Studies properties and solutions of partial differential equations. Covers methods of characteristics, well-posedness, wave, heat and Laplace equations, Green's functions, and related integral ...

Course on using spectral methods to solve partial differential equations. We will cover the exponential convergence of spectral methods for periodic and non-periodic problem, and a general framework ...

This is the 2nd part of a two course graduate sequence in analytical methods to solve partial differential equations of mathematical physics. Review of Separation of variables. Laplace Equation: ...

Finite element methods (FEM) constitute a foundational numerical approach for solving partial differential equations by discretising complex domains into smaller, manageable subdomains known as ...

Boundary value problems (BVPs) and partial differential equations (PDEs) are critical components of modern applied mathematics, underpinning the theoretical and practical analyses of complex systems.