Course Notes

• Syllabus
• Course Notes
• Homework
• Schedule

Detailed Learning Outcomes

• Course Concepts

Unit I – Probability Theory and Stochastic Processes

• Lecture 1 - Probability Basics, link
• Lecture 2 - Probability Distributions, link
  • Supplement – Examples of Probabililty Distributions (Jupyter notebook)
• Lecture 3 - Moments, link
  • Supplement – Taking Fourier Transforms (Mathematica notebook)
• Lecture 4 - Central Limit Theorem, link
• Lecture 5 - Bivariate Distribtutions, link
  • Supplement – 2D Normal Distribution (Jupyter notebook)
• Lecture 6 - Random Vectors, link
• Lecture 7 - Random Fields, link
• Lecture 8 - Stochastic Processes, link
  • Supplement – Example Stochastic Processes (Slide Deck)
• Lecture 9 - Markov Processes, link
• Lecture 10 - Stochastic Differential Equations, link

Unit 2 – Mechanics and Phase Space

• Lecture 11 - Lagrangian Mechanics, link
  • Story of your life
• Lecture 12 - Hamiltonain Mechanics and Phase Space, link
  • Supplement – Classical Mechanics Examples (Jupyter notebook)
• Lecture 13 - Waves and Particles, link
  • 3Blue1Brown on the uncertainty principle
  • Double slit experiment from Wikipedia
  • Image of traveling and standing waves from Wikipedia
• Lecture 14 - Quantum Mechanics, link
  • Supplement – Quantum Harmonic Oscillator (Jupyter notebook)
  • Feynman lectures on QM
  • 3Blue1Brown on the physics of light and QM

Unit 3 – Ensemble Theory

• Lecture 15 - Microcanonical Ensemble, link
• Lecture 16 - Thermodynamics from Ensembles, link
• Lecture 17 - The Canonical Ensemble, link
  • Supplement – Distributions of Energy of NVT Ensembles (Jupyter notebook)
• Lecture 18 - Thermodynamics in the NVT Ensemble, link
  • Supplement – Gibbs Entropy Formula for a Gaussian (Jupyter notebook)
• Lecture 19 - The Grand Canonical Ensemble, link
• Lecture 20 - The NPT Ensemble and Fluctuations, link
  • Supplement – Ideal Gas Entropy (Jupyter notebook)

Unit 4 – Pure Component Phase Behavior

• Lecture 21 - The Postulates and Laws of Thermodynamics, link
• Lecture 22 - Thermodynamics of Phase Equilibrium, link
• Lecture 23 - The van der Waals Fluid, link
  • Supplement – Thermodynamic Properties of the van der Waals Fluid, link
• Lecture 24 - Van der Waals Phase Behavior, link
  • Supplement – van der Waals Phase Diagram (Jupyter notebook)
• Future plans: liquids, solids, mixtures

Unit 5 – Soft Materials: polymers, colloids, electrolytes

• Next year!

Unit 6 – Non-equilibrium: transport and stochastic kinetics

• Next year!

Old Notes

• Polymer Physics Notes from Spring 2023: Link
• Stat Thermo Notes from Fall 2024: Link