These notes are preliminary and may contain errors.
| 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.) |