Recall that the solution of the initial-value problem \(y^\prime=ky\text{,}\) \(y(0)=A\text{,}\) is given by \(\ds y=Ae^{kx}\text{.}\) Solve the following problems ...

Ever since Newton, time evolution in physics has been understood as an initial value problem. This means that we identify the initial positions and momenta of all particles in the system and then ...

Iteration means repeatedly carrying out a process. To solve an equation using iteration, start with an initial value and substitute this into the iteration formula to obtain a new value ...