Differential Equations and Fourier Analysis for Physics (250-0-1)

Instructors

Michelle Driscoll

Meeting Info

Technological Institute F281: Mon, Wed, Fri 12:00PM - 12:50PM

Overview of class

This course teaches differential equations and Fourier methods as mathematical tools for modeling, interpreting, and predicting the behavior of physical systems. The emphasis here is on the physics mindset: using structure, approximation, and physical reasoning to apply the most effective methods. Selected topics include ordinary and partial differential equations, Fourier series and transforms, canonical systems such as the wave, heat, and Laplace equations, and basic numerical methods.

Registration Requirements

PHYSICS 135-1, MATH 230-1, MATH 240, or equivalents

Learning Objectives

This course teaches differential equations and Fourier methods as mathematical tools for modeling, interpreting, and predicting the behavior of physical systems. The emphasis here is on the physics mindset: using structure, approximation, and physical reasoning to apply the most effective methods. By the end of the course, students will be able to:

•Formulate ordinary and partial differential equations that describe physical systems and identify the appropriate initial or boundary conditions for well-posed problems
•Solve linear ODEs—including coupled and inhomogeneous equations—using characteristic equations, particular solutions, and related methods, and interpret transient and steady-state behavior in physical terms
•Use Fourier series and Fourier transforms to represent functions, solve differential equations, and translate between real-space and frequency-domain descriptions
•Apply orthogonality, inner products, and eigenfunction expansions to solve canonical PDEs including the wave, heat, and Laplace equations
•Implement basic numerical methods, including Euler schemes, ODE solvers, FFTs, and simple PDE algorithms, to approximate solutions and evaluate the reliability of numerical results

Class Materials (Required)

Garg, Anupam, Mathematics with a Scientific Sensibility, https://doi.org/10.21985/n2-d1sg-p781

Class Attributes

SoC Mathematics, Science, and Technology Distro

Enrollment Requirements

Enrollment Requirements: Prerequisites: PHYSICS 135-1 or PHYSICS 140-1, MATH 230-1, MATH 240-0, or equivalents