Advanced Differential Equations

A course covering advanced techniques for solving complicated ordinary and partial differential equations, alongside foundational numerical methods. Topics include modeling physical phenomena, power series solutions, Fourier expansions, and analytical algorithmic implementations. Role: Asstistant Professor

Offered: Spring 2025–26

Topics covered:

• Modeling physical systems with first-order ODEs
• Second-order ODEs with variable coefficients
• Power series solutions and the Frobenius method
• Fourier Series and orthogonal functions
• Solutions to boundary value problems and Sturm-Liouville methods
• Subtleties of solving Partial Differential Equations (PDEs)
• Separation of Variables method for PDEs
• Numerical solution of ODEs and PDEs in Julia/Python

Resources:

• Syllabus
• Lecture Notes