Numerical Methods Applied to Chemical Engineering

Calendar

SES #	Topics	KEY DATES
1	Introduction MATLAB® Programming
2	MATLAB® Programming (cont.)
3	Linear Systems Gaussian Elimination LU and Cholesky Decompositions
4	Sparse and Banded Matrices, Solving Linear BVPs with Finite Differences	HW 1 due
5	Ax=b as Linear Transformation Basis Sets and Vector Spaces Existence and Uniqueness of Solutions Determinants
6	Newton’s Method for Solving Sets of Nonlinear Algebraic Equations	HW 2 due
7	Quasi-Newton and Reduced-step Algorithms Example Applications
8	Orthogonal Matrices Matrix Eigenvalues and Eigenvectors Gershorgin’s Theorem
9	Schur Decomposition Normal Matrices Completeness of Eigenvector Bases Normal Forms	HW 3 due
10	Numerical Calculation of Matrix Eigenvalues, Eigenvectors Applications
11	Interpolation and Numerical Integration
12	ODE Initial Value Problems	HW 4 due
	Exam 1 covers Ses #1-10
13	Numerical Issues (Stiffness) and MATLAB® ODE Solvers
14	DAE Systems and Applications
15	Nonlinear Optimization Nonlinear Simplex, Gradient, and Newton Methods Unconstrained Problems
16	Treating Constraints and Optimization Routines in MATLAB®
17	Optimization Examples Boundary Value Problems – Finite Differences	HW 5 due
18	Nonlinear Reaction/Diffusion PDE-BVPs BVPs in Non-Cartesian Coordinates
19	Treating Convection Terms in PDEs
20	Finite Volume and Finite Element Methods
21	Introduction to Probability Theory	HW 6 due
	Exam 2 covers Ses #11-20
22	Random Variables, Binomial, Gaussian, and Poisson Distributions Central Limit Theorem
23	Random Walks Brownian Dynamics	HW 7 due
24	Brownian Dynamics and Stochastic Calculus
25	Theory of Diffusion
26	Monte Carlo Simulation
27	Monte Carlo Simulation (cont.) Simulated Annealing and Genetic Algorithms Monte Carlo Integration
28	Introduction to Statistics and Parameter Estimation
29	Linear Least Squares Regression Bayesian View of Statistics
30	Choosing Priors Basis of Least Squares Method t-distribution and Confidence-intervals
31	Non-linear Regression Single-response Regression in MATLAB®	HW 8 due
32	Bayesian Monte Carlo Methods for Single-response Regression
33	Applications of Bayesian MCMC Hypothesis Testing
34	Multi-response Parameter Estimation
35	Regression from Composite Single and Multi Response Data Sets	HW 9 due
36	Model Criticism and Validation Conclusion
	Exam 3 covers Ses #21-36