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Numerical Methods Applied to Chemical Engineering >> Content Detail



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SES #TopicsKEY DATES
1Introduction

MATLAB® Programming
2MATLAB® Programming (cont.)
3Linear Systems

Gaussian Elimination

LU and Cholesky Decompositions
4Sparse and Banded Matrices, Solving Linear BVPs with Finite DifferencesHW 1 due
5Ax=b as Linear Transformation

Basis Sets and Vector Spaces

Existence and Uniqueness of Solutions

Determinants
6Newton's Method for Solving Sets of Nonlinear Algebraic EquationsHW 2 due
7Quasi-Newton and Reduced-step Algorithms

Example Applications
8Orthogonal Matrices

Matrix Eigenvalues and Eigenvectors

Gershorgin's Theorem
9Schur Decomposition

Normal Matrices

Completeness of Eigenvector Bases

Normal Forms
HW 3 due
10Numerical Calculation of Matrix Eigenvalues, Eigenvectors

Applications
11Interpolation and Numerical Integration
12ODE Initial Value ProblemsHW 4 due
Exam 1 covers Ses #1-10
13Numerical Issues (Stiffness) and MATLAB® ODE Solvers
14DAE Systems and Applications
15Nonlinear Optimization

Nonlinear Simplex, Gradient, and Newton Methods

Unconstrained Problems
16Treating Constraints and Optimization Routines in MATLAB®
17Optimization Examples

Boundary Value Problems – Finite Differences
HW 5 due
18Nonlinear Reaction/Diffusion PDE-BVPs

BVPs in Non-Cartesian Coordinates
19Treating Convection Terms in PDEs
20Finite Volume and Finite Element Methods
21Introduction to Probability TheoryHW 6 due
Exam 2 covers Ses #11-20
22Random Variables, Binomial, Gaussian, and Poisson Distributions

Central Limit Theorem
23Random Walks

Brownian Dynamics
HW 7 due
24Brownian Dynamics and Stochastic Calculus
25Theory of Diffusion
26Monte Carlo Simulation
27Monte Carlo Simulation (cont.)

Simulated Annealing and Genetic Algorithms

Monte Carlo Integration
28Introduction to Statistics and Parameter Estimation
29Linear Least Squares Regression

Bayesian View of Statistics
30Choosing Priors

Basis of Least Squares Method

t-distribution and Confidence-intervals
31Non-linear Regression

Single-response Regression in MATLAB®
HW 8 due
32Bayesian Monte Carlo Methods for Single-response Regression
33Applications of Bayesian MCMC

Hypothesis Testing
34Multi-response Parameter Estimation
35Regression from Composite Single and Multi Response Data SetsHW 9 due
36Model Criticism and Validation

Conclusion
Exam 3 covers Ses #21-36

 








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