## 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