Special software is required to use some of the files in this section: .m.
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 (PDF)
Modularization
|
gausselim_pivot.m (M)
gauss.m (M)
|
| L4 |
When Algorithms Run into Problems: Numerical Error, Ill-conditioning, and Tolerances |
|
| L5 |
Introduction to Systems of Nonlinear Equations (PDF) |
|
| L6 |
Modern Methods for Solving Nonlinear Equations |
|
| L7 |
Introduction to Eigenvalues and Eigenvectors |
|
| L8 |
Constructing and Using the Eigenvector Basis |
|
| L9 |
Function Space vs. Real Space Methods for Partial Differential Equations (PDEs) |
|
| L10 |
Function Space |
|
| L11 |
Numerical Calculation of Eigenvalues and Eigenvectors (PDF)
Singular Value Decomposition (SVD)
|
interpolateV.m (M)
setup_interV.m (M)
|
| L12 |
Ordinary Differential Equation - Initial Value Problems (ODE-IVP) and Numerical Integration |
|
| L13 |
Stiffness
MATLAB® Ordinary Differential Equation (ODE) Solvers
|
|
| L14 |
Implicit Ordinary Differential Equation (ODE) Solvers
Shooting
|
|
| L15 |
Differential Algebraic Equations (DAEs)
Introduction: Optimization
|
|
| L16 |
Unconstrained Optimization |
|
| L17 |
Constrained Optimization |
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| L18 |
Optimization
Sensitivity Analysis
Introduction: Boundary Value Problems (BVPs)
|
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| L19 |
Boundary Value Problems (BVPs) Lecture 2 |
makeA_sparse.m (M)
makeAforLaplacian.m (M)
|
| L20 |
Boundary Value Problems (BVPs) Lecture 3: Finite Differences, Method of Lines, and Finite Elements |
|
| L21 |
TA Tutorial on BVPs, FEMLAB® |
|
| L22 |
Introduction: Models vs. Data |
|
| L23 |
Models vs. Data Lecture 2: Bayesian View |
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| L24 |
Uncertainties in Model Predictions |
|
| L25 |
Conclude Models vs. Data |
|
| L26 |
TA Led Review |
Review Exam 2 (PDF) (Courtesy of Sandeep Sharma. Used with permission.) |
| L27 |
Models vs. Data Recapitulation (PDF)
Monte Carlo and Molecular Dynamics
|
|
| L28 |
Guest Lecture on Monte Carlo / Molecular Dynamics: Frederick Bernardin |
Intro to Monte Carlo Methods (PDF) (Courtesy of Frederick Bernardin. Used with permission.) |
| L29 |
Genetic Algorithms |
|
| L30 |
Modeling Intrinsically Stochastic Processes
Multiscale Modeling
|
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| L31 |
Fluctuation-dissipation Theorem |
|
| L32 |
Kinetic Monte Carlo and Turbulence Modeling |
|
| L33 |
Operator Splitting
Strang Splitting
|
|
| L34 |
Fourier Transforms
Fast Fourier Transform (FFT)
|
|
| L35 |
Summary: Problem Solving (PDF) |
|
| L36 |
TA Led Final Review |
Review Final Exam (PDF) (Courtesy of Sandeep Sharma. Used with Permission.) |