Methods for solving linear, ordinary, and partial differential equations of mathematical physics. Green's functions, distribution theory, integral equations, transforms, potential theory, diffusion ...

Delay differential equations (DDEs) extend classical ordinary differential equations by incorporating dependencies on past states. This inclusion of time delays is critical for accurately modelling ...

To give you experience solving larger, more difficult problems involving multiple concepts, there will be three computer-based projects assigned during the semester. Suggested software is Matlab, ...

The study of large-time behavior of solutions to partial differential equations is a fundamental pursuit in mathematical analysis, with profound ...

Brownian motion and Langevin's equation. Ito and Stratonovich Stochastic integrals. Stochastic calculus and Ito's formula. SDEs and PDEs of Kolmogorov. Fokker-Planck, and Dynkin. Boundary conditions, ...

This work establishes the first asymptotic stability result for multi-wave patterns in damped wave equations with partially linearly degenerate flux. The authors prove that global solutions converge ...

Digital prototyping has become an essential tool to speed design cycles. It lets designers replace expensive hardware prototypes with virtual models to predict system behavior, providing insight into ...