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.

Volume 1: Fundamentals of Math and Physics

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

Lesson 1: How to Learn This Stuff on Your Own
Lesson 2: Introduction to Theoretical Physics
Lesson 3: Numbers and Operations
Lesson 4: Algebraic Expressions
Lesson 5: Introduction to the Wolfram Language
Lesson 6: Solving Linear Equations
Lesson 7: Quadratic Equations
Lesson 8: Symbolic Computation in the Wolfram Language and Higher-Order Equations
Lesson 9: Inequalities
Lesson 10: Programming in the Wolfram Language
Lesson 11: Logic and Proof
Lesson 12: Basic Geometry for Physics
Lesson 13: Physical Quantities and Units
Lesson 14: Sets, Relations, and Functions
Lesson 15: Trigonometry
Lesson 16: Coordinate Geometry, Vectors, and Matrices
Lesson 17: Plotting Functions in the Wolfram Language
Lesson 18: Calculus 1: Limits and Continuity
Lesson 19: Interactive Programming and Visualizations in the Wolfram Language
Lesson 20: Calculus 2: Differentiation in One Variable
Lesson 21: Logarithms and Exponents
Lesson 22: Calculus 3: Applications of Derivatives
Lesson 23: Calculus 4: Integration in One Variable
Lesson 24: Calculus 5: Techniques of Integration
Lesson 25: Calculus 6: Infinite Series
Lesson 26: Calculus 7: Power Series
Lesson 27: Random Processes in Physics
Lesson 28: Data Analysis in Physics
Lesson 29: Matrices and Determinants
Lesson 30: Linear Algebra
Lesson 31: Quadratic Forms and Diagonalization
Lesson 32: Kinematics
Lesson 33: First-Order Differential Equations
Lesson 34: Newton's Laws of Motion
Lesson 35: Second-Order ODEs
Lesson 36: Solving Differential Equations Numerically
Lesson 37: Multivariable Calculus
Lesson 38: Work, Energy, and Power
Lesson 39: Systems of Particles, Linear Momentum and Collisions
Lesson 40: Vector Calculus
Lesson 41: Rigid Bodies and Rotational Motion
Lesson 42: Using Matrices for System Dynamics
Lesson 43: Oscillations
Lesson 44: Complex Numbers in Dynamics
Lesson 45: Basic Thermodynamics
Lesson 46: Introducing Partial Differential Equations
Lesson 47: Introducing Continuum Mechanics
Lesson 48: Waves and Sound
Lesson 49: Solving Wave Equations
Lesson 50: End-of-Year Project

Volume 2: Intermediate Mathematics and Classical Physics

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

Volume 3: Advanced Classical Physics and an Introduction to Modern Physics

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

Volume 4: Quantum Mechanics and Statistical Mechanics

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

Volume 5: Advanced Modern Physics

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

Volume 6: Advanced Topics: Chaos Theory, Astrophysics, Atmospheric Physics, Biophysics, Quantum Computing

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