Special software is required to use some of the files in this section: .m.
These notes are preliminary and may contain errors.
Lecture notes files.
| SES # |
LECTURE NOTES |
ADDITIONAL FILES |
| L1 |
Using MATLAB® to evaluate and plot expressions (PDF) |
rate.m (M) |
| L2 |
Solving systems of linear equations (PDF) |
rate.m (M) |
| L3 |
Matrix factorization
Modularization (PDF)
|
gausselim_pivot.m (M)
gauss.m (M)
|
| L4 |
When algorithms run into problems: Numerical error, ill-conditioning, and tolerances (PDF) |
|
| L5 |
Introduction to systems of nonlinear equations (PDF) |
|
| L6 |
Modern methods for solving nonlinear equations (PDF) |
|
| L7 |
Introduction to eigenvalues and eigenvectors (PDF) |
|
| L8 |
Constructing and using the eigenvector basis (PDF) |
|
| L9 |
Function space vs. real space methods for partial differential equations (PDEs) (PDF) |
|
| L10 |
Function space (PDF) |
|
| L11 |
Numerical calculation of eigenvalues and eigenvectors
Singular value decomposition (SVD) (PDF)
|
interpolateV.m (M)
setup_interV.m (M)
|
| L12 |
Ordinary 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)
|
|
| L16 |
Unconstrained optimization (PDF) |
|
| L17 |
Constrained Optimization (PDF) |
|
| L18 |
Optimization
Sensitivity analysis
Introduction: Boundary value problems (BVPs) (PDF)
|
|
| L19 |
Boundary value problems (BVPs) lecture 2 (PDF) |
makeA_sparse.m (M)
makeAforLaplacian.m (M)
|
| L20 |
Boundary value problems (BVPs) lecture 3: Finite differences, method of lines, and finite elements (PDF) |
|
| L21 |
TA tutorial on BVPs, FEMLAB® (PDF) |
|
| L22 |
Introduction: Models vs. Data (PDF) |
|
| L23 |
Models vs. Data lecture 2: Bayesian view (PDF) |
|
| L24 |
Uncertainties in model predictions (PDF) |
|
| L25 |
Conclude models vs. data (PDF) |
|
| L26 |
TA 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)
|
|
| L28 |
Guest 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)
|
|
| L31 |
Fluctuation-dissipation theorem (PDF) |
|
| L32 |
Kinetic Monte Carlo and turbulence modeling (PDF) |
|
| L33 |
Operator splitting
Strang splitting (PDF)
|
|
| L34 |
Fourier transforms
Fast fourier transform (FFT) (PDF)
|
|
| L35 |
Summary: Problem solving (PDF) |
|
| L36 |
TA led final review (PDF) |
Review final exam (PDF) (Courtesy of Sandeep Sharma. Used with Permission.) |