# Calendar

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