APPLIED MATHEMATICS AND NUMERICAL METHODS FOR CHEMICAL ENGINEERS

Credit Hours: 3 · Undergraduate Upper-Level

Computer arithmetic, round-off and truncation errors, conditioning. Curve fitting and least squares, nonlinear regression. Systems of nonlinear equations: Picard’s method. Newton-Raphson, continuation methods. Initial Value Problems: Euler’s methods (explicit and implicit); Higher-order Runge-Kutta methods; Adaptive Runge-Kutta methods; Systems of ordinary differential equations; Numerical stability; Stiff systems; Multistep methods. Dynamical Systems: Equilibrium points and their stability, periodic solutions, limit cycles. Boundary Value Problems: ODE and PDE boundary value problems, finite difference approximations, Dirichlet, Neumann and mixed boundary conditions, Poisson’s equation, coupled BVPs. Time-dependent PDEs: Method of lines, numerical stability. Case studies from reaction engineering, thermodynamics, heat and mass transfer and fluid mechanics.