain
  3. Chapter 20Multiaxial Stress, Bending of Beams, and Torsion The Stress Tensor and Its Symmetry; Coordinate Transformation of Plane Stress, Principal Stresses, and Maximum Shear Stress; Mohr's Circle; The Generalized Hooke's Law, Thermal Strain and Thermal Stress, and Strain Energy Density; Bending of Beams (1) — Bending Stress and the Second Moment of Area; Bending of Beams (2) — Shear Force and Bending Moment Diagrams and Deflection; Torsion of Shafts with Circular Cross Sections
  4. Chapter 21Fundamentals of Fracture Mechanics — Stress Concentration, Griffith Theory, and Fracture Toughness Theoretical Strength and Inglis's Stress Concentration; Griffith's Energy Balance; The Stress Intensity Factor and the Stress Field at the Crack Tip; The Energy Release Rate $\mathcal G$ and the Two Fracture Criteria; Fracture Toughness $K_{\mathrm{IC}}$ and Its Measurement; The Plastic Zone at the Crack Tip and the J-Integral; The R-Curve and Toughening Mechanisms
  5. Chapter 22Fatigue, Scatter in Strength, and Environment-Assisted Fracture What Is Fatigue? — The S–N Curve and the Fatigue Limit; Basquin's Law — Fatigue Life Expressed by a Power Law; The Connection to Fracture Mechanics — The Paris Law and Integration of Crack Growth Life; Miner's Rule — The Linear Cumulative Damage Rule; The Ductile-to-Brittle Transition and the Charpy Impact Test; Weibull Statistics — The Weakest-Link Model and Scatter in Strength; The Weibull Plot, the Size Effect, and the Effective Volume; Thermal Shock Resistance; Stress Corrosion Cracking, Delayed Fracture, and Subcritical Crack Growth
Part IV Thermodynamics
  1. Chapter 23Heat and Temperature — Gas Laws and Changes of State Thermal Motion and Temperature Scales; Quantity of Heat, Specific Heat, Heat Capacity, and Conservation of Heat; Internal Energy; The First and Second Laws of Thermodynamics; Boyle's Law, Charles's Law, and the Boyle–Charles Law; The Equation of State of an Ideal Gas; Isochoric and Isobaric Processes; Isothermal and Adiabatic Processes; Coefficients of Linear and Volume Expansion
  2. Chapter 24The Kinetic Theory of Gases and the van der Waals Equation of State The Zeroth Law of Thermodynamics and Preparation for the Kinetic Theory of Gases; Derivation of the Kinetic Theory of Gases—The Relation between Pressure and the Kinetic Energy of Molecules; The Boltzmann Constant, Degrees of Freedom, and the Law of Equipartition of Energy; The van der Waals Equation of State and the Liquefaction of Gases
  3. Chapter 25Real Gases — The Principle of Corresponding States, the Compression Factor, and the Virial Expansion The Principle of Corresponding States and the Reduced Equation of State; Real Gases and the Compression Factor $Z$; The Virial Expansion and the Virial Equation of State; Virial Coefficients and the Boyle Temperature
  4. Chapter 26Thermodynamic Systems and State Quantities — Quasi-Static Processes and Work Classification of Systems — Isolated, Closed, and Open Systems; Energy, Work, Heat, and Internal Energy; State Functions and Path Functions; Quasi-Static, Reversible, and Irreversible Processes; Internal Energy as a State Quantity and the Degrees of Freedom of Molecular Motion; Rewriting the First Law of Thermodynamics, and Exact and Inexact Differentials; The General Expression for Work
  5. Chapter 27Heat Capacity, Enthalpy, and the Joule–Thomson Effect Work of Expansion — Constant-Pressure, Free, Reversible, and Isothermal Reversible Expansion; Heat Capacity and Heat Capacity at Constant Volume, Enthalpy and Heat Capacity at Constant Pressure; Relations for Adiabatic Processes and Poisson's Formula; The Total Differential of the Internal Energy, Internal Pressure, Expansion Coefficient, and Isothermal Compressibility; Mayer's Relation — The Ideal Gas and the General Case; The Total Differential of the Enthalpy and the Joule–Thomson Effect; Measuring the Isothermal Joule–Thomson Coefficient, the Inversion Temperature, and the Production of Liquid Helium
  6. Chapter 28The Carnot Cycle and the Efficiency of Heat Engines Two Statements of the Second Law of Thermodynamics and Their Equivalence; The Four Processes of the Carnot Cycle; Thermal Efficiency and the Reversed Carnot Cycle; Carnot's Theorem — The Efficiency of a Reversible Engine Is Maximal and Independent of the Working Substance; The Carnot Cycle of an Ideal Gas — Derivation of the Thermal Efficiency $\eta=1-T_1/T_2$; The Otto Cycle — A Cycle of Adiabatic and Isochoric Processes; The Diesel Cycle; Coefficients of Performance of Refrigerators and Heat Pumps
  7. Chapter 29Entropy — Definition and Proof That It Is a State Quantity The Definition of Entropy — Motivation from the Carnot Cycle; The Entropy of an Ideal Gas; The Entropy of a van der Waals Gas; $\Delta S$ for the Isothermal Reversible Expansion of an Ideal Gas; Proof That Entropy Is a State Quantity; How to Measure $\eta$ — Determining Temperature with a Triple-Point Cell; The Clausius Equality and Inequality and the Law of Entropy Increase; Is the Adiabatic Free Expansion of an Ideal Gas Spontaneous?
  8. Chapter 30Free Energies — Direction of Change and Maximum Work The Direction of Heat Transfer; Entropy Change at a Phase Transition; Entropy Change with Temperature and the Entropy at Absolute Zero (A Preview of the Third Law); Introduction of the Helmholtz Free Energy and the Gibbs Energy; Maximum Work and Maximum Non-Expansion Work; Temperature Dependence of the Gibbs Energy and the Gibbs–Helmholtz Equation
  9. Chapter 31Thermodynamic Relations and the Maxwell Relations The Total Differential of the Internal Energy $U$ and Maxwell Relation (I); The Total Differential of the Enthalpy $H$ and Maxwell Relation (II); The Total Differential of the Helmholtz Free Energy $A$ and Maxwell Relation (III); The Total Differential of the Gibbs Energy $G$, Maxwell Relation (IV), and a Summary — The Thermodynamic Square; Advanced Topic: Natural Variables and the Legendre Transformation; The Thermodynamic Equation of State and the Internal Pressure of a Gas; Derivation of the General Mayer Relation; Conditions for Thermodynamic Stability
  10. Chapter 32The Third Law of Thermodynamics and Rules for Phase Transitions Nernst's Theorem and Its History; Absolute Entropy and the Third Law of Thermodynamics (Sommerfeld's Formulation); Heat Capacity and the Thermal Expansion Coefficient at Absolute Zero; Trouton's Rule and Richards's Rule; Advanced Topic: The Clausius–Clapeyron Equation; Advanced Topic: The $p$-$T$ Phase Diagram of Water and the Unattainability of Absolute Zero
  11. Chapter 33The Heat Conduction Equation Derivation of the Heat Conduction Equation; The Steady-State Solution — When the Two Ends Are at Different Temperatures; Separation of Variables and Fourier Series — When the Initial Temperature Distribution Is Given, Case 1; When the Initial Temperature Distribution Is Given, Case 2 — Decomposition into Steady and Transient Terms
  12. Chapter 34Gateway to Statistical Thermodynamics — Maxwell's Velocity Distribution The Aim of Statistical Thermodynamics; The Distribution Function and Maxwell's Hypothesis of Independence; Collisions of Gas Molecules and Pressure; Maxwell's Velocity Distribution Law; Checking the Consistency of the Hypothesis and the Distribution of Speeds
Part V Electromagnetism
  1. Chapter 35Coulomb's Law and Gauss's Law The Coulomb Force and Universal Gravitation — The Difference between Two Inverse-Square Laws; The Idea of the Electric Field — From Action at a Distance to Local Action; Derivation of Maxwell's Equation No. 1 — From Coulomb's Law to the Divergence Theorem; The Electric Displacement $\bm D$ and the Completion of Gauss's Law; The Physical Meaning of Gauss's Law; Verification: Electrostatic Induction on a Conducting Sphere
  2. Chapter 36Electric Potential and Capacitors Potential Difference and the Work Done by an Electrostatic Field; The Potential of a Uniform Electric Field and the Potential Referenced to Infinity; Potential Energy of a Charge and Electrostatic Induction; Calculating Electric Fields with Gauss's Law — The Infinite Plane and the Infinite Line; Electric Field and Potential of a Spherically Symmetric Charge Distribution; The Parallel-Plate Capacitor — Formula and Energy; Spherical and Cylindrical Capacitors and Poisson's Equation; Potential and Field of Continuously Distributed Charge, and the Electric Dipole
  3. Chapter 37Steady Current and Electric Circuits The Definition of Current and Three Ways to Express It; Current Density and Conservation of Charge (the Continuity Equation); Ohm's Law and the Microscopic Model of Resistance; Joule Heating and Electric Power; Resistors in Series and in Parallel; Kirchhoff's Laws; Transient Phenomena in RC Circuits — Charging and Discharging a Capacitor
  4. Chapter 38Sources of the Magnetic Field — The Biot–Savart Law and Ampère's Law Magnetic Force, Magnetic Field, and Magnetic Flux Density; Magnetic Flux and the Biot–Savart Law; The Magnetic Field of a Straight Current; The Magnetic Fields of a Circular Current and a Solenoid; Ampère's Law — Integral and Differential Forms; The Magnetic Dipole Moment and the Far Field of a Circular Current
  5. Chapter 39Magnetic Forces on Currents and Charged Particles — The Lorentz Force and the Hall Effect The Ampère Force — The Force on a Current in a Magnetic Field; The Force between Two Parallel Wires; Why Does the Ampère Force Arise? — The Picture of Magnetic Field Lines; The Lorentz Force; Equivalence of the Lorentz Force and the Ampère Force; Circular Motion of a Charged Particle in a Uniform Magnetic Field — Cyclotron Motion; Helical Motion for Oblique Incidence and the Aurora; The Hall Effect
  6. Chapter 40Electromagnetic Induction and Inductance The Discovery of Electromagnetic Induction and Lenz's Law; Faraday's Law of Induction — From Integral to Differential Form; The Induced Electromotive Force in a Conducting Rod Moving across a Magnetic Field; The Electromotive Force Viewed from the Lorentz Force; Self-Inductance — The Solenoid as an Example; Mutual Inductance; Energy Stored in a Coil and the Energy Density of the Magnetic Field; Transient Phenomena in RL Circuits; Electrical Oscillations in LC Circuits — Correspondence with Simple Harmonic Motion; Generators and Transformers
  7. Chapter 41Electric and Magnetic Fields in Matter — Dielectrics and Magnetic Materials Dielectrics and Polarization; Magnetic Materials and Magnetization; Gauss's Law and Ampère's Law in Matter, and Boundary Conditions
  8. Chapter 42Maxwell's Equations and Electromagnetic Waves Displacement Current and the Ampère–Maxwell Law; The Four Maxwell Equations — The Completion of Electromagnetism; Derivation of the Wave Equation for Electromagnetic Waves; Properties of Plane Electromagnetic Waves — $\bm E\perp\bm B\perp\bm k$ and $E=cB$; Energy of the Electromagnetic Field and the Poynting Vector; The Electromagnetic Spectrum; An Example of the Two-Dimensional Wave Equation — Applications to Waveguides and Cavity Resonators; Summary of Part V: Electromagnetism
Part VI Analytical Mechanics
  1. Chapter 43Lagrange's Equations of Motion — Generalized Coordinates and Generalized Forces Degrees of Freedom and Generalized Coordinates — Why Change Coordinates?; Generalized Momentum; Generalized Force; Lagrange's Equations of Motion for Conservative Forces — $L=T-U$; Lagrange's Equations of Motion with Nonconservative Forces; d'Alembert's Principle and the Principle of Virtual Work; Examples: One-Dimensional Linear Motion and Two-Dimensional Rotational Motion
  2. Chapter 44Applications of the Lagrangian Formalism and Variational Principles The Significance of Lagrange's Equations of Motion — What Do We Gain?; Applications: Falling Motion, Simple Harmonic Motion, and the Simple Pendulum; Application: Planetary Motion — Comparison with the Results of Chapter 8; Functionals and the Action — Hamilton's Principle (the Principle of Least Action); Derivation of the Euler–Lagrange Equation by the Calculus of Variations; Applications of Variational Principles — Shortest Paths, Fermat's Principle, and the Brachistochrone; The Method of Lagrange Multipliers — Finding Constraint Forces Explicitly
  3. Chapter 45Hamilton's Canonical Equations and Phase Space From Generalized Momenta to the Hamiltonian — The Legendre Transformation; Derivation of Hamilton's Canonical Equations; The Hamiltonian $H=T+U$ of a Natural System and Conservation of Energy; Examples: The Hamiltonian Formalism for the Simple Pendulum and Planetary Motion; Phase Space and Phase Trajectories; Cyclic Coordinates and Conserved Momenta
  4. Chapter 46Symmetry and Conservation Laws, Poisson Brackets, and Canonical Transformations Cyclic Coordinates and the Energy Function — The First Face of Conserved Quantities; Symmetry and Conservation Laws — Noether's Theorem; The Poisson Bracket; Canonical Transformations; Liouville's Theorem and the Hamilton–Jacobi Equation — A Bridge to Part VII
Part VII Statistical Mechanics
  1. Chapter 47Mathematics for Statistical Mechanics — The n-Dimensional Ball, Stirling's Formula, and the Zeta Function Why Do We Need “n-Dimensional” Mathematics? — The Volume of an n-Dimensional Ball; Proof of the Volume of an n-Dimensional Ball — The Route via the n-Fold Gaussian Integral; Stirling's Formula; Definition and Convergence of the Zeta Function; Integrals Involving the Zeta Function — Bose-Type and Fermi-Type Integrals
  2. Chapter 48Microstates and the Principle of Equal A Priori Probability — The Microcanonical Distribution Microstates and Macrostates; Phase Space in Classical Mechanics — Counting Microstates; The Ergodic Hypothesis — Time Averages and Phase Averages; The Principle of Equal A Priori Probability and the Microcanonical Distribution; Examples of Counting States — The Two-Level Spin System and the Einstein Solid; Phase-Space Volume of an Ideal Gas — Calculation with an $n$-Dimensional Ball
  3. Chapter 49Thermodynamic Weight and Boltzmann's Principle The Thermodynamic Weights $\Omega(E)$ and $W(E)$ — The Phase-Space Volume of an Ideal Gas; Boltzmann's Principle $S=k_{\mathrm B}\ln W$; General Properties of Entropy — Extensivity and the Equivalence of the Two Definitions; Thermal Contact and the Most Probable Partition — The Statistical Definition of Temperature; Pressure, Chemical Potential, and the Partial Derivatives of the Entropy; The Entropy of an Ideal Gas — The Sackur–Tetrode Equation; The Gibbs Paradox and the Entropy of Mixing; Advanced Topic: Connection with the Third Law of Thermodynamics
  4. Chapter 50The Canonical Distribution and the Partition Function The Canonical Ensemble and the Boltzmann Factor; A System and a Heat Bath — Derivation of the Boltzmann Factor; The Partition Function and the Physical Quantities Obtained from It; Applications — The Altitude Distribution of Air Pressure and a Rederivation of the Maxwell Distribution; Energy Fluctuations and Heat Capacity; Equivalence with the Microcanonical Distribution; The Equipartition Theorem; Another Viewpoint: The Canonical Distribution via Lagrange Multipliers
  5. Chapter 51Applications of the Canonical Distribution — Ideal Gases, Specific Heat of Solids, and Paramagnetism The Partition Function of a Monatomic Ideal Gas; The Harmonic Oscillator and the Specific Heat of the Einstein Model; Two-Level Systems, Schottky Heat Capacity, and Negative Temperature; Spin-$1/2$ Paramagnets and Curie's Law; Rotation and Vibration of Diatomic Molecules and Specific Heat (Qualitatively)
  6. Chapter 52The Grand Canonical Distribution and Quantum Statistics — The Fermi and Bose Distributions Open Systems and Derivation of the Grand Canonical Distribution; The Grand Partition Function $\Xi$ and the Grand Potential; The Meaning of the Chemical Potential $\mu$; Quantum Statistics of Identical Particles — Fermions and Bosons; Derivation of the Fermi–Dirac Distribution; Derivation of the Bose–Einstein Distribution; The Classical Limit — Reduction to the Boltzmann Distribution; The Three-Dimensional Density of States and the Fermi Energy of a Free Electron Gas; Specific Heat of a Degenerate Fermi Gas; Bose–Einstein Condensation
  7. Chapter 53Statistics of Photons and Phonons — Black-Body Radiation and the Debye Model The Photon Gas and the Chemical Potential $\mu=0$; Counting the Modes of Electromagnetic Waves in a Cavity; Planck's Radiation Law; Wien's Displacement Law; The Stefan–Boltzmann Law and the Thermodynamics of the Photon Gas; The Cosmic Microwave Background; Lattice Vibrations of Solids and Phonons; The Debye Model — Density of States, Debye Frequency, and Debye Temperature; Specific Heat in the Debye Model — The $T^3$ Law and the Dulong–Petit Law; Photons and Phonons — Two Bose Gases
Part VIII Special Relativity
  1. Chapter 54From Galilean Relativity to the Lorentz Transformation Galilean Relativity; The Puzzle of the Speed of Light — Maxwell's Equations and the Galilean Transformation; The Michelson–Morley Experiment; Einstein's Two Principles; Derivation of the Lorentz Transformation; The Lorentz Factor $\gamma$ and the Limit to the Galilean Transformation; The Lorentz Transformation in Matrix Form
  2. Chapter 55Lorentz Contraction, Time Dilation, and the Transformation of Velocities Lorentz Contraction — The Length of a Moving Rod; The Slowing of Clocks — Proper Time and Time Dilation; Relativistic Effects on the Muon (μ Meson); Redshift — The Relativistic Doppler Effect of Light; The Rocket Problem — Including the Time for Light to Arrive; The Lorentz Velocity Transformation; Application: Correcting the Clocks of GPS Satellites
  3. Chapter 56Minkowski Spacetime — Relativity of Simultaneity and Proper Time Transformation of Coordinate Differences and the Velocity Addition Law; The Relativity of Simultaneity; Spacetime Diagrams — World Lines, Light Cones, and the Coordinate Axes of S′; The Invariant Interval and Causality; Proper Time; The Twin Paradox; Rapidity — The Lorentz Transformation Is a Hyperbolic Rotation
  4. Chapter 57Four-Vectors and Relativistic Dynamics — E=mc² and the Kinematics of Particles The Four-Position Vector and the Index Convention; The Metric and the Inner Product — Raising and Lowering Indices and the Einstein Summation Convention; The Lorentz Transformation $\Lambda^\mu{}_\nu$ and Four-Vectors; The Four-Velocity; The Four-Momentum and $E^2=(pc)^2+(mc^2)^2$; The Equivalence of Mass and Energy — Rest Energy and Kinetic Energy; Conservation of Four-Momentum and Two-Body Decay; Invariant Mass and Collisions — Threshold Energy; Kinematics of Compton Scattering
  5. Chapter 58Natural Units and the Four-Vector Formulation of Electromagnetism — Preparing for Particle Physics Natural Units $c=\hbar=1$ — Removing Units to Make Equations Easier to Read; The Four-Gradient $\partial_\mu$ and the d'Alembertian $\Box$ — Lorentz Invariance of the Wave Equation; The Four-Current and Conservation of Charge; The Vector Potential and the Four-Potential; The Field-Strength Tensor $F^{\mu\nu}$ — Combining the Electric and Magnetic Fields into One; The Covariant Form of Maxwell's Equations and the Lorenz Condition; Transformation of Electric and Magnetic Fields — They Mix for Different Observers; The Covariant Lorentz Force; The Relativistic Lagrangian of a Free Particle; From $E^2=p^2c^2+m^2c^4$ to Relativistic Quantum Mechanics — A Look Back at the Whole Book
Appendices
  1. Appendix ASolutions to the Exercises Complete solutions to the exercises at the end of each chapter
  2. Appendix BPhysical Constants, Units, and Symbols Physical constants (CODATA 2018), SI units and prefixes, how to read the Greek letters, and an index of the symbols used in this book with the chapters where they first appear

Source

Mochizuki Research Group, Department of Materials Science and Technology, Faculty of Advanced Engineering, Tokyo University of Science — Advanced Resources AD 03
← Back to Educational Resources