Mathematical Methods for Physicists (PHY 415)

Welcome to the course materials for PHY 415: Mathematical Methods for Physicists, a comprehensive exploration of mathematical approaches used throughout physics.

📚 About This Repository

This repository contains the complete course materials for PHY 415 (Fall 2023), a course designed to bring together mathematical approaches commonly used in physics and apply them to a variety of problems. The site is built with Hugo and features interactive notes, activities, and assignments.

• Course Title: Mathematical Methods for Physicists
• Instructors: Danny Caballero, Alia Valentine
• Content: Lecture notes, activities, problem sets, and projects
• Audience: Physics students and anyone interested in mathematical modeling in physics

🧭 Structure

• content/ — All course content organized by unit
  • 0---intro-and-syllabus/ — Course overview, learning objectives, and syllabus
  • 1---mechanics-and-odes/ — Mechanics, differential equations, and phase space analysis
  • 2---em-and-pdes/ — Electromagnetism and partial differential equations
  • 3---waves-and-oscillations/ — Wave equations, Fourier methods, and FFT
  • 4---randomness-and-distributions/ — Probability, distributions, and stochastic models
  • assignments/ — Problem sets and projects
  • appendices/ — Reference materials and supplementary topics
• layouts/ — Custom Hugo templates for course content
• static/ — Images, diagrams, and static assets
• config.toml — Hugo configuration

📖 Course Units

Unit 1: Mechanics and ODEs – Covers coordinate systems, Lagrangian mechanics, numerical integration, phase space analysis, and nonlinear dynamics (linearization, Van der Pol oscillator, Duffing oscillator).

Unit 2: E&M and PDEs – Explores electromagnetic fields, electric potential, boundary value problems using separation of variables, relaxation methods, and numerical solutions in Cartesian and spherical coordinates.

Unit 3: Waves and Oscillations – Investigates coupled oscillations, wave equations, solving wave equations analytically, Fourier methods, signal analysis, and fast Fourier transforms (FFT).

Unit 4: Randomness and Distributions – Examines probability, probability distributions, statistical modeling, and stochastic differential equations.

🚀 Building the Site

This site uses Hugo. To build and serve locally:

hugo server

The site will be available at http://localhost:1313/.

To build for production:

hugo

This generates the static site in the public/ directory.

📄 License

Content is licensed under the MIT License.