# Lecture Notes

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.)