Numerical Methods Applied to Chemical Engineering

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.

• 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