Courses:

Numerical Methods Applied to Chemical Engineering >> Content Detail



Lecture Notes



Lecture Notes

Special software is required to use some of the files in this section: .m.

These notes are preliminary and may contain errors.


SES #LECTURE NOTESADDITIONAL FILES
L1Using MATLAB® to evaluate and plot expressions (PDF)rate.m (M)
L2Solving systems of linear equations (PDF)rate.m (M)
L3

Matrix factorization

Modularization (PDF)

gausselim_pivot.m (M)

gauss.m (M)

L4When algorithms run into problems: Numerical error, ill-conditioning, and tolerances (PDF)
L5Introduction to systems of nonlinear equations (PDF)
L6Modern methods for solving nonlinear equations (PDF)
L7Introduction to eigenvalues and eigenvectors (PDF)
L8Constructing and using the eigenvector basis (PDF)
L9Function space vs. real space methods for partial differential equations (PDEs) (PDF)
L10Function space (PDF)
L11

Numerical calculation of eigenvalues and eigenvectors

Singular value decomposition (SVD) (PDF)

interpolateV.m (M)

setup_interV.m (M)

L12Ordinary differential equation - initial value problems (ODE-IVP) and numerical integration (PDF)
L13

Stiffness

MATLAB® ordinary differential equation (ODE) solvers (PDF)

L14

Implicit ordinary differential equation (ODE) solvers

Shooting (PDF)

L15

Differential algebraic equations (DAEs)

Introduction: Optimization (PDF)

L16Unconstrained optimization (PDF)
L17Constrained Optimization (PDF)
L18

Optimization

Sensitivity analysis

Introduction: Boundary value problems (BVPs) (PDF)

L19Boundary value problems (BVPs) lecture 2 (PDF)

makeA_sparse.m (M)

makeAforLaplacian.m (M)

L20Boundary value problems (BVPs) lecture 3: Finite differences, method of lines, and finite elements (PDF)
L21TA tutorial on BVPs, FEMLAB® (PDF)
L22Introduction: Models vs. Data (PDF)
L23Models vs. Data lecture 2: Bayesian view (PDF)
L24Uncertainties in model predictions (PDF)
L25Conclude models vs. data (PDF)
L26TA led review (PDF)Review exam 2 (PDF) (Courtesy of Sandeep Sharma. Used with permission.)
L27

Models vs. Data recapitulation

Monte Carlo and molecular dynamics (PDF)

L28Guest lecture on Monte Carlo / molecular dynamics: Frederick Bernardin (PDF)Intro to Monte Carlo methods (PDF) (Courtesy of Frederick Bernardin. Used with permission.)
L29

Global optimization

Multiple minima (PDF)

L30

Modeling intrinsically stochastic processes

Multiscale modeling (PDF)

L31Fluctuation-dissipation theorem (PDF)
L32Kinetic Monte Carlo and turbulence modeling (PDF)
L33

Operator splitting

Strang splitting (PDF)

L34

Fourier transforms

Fast fourier transform (FFT) (PDF)

L35Summary: Problem solving (PDF)
L36TA led final review (PDF)Review final exam (PDF) (Courtesy of Sandeep Sharma. Used with Permission.)

 








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