| 1 |
Introduction
MATLAB® Programming |
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| 2 |
MATLAB® Programming (cont.) |
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| 3 |
Linear Systems
Gaussian Elimination
LU and Cholesky Decompositions |
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| 4 |
Sparse and Banded Matrices, Solving Linear BVPs with Finite Differences |
HW 1 due |
| 5 |
Ax=b as Linear Transformation
Basis Sets and Vector Spaces
Existence and Uniqueness of Solutions
Determinants |
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| 6 |
Newton's Method for Solving Sets of Nonlinear Algebraic Equations |
HW 2 due |
| 7 |
Quasi-Newton and Reduced-step Algorithms
Example Applications |
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| 8 |
Orthogonal Matrices
Matrix Eigenvalues and Eigenvectors
Gershorgin's Theorem |
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| 9 |
Schur Decomposition
Normal Matrices
Completeness of Eigenvector Bases
Normal Forms |
HW 3 due |
| 10 |
Numerical Calculation of Matrix Eigenvalues, Eigenvectors
Applications |
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| 11 |
Interpolation and Numerical Integration |
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| 12 |
ODE Initial Value Problems |
HW 4 due |
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Exam 1 covers Ses #1-10 |
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| 13 |
Numerical Issues (Stiffness) and MATLAB® ODE Solvers |
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| 14 |
DAE Systems and Applications |
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| 15 |
Nonlinear Optimization
Nonlinear Simplex, Gradient, and Newton Methods
Unconstrained Problems |
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| 16 |
Treating Constraints and Optimization Routines in MATLAB® |
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| 17 |
Optimization Examples
Boundary Value Problems – Finite Differences |
HW 5 due |
| 18 |
Nonlinear Reaction/Diffusion PDE-BVPs
BVPs in Non-Cartesian Coordinates |
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| 19 |
Treating Convection Terms in PDEs |
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| 20 |
Finite Volume and Finite Element Methods |
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| 21 |
Introduction to Probability Theory |
HW 6 due |
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Exam 2 covers Ses #11-20 |
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| 22 |
Random Variables, Binomial, Gaussian, and Poisson Distributions
Central Limit Theorem |
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| 23 |
Random Walks
Brownian Dynamics |
HW 7 due |
| 24 |
Brownian Dynamics and Stochastic Calculus |
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| 25 |
Theory of Diffusion |
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| 26 |
Monte Carlo Simulation |
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| 27 |
Monte Carlo Simulation (cont.)
Simulated Annealing and Genetic Algorithms
Monte Carlo Integration |
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| 28 |
Introduction to Statistics and Parameter Estimation |
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| 29 |
Linear Least Squares Regression
Bayesian View of Statistics |
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| 30 |
Choosing Priors
Basis of Least Squares Method
t-distribution and Confidence-intervals |
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| 31 |
Non-linear Regression
Single-response Regression in MATLAB® |
HW 8 due |
| 32 |
Bayesian Monte Carlo Methods for Single-response Regression |
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| 33 |
Applications of Bayesian MCMC
Hypothesis Testing |
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| 34 |
Multi-response Parameter Estimation |
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| 35 |
Regression from Composite Single and Multi Response Data Sets |
HW 9 due |
| 36 |
Model Criticism and Validation
Conclusion |
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Exam 3 covers Ses #21-36 |
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