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Modeling and numerical approximations are one of the most important scientific subjects because of its numerous engineering applications. In this book, we are interested in the numerical analysis The objective of this book is to determine methods to calculate the numerical value of the solution of partial derivative equations or a system of equations, by using a computer. The first part is devoted to the resolution of the Partial Differential Equations by using finite difference method. After a definition and classification of the equations, and the calculus of partial derivatives, we present the consistency of the used scheme of discretization with the origin equation and its stability as well as the convergence of the approximate solution. The second part is devoted to principles of the control volume method applied to the transport phenomena by diffusion and by both diffusion and convection in steady and transient states.