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 
QuasiNewton and Reducedstep 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 #110  
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 PDEBVPs
BVPs in NonCartesian 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 #1120  
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 tdistribution and Confidenceintervals 

31 
Nonlinear Regression
Singleresponse Regression in MATLAB® 
HW 8 due 
32  Bayesian Monte Carlo Methods for Singleresponse Regression  
33 
Applications of Bayesian MCMC
Hypothesis Testing 

34  Multiresponse 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 #2136 
Calendar
Course Info
Instructor
Departments
As Taught In
Fall
2005
Level
Topics
Learning Resource Types
grading
Exams with Solutions
assignment_turned_in
Problem Sets with Solutions