Because linear equations are so much easier to solve than nonlinear ones, much research across a range of disciplines is devoted to finding linear approximations of nonlinear phenomena.

Use Newton's Method with the initial approximation x1 =1 x 1 = 1 to find x2 x 2 and x3, x 3, the second and the third approximations to the root a a of the equation x6 −x−1 =0. x 6 x 1 = 0 You may use ...

Formulate linear and integer programming problems for solving commonly encountered optimization problems. Understand how approximation algorithms compute solutions that are guaranteed to be within ...

We construct explicit solutions of the inhomogeneous parabolic wave equation in a linear and quadratic approximation. As examples, oscillating laser beams in a 1D parabolic waveguide, spiral light ...