Welcome to Mathematical Modeling in Physics#
PHY 415, called, “Mathematical Methods for Physicists” is a course the brings together many of the mathematical approaches that we commonly use in physics and apply them to variety of problems. In this course, we will take a modeling-based approach where we focus on the mathematical descriptions of physical phenomenon and determine what mathematical and analytical approaches are useful in exploring those models.
To get a sense of the course, please read all the pages associated with our syllabus.
Updates#
Last updated: 20 Nov 2023
Site updates
The last activity for class is posted
Upcoming Deadlines
The last project is due 14 Dec 2023.
Learning Objectives#
In this course, you will learn to:
investigate physical systems using a variety of tools and approaches,
construct and document a reproducible process for those investigations,
use analytical, computational, and graphical approaches to answer specific questions in those investigations,
provide evidence of the quality of work using a variety of sources, and
collaborate effectively and contribute to a inclusive learning environment
Table of Contents#
- 29 Aug 23 - Activity: What is a Model?
- 29 Aug 23 - Notes: Simple Harmonic Oscillator
- 31 Aug 23 - Notes: Frames and Coordinates
- 31 Aug 23 - Activity: Frames and Coordinates
- 5 Sept 23 - Notes: Lagrangian Dynamics
- 5 Sep 23 - Activity: Calculus of Variations and Lagrangian Dynamics
- 7 Sept 23 - Notes: Numerical Integration in 1D
- 7 Sep 23 - Activity: Numerical Integration and More Lagrangians
- 12 Sept 23 - Notes: Dynamical Systems and Phase Space
- 12 Sep 23 - Activity: The Dynamical Systems Approach and Phase Portraits
- 14 Sept 23 - Conducting a complete analysis of an ODE
- 19 Sep 23 - Notes: Heading towards Chaos
- 19 Sep 23 - The Duffing Oscillator
- 26 Sept 23 - Notes: Maxwell’s Equations
- 26 Sept 23 - Notes: Static Fields
- 26 Sep 23 - Activity: Electrostatic Fields
- 28 Sep 23 - Activity: Superposition of Fields
- 3 Oct 23 - Notes: Electric Potential - a scalar field
- 3 Oct 23 - Activity: PDEs and Separation of Variables
- 5 Oct 23 - Activity: Solving PDEs in Spherical Coordinates
- 9 Oct 23 - Notes: Method of Relaxation
- 10 Oct 23 - Activity: Matching Boundary Conditions and Plotting the Potential
- 12 Oct 23 - Activity: Method of Relaxation
- 16 Oct 23 - Notes: Coupled Oscillations
- 16 Oct 23 - Notes: Introduction to Waves
- 17 Oct 23 - Activity: Normal Modes
- 19 Oct 23 - Activity: Normal Modes of N Coupled Oscillators
- 25 Oct 23 - Notes: Solutions to The Wave Equation
- 26 Oct 2023 - Activity: 1-Dimensional Travelling Waves
- 30 Oct 2023 - Notes: Deconstructing Waves
- 31 Oct 23 - Activity: Signal Deconstruction
- 2 Nov 23 - Activity: Automated Signal Deconstruction & Reconstruction
- 6 Oct 23 - Notes: Fast Fourier Transform
- 7 Nov 23 - Activity: The Fast Fourier Transform
- 9 Nov 23 - Activity: Applying The Fast Fourier Transform
- 13 Nov 23 - Notes: Applications of FFTs
- 14 & 16 Nov 23 - Using the FFT with Real Data
- 20 Nov 23 - Notes: Random Processes
- Macrostates
- 21 Nov 23 - Activity: Introduction to Random Processes
- 27 Nov 23 - Notes: Counting and Combinatorics
- 27 Nov 23 - Notes: Monte Carlo Simulations
- 28 Nov 23 - Activity: Model of Two Bodies in Thermal Contact
- 30 Nov 23 - Activity: Monte Carlo Integration
- 4 Dec 23 - Notes: Markov Chain Monte Carlo Modeling
- 7 Dec 23 - Activity: Modeling
- Updated Rubric for Worked Problems and Projects
- Worked Problem Assignment 1
- Worked Problem Assignment 2
- Project 1 - Classical Mechanics and ODEs
- Worked Problem Assignment 3
- Worked Problem Assignment 4
- Project 2 - PDEs, Laplace’s Equation, and the Method of Relaxation
- Worked Problem Assignment 5
- Worked Problem Assignment 6
- Project 3 - Waves and Fourier Analysis
- Worked Problem Assignment 7
- Project 4 - Probabilistic Modeling