Catalog

Numerical Methods Applied to Chemical Engineering

Chemical Engineering MIT CC BY-NC-SA 4.0 23 lectures

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

  1. 1 Session 5: Eigenvalues and Eigenvectors
  2. 2 Session 6: Singular Value Decomposition; Iterative Solutions of Linear Equations
  3. 3 Session 7: Solutions of Nonlinear Equations; Newton-Raphson Method
  4. 4 Session 8: Quasi-Newton-Raphson Methods
  5. 5 Session 9: Homotopy and Bifurcation
  6. 6 Session 11: Unconstrained Optimization; Newton-Raphson and Trust Region Methods
  7. 7 Session 12: Constrained Optimization; Equality Constraints and Lagrange Multipliers
  8. 8 Session 13: ODE-IVP and Numerical Integration 1
  9. 9 Session 16: ODE-IVP and Numerical Integration 4
  10. 10 Session 18: Differential Algebraic Equations 2
  11. 11 Session 19: Differential Algebraic Equations 3
  12. 12 Session 20: Boundary Value Problem 1
  13. 13 Session 21: Boundary Value Problems 2
  14. 14 Session 22: Partial Differential Equations 1
  15. 15 Session 25: Review Session
  16. 16 Session 26: Partial Differential Equations 2
  17. 17 Session 27: Probability Theory 2
  18. 18 Session 28: Models vs. Data 1
  19. 19 Session 30: Models vs. Data 3
  20. 20 Session 33: Monte Carlo Methods 2
  21. 21 Session 34: Stochastic Chemical Kinetics 1
  22. 22 Session 35: Stochastic Chemical Kinetics 2
  23. 23 Session 36: Final Lecture

Course materials