Mathematicians finally understand the behavior of an important class of differential equations that describe everything from ...

Sometimes, it’s easy for a computer to predict the future. Simple phenomena, such as how sap flows down a tree trunk, are straightforward and can be captured in a few lines of code using what ...

Calculation: A representation of a network of electromagnetic waveguides (left) being used to solve Dirichlet boundary value problems. The coloured diagrams at right represent the normalized ...

If today's college students could find a way to get their hands on a copy of Facebook's latest neural network, they could cheat all the way through Calc 3. They could even solve the differential ...

When integrating simple expressions, the constant of integration, the \(+ c\) term, may remain an unknown. The value of \(c\) can be worked out when additional information is given in the question, .

Exact solutions of the Schrödinger equation have long provided fundamental insights into quantum mechanics by furnishing explicit analytical expressions for wave functions and energy spectra. These ...