Review for MIDTERM EXAM II (Friday, April 29, 2011).


CHAPTER 2, Solutions of Linear Systems. Section 2.5 Iterative methodes
Jacobi and Gauss-Seidel Iteration, algorithms. 
Diagonally dominant matrices: 
Convergence of Jacobi and Gauss-Seidel Iteration 
-Review problems:

2.5 # 1, a, b.
See Example 2.22, page 114 or class notes

CHAPTER 3 Interpolation, Sections 3.1, 3.2
Lagrange coefficient polynomials (Cardinal functions) , Lagrange Interpolation, Newton's Divided Differences, Theorem 3.3, page 154
Runge phenomenon

-Review problems:
3.1: # 1a,b, 2, 7, 8
3.2: # 1, 3
3.2 CP #3, page 160


CHAPTER 4 Least squares, Sections 4.1 and 4.2 
Linear models
The exponential model
Know Normal equations and how to solve NE using MATLAB
2-norm and RMSE 

-Review problems:
4.1: # 1a,b, 8, 9, 12
4.2: # 1b, 6


Chapter 5 Numerical Differentiation and Integration,Sections 5.1,5.2, 5.5 
Know how to deduce:
  -Two point forward difference formula
  -Three-point centered-difference formulas for f' and f''.  
Trapezoid Rule, Simpson's Rule, and the composite versions of TR and SR.
Degree of precision 

-Review problems:
5.1: # 5, 7, 15
5.2: 2, 3a, 7, 9, 10, Example 5.6, page 257

KNOW how to use the MATLAB functions: \, norm, polyval, polyfit, 
 as showed in Homework 5-7.