Computer simulation is beginning to challenge theoretical mathematics as the dominant solution technique in applied and engineering mathematics. This debate can only benefit engineering education, as computer simulation presents so many solution approaches (to difficult engineering problems) that are not available with the traditional mathematics techniques. The author's experience teaching an undergraduate simulation based course called Computer Optimization is presented along with the results of teaching an MBA course called Managerial Problem Solving. The MBA course is frequently taken by engineers and also makes heavy use of simulation, computer packages and traditional calculus based solution techniques. The course is a good vehicle for comparisons. Two nonlinear multivariate problems also are presented and solved with simulation, in order to make the comparisons more specific.