Japanese mathematician Masaki Kashiwara wins Abel Prize for contributions to algebraic analysis and representation theory at ...

Linear and quasilinear first order PDE. The method of characteristics. Conservation laws and propagation of shocks. Basic theory for three classical equations of mathematical physics (in all spatial ...

Abstract: Curved spaces, such as surfaces, provide a rich setting for the study of partial differential equations (PDEs). Building upon the extensive research conducted on PDEs in flat spaces, the ...

Abstract: In this paper, a novel approach leveraging artificial neural networks is introduced to approximate solutions for partial differential equations. The one ...

In January I wrote a piece titled “ 5 Physics Equations Everyone Should Know .” Lots of you weighed in with your own ...

A team of international physicists has brought Bayes’ centuries-old probability rule into the quantum world. By applying the ...

Simo Särkkä and Arno Solin (2019). Applied Stochastic Differential Equations. Cambridge University Press. Cambridge, UK. The book can be ordered through Cambridge University Press or, e.g., from ...

It can be tempting to only pay the minimum amount due on your credit card bill each month, but doing so can come with a cost. The minimum payment is the smallest amount of money that you have to pay ...

A 20-story chimney running along the side of a NYCHA building in The Bronx collapsed Wednesday morning, and the FDNY is investigating whether an explosion in the boiler room on the first day of heat ...

First‑order differential equations, linear and separable equations, integrating factors, applications. Second‑order linear differential equations. Fundamental solutions, linear independence, Wronskian ...