The study of chemotaxis, the directed movement of cells or organisms in response to chemical gradients, is fundamentally linked to the development and analysis of partial differential equations (PDEs) ...

Harmonic functions, defined as twice continuously differentiable functions satisfying Laplace’s equation, have long been a subject of intense study in both pure and applied mathematics. Their ...

This is the first part of a two course graduate sequence in analytical methods to solve ordinary and partial differential equations of mathematical physics. Review of Advanced ODE’s including power ...

Partial Differential Equations (PDEs) are central to both pure and applied mathematics. Any quantity which changes in space and time will satisfy certain partial differential equations because the ...