Theoretical Physics for Amateurs

Welcome to "Theoretical Physics for Amateurs," a comprehensive six-volume set of writings designed to guide enthusiastic learners through the fundamentals and advanced concepts of theoretical physics. Authored by George Hrabovsky and inspired by resources like Leonard Susskind's The Theoretical Minimum, this series provides a structured path for self-study, covering essential mathematical and physical principles. Each volume builds on the previous one, offering a deep dive into the fascinating world of theoretical physics. Click on each volume below to explore its contents. (Please note that as this is developed the list is subject to change, so keep coming back for more changes).

This series is part of the Madison Area Science and Technology (MAST) initiative to support amateur scientists. For more resources, visit our main page.

This volume introduces the core concepts of theoretical physics, focusing on the basic mathematical tools and physical principles needed to understand classical mechanics and beyond. It covers topics such as algebra, calculus, and introductory physics concepts, making it accessible for beginners with a high school background in science and mathematics.

Lessons in Volume 1

Lessons in Volume 2

  • Lesson 1: The Pillars of Mathematical Physics I Algebra
  • Lesson 2: The Pillars of Mathematical Physics II Geometry and Topology
  • Lesson 3: The Pillars of Mathematical Physics III Analysis
  • Lesson 4: A Deeper Look at Partial Derivatives
  • Lesson 5: A Deeper Look a Multiple Integrals
  • Lesson 6: Vector Fields
  • Lesson 7: Vector Integration
  • Lesson 8: Higher-Order ODEs
  • Lesson 9: Variable Coefficients Theory
  • Lesson 10: Series Solutions of ODEs and Special Functions
  • Lesson 11: Systems of ODEs
  • Lesson 12: Laplace Transforms
  • Lesson 13: Boundary-Value Problems for ODEs
  • Lesson 14: Analytical Mechanics
  • Lesson 15: The Calculus of Variations
  • Lesson 16: The Principle of Virtual Work and D'Alembert's Principle
  • Lesson 17: The Lagrangian Formulation
  • Lesson 18: Symmetries and Conservation Laws
  • Lesson 19: Motion in a Central Potential
  • Lesson 20: Fourier Series
  • Lesson 21: Small Oscillations
  • Lesson 22: Hamiltonian Dynamics
  • Lesson 23: Phase space
  • Lesson 24: Another Look at Thermodynamics
  • Lesson 25: A Glimpse of Chaos
  • Lesson 26: Poisson Brackets
  • Lesson 27: Group Theory
  • Lesson 28: Canonical Transformations
  • Lesson 29: Hamilton-Jacobi Theory
  • Lesson 30: Action-Angle Variables
  • Lesson 31: Perturbation Tehory
  • Lesson 31: Other Formulations of Classical Mechanics
  • Lesson 32: Electrostatics in a Vacuum
  • Lesson 33: Electric Fields in Dielectrics
  • Lesson 34: Complex Analysis for Physics
  • Lesson 35: Magnetostatics
  • Lesson 36: Tensors in Physics
  • Lesson 37: Rotational Mechanics
  • Lesson 38: Electromagnetic Induction
  • Lesson 39: Electric Circuits
  • Lesson 40: Maxwell's Equations
  • Lesson 41: Tensor Operations
  • Lesson 42: Christoffel Symbols
  • Lesson 43: Applications of Tensors in Physics
  • Lesson 44: The Basics of Continuum Mechanics
  • Lesson 45: Elastostatics
  • Lesson 46: Elastodynamics
  • Lesson 47: Basic Fluid Dynamics
  • Lesson 48: The Basics of Computational Fluid Dynamics
  • Lesson 49: Electromagnetic Waves
  • Lesson 50: Boundary-Value Problems for PDEs

Lessons in Volume 3

  • Lesson 1: Potentials and Gauge Transformations
  • Lesson 2: Geometrical Optics
  • Lesson 3: Optical Instruments
  • Lesson 4: Wave Optics
  • Lesson 5: More About Wave Equations
  • Lesson 6: Standing Waves and Resonance
  • Lesson 7: Wave Interference and Diffraction
  • Lesson 8: Polarization
  • Lesson 9: Introduction to Quantum Mechanics
  • Lesson 10: Atoms and Molecules
  • Lesson 11: Lasers and Coherence
  • Lesson 12: The Laws of Thermodynamics
  • Lesson 13: Entropy and Gibbs Free Energy
  • Lesson 14: Thermodynamics and Legendre Transforms
  • Lesson 15: Gases
  • Lesson 16: Phase Transitions
  • Lesson 17: The Statistical Interpretation of Thermodynamics
  • Lesson 18: Monte Carlo Methods
  • Lesson 19: Molecular Dynamics Simulation
  • Lesson 20: Physical Chemistry I: Thermal Physics
  • Lesson 21: Physical Chemistry II: Chemical Kinetics
  • Lesson 22: Physical Chemistry III: Quantum Chemistry
  • Lesson 23: Viscosity and Flow Types
  • Lesson 24: The Navier-Stokes Equation
  • Lesson 25: Reynolds Number and Turbulence
  • Lesson 26: Special Relativity
  • Lesson 27: Some Necessary Topology and Differential Geometry
  • Lesson 28: Special Relativity in the Language of Differential Geometry
  • Lesson 29: Groups in Special Relativity
  • Lesson 30: Fields in Special Relativity
  • Lesson 31: More Differential Geometry
  • Lesson 32: Constructing a Field Theory from a Lagrangian
  • Lesson 33: Another Look at Elastic Solids
  • Lesson 34: Another Look at Fluids
  • Lesson 35: Vorticity
  • Lesson 36: Waves in Fluids
  • Lesson 37: Convection and Advection
  • Lesson 38: Electromagnetic Fields in Matter
  • Lesson 39: Magnetohydrodynamics
  • Lesson 40: Plasma Kinetics
  • Lesson 41: Stability Analysis in Simulations
  • Lesson 42: Error Analysis and Convergence
  • Lesson 43: Particles in Plasmas
  • Lesson 44:  Waves in Plasmas
  • Lesson 45: Warm Plasmas
  • Lesson 46: Plasma Dynamics
  • Lesson 47: Problems with Classical Physics
  • Lesson 48: Just Enought Math for Quantum  Mechanics
  • Lesson 49: The Postulates of Quantum Mechanics
  • Lesson 50: Simple Quantum Problems

Lessons in Volume 4

  • Lesson 1: Measure and Integration
  • Lesson 2: Banach Spaces
  • Lesson 3: Hilbert Spaces
  • Lesson 4: The Quantum Harmonic Oscillator
  • Lesson 5: Indeterminacy
  • Lesson 6: Quantum Systems
  • Lesson 7: Symmetries
  • Lesson 8: Angular Momentum
  • Lesson 9: Quantum Mechanics in a Central Potential
  • Lesson 10: Spin
  • Lesson 11: More About Angular Momentum
  • Lesson 12: Variational and WKB Methods
  • Lesson 13: Time-Independent Perturbation Theory
  • Lesson 14: Time-Dependent Perturbation Theory
  • Lesson 15: Scattering Theory
  • Lesson 16: Path Integrals
  • Lesson 17: Other Formulations of Quantum Mechanics
  • Lesson 18: Creation and Annihilation Operators
  • Lesson 19: Entanglement and Measurement
  • Lesson 20: The Basics of Quantum Electrodynamics
  • Lesson 21: Introduction to Feynman Diagrams
  • Lesson 22: Second Quantization
  • Lesson 23: Relativistic Wave Equations and Field Theories
  • Lesson 24: Gauge Fields
  • Lesson 25: Interacting Relativistic Field Theories
  • Lesson 26: The S-Matrix and Cross Sections
  • Lesson 27: Renormalization Concepts
  • Lesson 28: Lie Theory
  • Lesson 29: Kinetic Theory
  • Lesson 30: Ensemble Thteory
  • Lesson 31: The Canonical Ensemble
  • Lesson 32: Equilibrium Statistical Mechanics
  • Lesson 33: Statistical Thermodynamics
  • Lesson 34: Stochastic Processes
  • Lesson 35: Information Theory in Physics
  • Lesson 36: Fermi-Dirac and Bose-Einstein Statistics
  • Lesson 37: Phase Transitions in Statistical Mechanics
  • Lesson 38: Monte Carlo Methods in Statistical Mechanics
  • Lesson 39: Quantum Monte Carlo Methods
  • Lesson 40: Complex Systems
  • Lesson 41: Quantum Gases
  • Lesson 42: Molecular Orbitals
  • Lesson 43: Hatree-Foch
  • Lesson 44: Other Molecular Models
  • Lesson 45: The Basics of Density Functional Theory
  • Lesson 46: Crystals and Nanostructures
  • Lesson 47: Electronic Structure
  • Lesson 48: Lattice Vibrations
  • Lesson 49: Transport and Equilibrium Properties
  • Lesson 50: Optical Properties

Lessons in Volume 5

  • Lesson 1: Liquids and Interacting Gases
  • Lesson 2: Special States of Matter
  • Lesson 3: The Structure of Condensed Matter
  • Lesson 4: Thermal Physics of Condensed Matter
  • Lesson 5: Mean Field Theory
  • Lesson 6: Critical Phenomena in Condensed Matter and Renormalization
  • Lesson 7: Another Look at Elastic Solids
  • Lesson 8: Correlation and Response
  • Lesson 9: Another Look at Hydrodynamics
  • Lesson 10: Topological Defects
  • Lesson 11: Domain Walls
  • Lesson 12: The Equivalence Principle
  • Lesson 13: Riemannnian Geometry
  • Lesson 14: More Riemannian Geometry
  • Lesson 15: Classical Mechanics in Curved Manifolds
  • Lesson 16: Physics in Curved Manifolds
  • Lesson 17: General Relativity I
  • Lesson 18: General Relativity II
  • Lesson 19: General Relativity III
  • Lesson 20: The Variational Approach
  • Lesson 21: Black Holes
  • Lesson 22: Cosmology
  • Lesson 23: Gravitational Waves
  • Lesson 24: Numerical Relativity
  • Lesson 25: The Fundamental Particles
  • Lesson 26: Pasrticle Experiments
  • Lesson 27: INternal Symmetries and Conserved Quantities
  • Lesson 28: Particle Experiments
  • Lesson 29: Quantum Chromodynamics (QCD)
  • Lesson 30: Electroweak Theory
  • Lesson 31: The Higgs Mechanism
  • Lesson 32: Neutrino Physics
  • Lesson 33: Beyond the Standard Model
  • Lesson 34: N uclear Models
  • Lesson 35: Nuclear Reactions
  • Lesson 36: Fission and Fusion
  • Lesson 37: Robertson-Walker Metric
  • Lesson 38: The Friedmann Models
  • Lesson 39: Age and Distance Scales
  • Lesson 40: The Hubble Constant
  • Lesson 41: The Cosmological Constant
  • Lesson 42: The Thermal Hiistory of the Universe
  • Lesson 43: Gravitational Lensing
  • Lesson 44: Structure Formation
  • Lesson 45: The Cosmic Microwave Background Radiation
  • Lesson 46: Formation of Baryonic Structures
  • Lesson 47: Singularities
  • Lesson 48: The Early Universe
  • Lesson 49: Topological Defects in Cosmology
  • Lesson 50:The Very Early Universe and Inflation

Lessons in Volume 6

  • Lesson 1: Flows in Phase Space
  • Lesson 2: Integrability and Chaos
  • Lesson 3: Parameter-Driven Transformations
  • Lesson 4: Transformation ins Configuration Space
  • Lesson 5: Noncanonical Flows
  • Lesson 6: Transformations in Phase Space
  • Lesson 7: Integrable Canonical Flows
  • Lesson 8: Nonintegrable Canonical Flows
  • Lesson 9: Methods in Chaotic Dynamics
  • Lesson 10: Stellar Structure
  • Lesson 11: Stellar Evolutioon
  • Lesson 12: Compact Objects
  • Lesson 13: Compact Objects
  • Lesson 14: Binary Stars and Accretion
  • Lesson 15: The Solar System
  • Lesson 16: The Interstellar Medium
  • Lesson 17: Globulat Clusters
  • Lesson 18: Galactic Structure and Dynamics
  • Lesson 19: Active Galactic Nuclei
  • Lesson 20: The Intergalactic Medium
  • Lesson 21: Introduction to the Atmosphere
  • Lesson 22: Atmospheric Thermodynamics
  • Lesson 23: Atmsopheric Radiation
  • Lesson 24: Atmospheric Fluid Dynamics
  • Lesson 25: Chemical Reactions
  • Lesson 26: Stratospheric Chemistry
  • Lesson 27: Remoe Sensing
  • Lesson 28: Climate and Climate Change
  • Lesson 29: Atmospheric Modeling
  • Lesson 30: Organic Chemistry
  • Lesson 31: Molecular Modeling
  • Lesson 32: Molecular Biophysics I: Biopolymers
  • Lesson 33:Molecular Biophysics II: Membranes
  • Lesson 34: Bioenergetics
  • Lesson 35: Biomechanics
  • Lesson 36: Neurobiophysics
  • Lesson 37: Physical Aspects of Computing
  • Lesson 39: A Single Qubit
  • Lesson 40: Multiple Qubits
  • Lesson 41: Quantum Programming
  • Lesson 42: Quantum Protocols
  • Lesson 43: Quantum Algorithms
  • Lesson 44: Science Communication
  • Lesson 45: Peer Review Simulation
  • Lesson 46: Ethics in Physics Research
  • Lesson 47: Intellectual Property in Physics
  • Lesson 48: The Philosophy of Physics
  • Lesson 49: Final Project
  • Lesson 50: Project Presentation and Defense