Mathematical modeling is at the core of modern approach to design and analysis of engineered systems. Numerical analysis plays a key role in the process of design and analysis. To observe a physical phenomenon, we need sensors or measuring instruments that can collect observations. A sensor transform an original physical variable of interest into a measurable physical quantity. A collection of measured observations can then be used to interpret the behavior of the physical system under consideration. In the context of understanding behavior of a mathematical model of an engineered system, the numerical analysis plays a role analogous to a sensor or a measuring instrument. The mathematical model is often a collection of complex, coupled and nonlinear differential and / or algebraic equations, which can seldom be solved analytically. We, however, know how to solve, exactly or approximately, certain class of problems, which have some ideal simplified structure. Numerical analysis helps in transforming a mathematical problem into a computable form, which can be handled using one or more of known analytical / approximate solution approaches. Approximate solutions constructed using numerical analysis can then be used to understand a system behavior. The transformation process, however, takes its toll. Like sensors add their own dynamics and / or errors (noise) to measured physical quantities, the numerical procedures distort the true solution of the mathematical problem at hand. To keep these distortions at the minimum, we need to have a thorough understanding of how these numerical solution schemes or recipes are concocted. Like in the area of measuring instruments, where one can go on refining capabilities of an instrument, very often there a scope to come up with better and better recipe for constructing an approximate solution that is closer to the true solution. A deeper understanding of how numerical recipes are constructed becomes necessary of you have to concoct a new or improved recipe to solve a given problem at hand.