1 Introduction 1.1 Why Numerical Methods? Engineers and scientists frequently encounter linear and nonlinear mathematical equa- tions, integrals, differential equations, and data to be manipulated. Sometimes the ma- nipulations to be performed are easy and straightforward; often they are not. This is particularly true of nonlinear problems, that is, problems in which variables occur as products, including products of themselves, or as functions of transcendental functions, like the trigonometric or logarithmic relations. If the mathematics to be performed can- not be done in closed form (i.e., an exact analytic symbolic solution is obtained), recourse must be made to numerical approximations. Fortunately, these methods, when properly understood and used, are powerful and accurate. It should be understood that recourse to a numerical solution is always a fall-