The course gives an introduction to analytical techniques for partial differential equations, in particular to separation of variables. In addition the course treats qualititative properties of ...

We study the classical linear partial differential equations: Poisson's equation and the heat equation. We learn about representation formulas for solutions, maximum principles, and energy estimates.

Generate an unlimited number of Chladni patterns by solving the rectangular and polar wave equation via separation of variables and eigenvalues.

Introduction to differential equations with an emphasis on engineering applications. Topics include first-order equations, higher-order linear equations with constant coefficients, and systems of ...

Nonlinear waves; integrable systems; solitons; mathematical modeling in social and behavioral science. The study of wave phenomena by means of mathematical models often leads to a certain class of ...

Abstract: Problems involving the classical linear partial differential equations of mathematical physics can be reduced to algebraic ones of a very much simpler structure by replacing the ...

py-pde is a Python package for solving partial differential equations (PDEs). The package provides classes for grids on which scalar and tensor fields can be defined. The associated differential ...

If pure math can teach us anything, it’s this: occasionally, your special interest might just change the world. For Joshua ...

In math and computer science, researchers have long understood that some questions ... Two new approaches allow deep neural networks to solve entire families of partial differential equations, making ...

Known for its advanced computational capabilities, Julius has garnered the trust of over 1.2 million users worldwide. With Julius, you can solve complex math equations, including algebra, calculus, ...