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