ABSTRACT
This chapter reviews the fundamentals of the theory behind the numerical techniques accessible in programs such as Matlab® or Mathematica and explores readers to novel applications in engineering. Numerical methods are techniques by which real world problems are simplified into mathematical models and then mathematical problems are formulated so that they can be solved using arithmetic and logic operations. Numerical computation introduces numerical errors, which are generally defined based on accuracy and precision. There are two kinds of numerical errors, namely, the round-off error and the truncation error. The finite difference method is a numerical method to approximate derivatives using finite difference equations. The chapter reviews matrix notations and computation, and discusses how to use finite difference methods for solving boundary value problems, sets of linear and nonlinear algebraic equations. A boundary value problem is a differential equation with a set of boundary condition constraints.
