(324a) Mathematics Taught in Chemical Engineering, What Material Should Be Covered? What Should Be the Complexity?

This presentation will discuss the contents of mathematics that should be taught in the undergraduate programs of chemical engineering, what material should be covered, what is the complexity and where begins the border with the mathematics taught in graduate programs. According to a performed study, so far, in the best cases, the maximum level is the topic of partial differential equations using separation of variables, including Fourier series and Bessel functions. However, it is possible to teach more, according to the experience of the authors. Several exercises are presented, they were solved and presented as seminars by the authors, who are or were students in the undergraduate program of chemical engineering in Unviersidad Autonoma de Zacatecas, Mexico. The solved problems are: 1) A model of laminar flow through a lubricated tube. This is one problem of momentum transport more complicated than that for a tube filled with only one fluid, and without lubricant, since it leads to the formulation of one set of differential equations requiring the use of continuity boundary conditions for determining the velocity profiles of both fluids. 2) Slow flow over a solid sphere. This problem requires the analysis of momentum transport and more complicated procedures than those traditionally taught in the undergraduate programs, it leads to the deduction of Stokes law. 3) Transient flow inside a cylindrical tube. This problem requires the solution of a partial differential equation that describes the starting of a liquid flow, due to a pressure difference. The Sturm Liouville problem is solved, the variable separation method is used, and one of the differential equations is solved using Bessel functions since it has variable coefficients. The velocity profiles changing with time are determined. 4) Non stationary heat conduction in a cylindrical metallic bar. The partial differential equation describing the heating of a metallic bar in one of its ends, with different boundary conditions, is solved using finite differences and the weighted residual methods, mainly, the orthogonal collocation method. 5.- Potential flow over a cylindrical tube. A partial differential equation is solved using the method of separation of variables and the Euler equation to find the angular component of velocity. Once the capacity of the undergraduate students to solve these kinds of problems is reached, an optional applied mathematics undergraduate course may be proposed. This course may include, among others, the indicated topics above. It is considered that the knowledge, proficiency and familiarity with mathematics, will guide and motivate the students to pursue graduate studies and to perform scientific research.