_________________________________________________________________________________ a Department of Water Engineering, Faculty of Agriculture, University of Tabriz, Tabriz, Iran. b School of Engineering, University of St. Thomas, 2115 Summit Avenue St. Paul, Minnesota-55105, USA. ++ Professor; *Corresponding author: E-mail: jpabraham@stthomas.edu; Chapter 11 Print ISBN: 978-81-19102-06-8, eBook ISBN: 978-81-19102-02-0 On the Finite Differences Method Using Microsoft Excel Farzin Salmasi a++ and John Abraham b++* DOI: 10.9734/bpi/rhmcs/v6/5540A Abstract In numerical analysis, finite-difference methods (FDM) are a class of numerical techniques for solving differential equations by approximating derivatives with finite differences. Both the spatial domain and time interval (if applicable) are discretized, or broken into a finite number of steps, and the value of the solution at these discrete points is approximated by solving algebraic equations containing finite differences and values from nearby points. Finite difference methods convert ordinary differential equations (ODE) or partial differential equations (PDE), which may be nonlinear, into a system of linear equations that can be solved by matrix algebra techniques. Modern computers can perform these linear algebra computations efficiently which, along with their relative ease of implementation, has led to the widespread use of FDM in modern numerical analysis. Today, FDMs are one of the most common approaches to solving PDEs, along with finite element methods. This paper suggests a solution by building up a library of solvers using spreadsheets, with the effect that the encapsulated knowledge of building modelling solvers can later be used for education or real-world problems. This study raises concern about the encapsulated body of knowledge that has contributed to the emergence and the establishment of modelling software applications since 1980. This body of knowledge comprises a deep understanding of differential equations that describe physical problems and their numerical transformation into systems of linear equations. Keywords: Finite difference method; ordinary differential equations; numerical computations; partial differential equations. 1 Introduction Gaining insight into reality and invoking critical thinking in students’ minds are two important pedagogical issues in engineering and sciences. Mathematical models supported by software applications facilitate gaining insight into the physical but they are poor for training critical thinking or for encapsulating the hardcore mathematical equations describing the problems. Arguably, an insight is a comprehensive