Code: EQM868 – Fundamental module
Audience: Master´s and Doctoral degree
Teaching hours: 45h
Credits: 3
Content: Sources of computer errors and strategies to minimize them. Development of algorithms for computing nonlinear functions (review of programming logic and application of the concept of truncation error). Solution of systems of linear equations (analysis and minimization of the propagation of rounding errors). Polynomial interpolation using the solution of linear systems and the Lagrange formula. Numerical solution of non-linear equations and systems of non-linear equations. Numerical integration of ordinary differential equations and systems of ordinary differential equations (implicit and explicit methods, truncation errors, and stability). Finite Difference Method for the numerical solution of ordinary and partial differential equations (order of approximations, contour treatment strategies, mesh convergence). Solutions to Specific Problems linked to the Fundamentals of Chemical Engineering and Chemical Processes (projects).
Bibliography:
PINTO, J. C., LAGE, P. L. C., Métodos matemáticos em Problemas de Engenharia Química – Série Escola Piloto em Engenharia Química – COPPE/UFRJ, Rio de Janeiro, Editora e-papers, 2001.
CHAPRA, Steven C; CANALE, Raymond P. Numerical methods for engineers. 5th. ed. New York: McGraw-Hill, 2006.
CUTLIP, Michael B; SHACHAM, Mordechai. Problem solving in chemical engineering with numerical methods. Upper Saddle River, NJ: Prentice Hall PTR, 1999.
SPERANDIO, D.; Mendes, J. T.; Silva, L. H. M.; Cálculo Numérico: características matemáticas e computacionais dos métodos numéricos. Ed. Prentice Hall, 2003.
RICE, John R. Numerical methods, software and analysis. New York ; St. Louis: McGraw-Hill, 1983.