Ordinary differential equations (ODEs) are also called initial value problems because a time zero value for each first-order differential equation is needed. The following is an example of a ...

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 ...

Approximate solutions to more complex equations can be found using a process called iteration. Iteration means repeatedly carrying out a process. To solve an equation using iteration, start with an ...

We examine a heat problem in 1D. Assume that a rod with given temperature distribution u_0(x) is cooled to temperature 0 on the exteriors at 0 and pi. Assume that u(x,t) for the Temperature at point x ...

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 ...