A Byte of PhysicsLogo

A Byte of Physics

Physics, explained from a programmer's point of view. Each lesson turns a physical question into inputs, state, a rule, observable output, and a testable limit.

Start with From Equations to Code · Open the shared glossary

Table of contents

PART I — COMPUTATIONAL FOUNDATIONS OF PHYSICS

1. Physics as Computation
Why Code Makes Physics Easier
From Equations to Code
What Can and Cannot Be Simulated
Numerical vs Symbolic Thinking
Units, Precision, and Floating-Point Errors
Your First Physics Notebook
2. Measurement, Units, and Uncertainty
Physical Quantities as Data
SI Units as Data Types
Dimensional Analysis with Code
Significant Figures and Rounding Errors
Propagation of Uncertainty (Monte Carlo approach)
Symbolic Unit Checking

PART II — MOTION AS DATA

3. One-Dimensional Motion
Position, Velocity, and Acceleration as Functions
Discrete vs Continuous Motion
Numerical Differentiation and Integration
Solving Motion with Initial Conditions
Piecewise Motion Models
Motion with Constraints
4. Vectors and Coordinate Systems
Vectors as Arrays
Coordinate Systems and Basis Changes
Dot and Cross Products Computationally
Vector Fields
Visualizing Vectors and Fields
Symbolic Vector Calculus
5. Motion in 2D and 3D
Parametric Motion
Projectile Motion as Simulation
Relative Motion
Curvilinear Coordinates
Numerical Stability in Trajectory Simulation
Constraints and Manifolds

PART III — FORCES, ENERGY, AND CONSERVATION

6. Forces and Laws of Motion
Newton’s Laws as Update Rules
Free-Body Diagrams in Code
Force Models as Functions
Solving Coupled Equations of Motion
Constraint Forces
Numerical Instability and Chaos
7. Energy, Work, and Power
Work as Path Integrals
Kinetic Energy from Data
Conservative vs Non-Conservative Forces
Power and Energy Flow
Numerical Energy Conservation
Symbolic Energy Methods
8. Potential Energy and Conservation Laws
Potential Energy Landscapes
Energy-Based Motion Solvers
Stability and Equilibrium Points
Phase Space Visualization
Energy Minimization
Symmetry and Conservation
9. Momentum and Collisions
Linear Momentum as State
Center of Mass Computation
Elastic and Inelastic Collisions
Many-Body Systems
Momentum Conservation Tests
Impulse and Time Integration

PART IV — ROTATION AND CONTINUOUS SYSTEMS

10. Rotational Motion
Angular Variables as State Vectors
Torque as Cross Product
Moment of Inertia by Integration
Rotational Dynamics Simulation
Coupled Translational–Rotational Motion
Numerical Drift in Rotation
11. Rolling, Angular Momentum, and Gyroscopes
Rolling Constraints
Angular Momentum Conservation
Gyroscopic Stability
Precession and Nutation
Rigid Body Approximation
Symbolic Rigid Body Models
12. Equilibrium and Elasticity
Static Equilibrium as Linear Systems
Stress and Strain
Elastic Energy
Deformation Models
Numerical Solutions of Elastic Systems
Stability Analysis

PART V — FIELDS AND CONTINUUM PHYSICS

13. Gravitation
Gravitational Fields as Vector Fields
Orbits as Numerical Experiments
Two-Body and N-Body Problems
Escape Velocity and Energy
Stability of Orbits
Chaos in Gravity
14. Fluids
Fluids as Continuous Media
Pressure Fields
Buoyancy Simulations
Flow Rate and Continuity
Bernoulli’s Equation Computationally
Introduction to CFD Concepts

PART VI — OSCILLATIONS, WAVES, AND SIGNALS

15. Oscillations
Simple Harmonic Motion as ODE
Damped Oscillations
Driven Systems and Resonance
Phase Space and Stability
Nonlinear Oscillators
Numerical Chaos
16. Waves I — Mechanical Waves
Waves as Propagating Data
Superposition Principle
Standing Waves
Energy Transport
Boundary Conditions
Fourier Perspective
17. Waves II — Analysis and Transformations
Fourier Series
Fourier Transform
Wave Packets
Dispersion
Numerical Signal Processing
Information in Waves

PART VII — THERMODYNAMICS AND STATISTICS

18. Temperature and the First Law
Temperature as Emergent Quantity
Internal Energy Models
Work and Heat in Simulations
Thermodynamic Processes
Cycles and Engines
Energy Accounting in Code
19. Kinetic Theory of Gases
Microscopic vs Macroscopic Views
Molecular Dynamics Simulations
Velocity Distributions
Pressure from Collisions
Equipartition Theorem
Emergence from Chaos
20. Entropy and the Second Law
Probability and Microstates
Entropy as Information
Irreversibility in Simulation
Heat Death and Equilibrium
Statistical Fluctuations
Computational Arrow of Time

PART VIII — ELECTROMAGNETISM AS FIELD THEORY

21. Electrostatics
Charge as Discrete Entities
Coulomb’s Law as Field Generator
Electric Field Visualization
Continuous Charge Distributions
Energy in Fields
Symbolic Field Calculations
22. Electric Potential and Capacitance
Scalar Potentials
Field–Potential Relationship
Equipotential Surfaces
Capacitor Models
Energy Storage
Numerical Boundary Problems
23. Currents and Circuits
Current as Charge Flow
Resistance and Microscopic View
Kirchhoff’s Laws as Linear Algebra
Transient Analysis
Power Dissipation
Circuit Simulation
24. Magnetism and Induction
Magnetic Fields from Motion
Lorentz Force Simulations
Fields Due to Currents
Electromagnetic Induction
Inductance Models
Energy in Magnetic Fields
25. Maxwell’s Equations and EM Waves
Fields as Partial Differential Equations
Maxwell’s Equations Symbolically
EM Wave Solutions
Polarization
Energy and Momentum in EM Waves
Numerical Field Evolution

PART IX — LIGHT, QUANTA, AND MODERN PHYSICS

26. Geometric and Wave Optics
Reflection and Refraction
Mirrors and Lenses
Interference
Diffraction
Wave Properties of Light
Optical Instruments
27. Relativity
Spacetime as Geometry
Lorentz Transformations
Time Dilation and Length Contraction
Relativistic Energy and Momentum
Causality and Light Cones
Computational Relativity
28. Quantum Beginnings
Photons and Quantization
Matter Waves
Schrödinger Equation Numerically
Operators and Observables
Wavefunction Evolution
Measurement and Probability
29. Atoms and Solids
Atomic Structure
Energy Levels
Electron Bands
Conduction Models
Semiconductors
Computational Materials
30. Nuclear and Particle Physics
Nuclear Structure
Radioactive Decay Simulation
Nuclear Energy
Fundamental Particles
Standard Model Overview
Cosmology and the Big Bang

EPILOGUE — THINKING LIKE A COMPUTATIONAL PHYSICIST

Epilogue
Physics as Modeling
When Models Fail
Numerical Ethics
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