Numerical Methods Applied to Chemical Engineering

Overview

Numerical methods for solving problems arising in heat and mass transfer, fluid mechanics, chemical reaction engineering, and molecular simulation. Topics: Numerical linear algebra, solution of nonlinear algebraic equations and ordinary differential equations, solution of partial differential equations (e.g. Navier-Stokes), numerical methods in molecular simulation (dynamics, geometry optimization). All methods are presented within the context of chemical engineering problems. Familiarity with structured programming is assumed.

Syllabus

Session 5: Eigenvalues and Eigenvectors
Session 6: Singular Value Decomposition; Iterative Solutions of Linear Equations
Session 7: Solutions of Nonlinear Equations; Newton-Raphson Method
Session 8: Quasi-Newton-Raphson Methods
Session 9: Homotopy and Bifurcation
Session 11: Unconstrained Optimization; Newton-Raphson and Trust Region Methods
Session 12: Constrained Optimization; Equality Constraints and Lagrange Multipliers
Session 13: ODE-IVP and Numerical Integration 1
Session 16: ODE-IVP and Numerical Integration 4
Session 18: Differential Algebraic Equations 2
Session 19: Differential Algebraic Equations 3
Session 20: Boundary Value Problem 1
Session 21: Boundary Value Problems 2
Session 22: Partial Differential Equations 1
Session 25: Review Session
Session 26: Partial Differential Equations 2
Session 27: Probability Theory 2
Session 28: Models vs. Data 1
Session 30: Models vs. Data 3
Session 33: Monte Carlo Methods 2
Session 34: Stochastic Chemical Kinetics 1
Session 35: Stochastic Chemical Kinetics 2
Session 36: Final Lecture