Calendar#

In this course, we will cover four principal topics in physics (in this order):

  1. Classical Mechanics and Ordinary Differential Equations

  2. Electromagnetism and Partial Differential Equations

  3. Waves and Fourier Analysis

  4. Statistical Mechanics and Monte Carlo models

The class is roughly broken into equal parts for each section. Below we indicate how each week will be spent. This is subject to change based on your input and feedback. But roughly you can expect the following:

Classical Mechanics and Ordinary Differential Equations#

  • Week 1 - Introduction to the Course, Python, and Jupyter notebooks; Modeling; Coordinate Systems and Frames

  • Week 2 - Calculus of Variations; Lagrangian Mechanics; Equations of Motion; Numerical Integration and Trajectories

    • Worked Problem 1 Assigned; due end of Week 3; 9/15

  • Week 3 - Dynamical Systems; Phase Space; Stability

    • Worked Problem 2 Assigned; due end of Week 4; 9/22

  • Week 4 - Chaos; Dynamical Analysis of ODEs

  • Project 1 (CM and ODEs) Due 9/29

Electromagnetism and Partial Differential Equations#

  • Week 5 - Introduction to Electrostatics; Vector fields; Numerical superposition; Laplace’s Equation; Separation of Variables

    • Worked Problem 3 Assigned; due end of Week 6; 10/6

  • Week 6 - 2D Partial Differential Equations; Boundary Conditions; Numerical Solutions; Method of Relaxation

    • Worked Problem 4 Assigned; due end of Week 7; 10/13

  • Week 7 - Magnetic Fields; Maxwell’s Equations; Vector Calculus; EM Wave Equation

  • Project 2 (EM and PDEs) Due 10/20

Waves and Fourier Analysis#

  • Week 8 - Introduction to Waves; Normal Modes; Matrix Methods; Beats and Superposition

    • Worked Problem 5 Assigned; due end of Week 9; 10/27

  • Week 9 - Wave formulations; Complex analysis; the Fourier Transform

    • Worked Problem 6 Assigned; due end of Week 10; 11/3

  • Week 10 - Discrete Fourier Transform; Fast Fourier Transform; Applications of Fourier Analysis

  • Project 3 (Waves and Fourier) Due 11/10

Statistical Mechanics and Monte Carlo models#

  • Week 11 - Distributions; Counting and Probability; Boltzmann Distribution

    • Worked Problem 7 Assigned; due end of Week 12; 11/17

  • Week 12 - Statistical Mechanics; The Ideal Gas; Monte Carlo methods

    • Worked Problem 8 Assigned; due end of Week 14; 12/1

  • Week 13 - Thanksgiving break

  • Week 14 - Markov Chains; Metropolis Algorithm; Applications

  • Project 4 (Distributions and Monte Carlo) Due 12/8