Review for FINAL.

3.1-3.3 Bisection method, Newton's method, Secant method. 
-Review problem: 3.1 #8; 3.2  #1, 9, 23; 3.3 #1, 2, 4.  

4.1 Polynomial Interpolation. 
-Interpolating Polynomial: Lagrange Form
-Interpolating Polynomial: Newton Form and Divided Differences
-Review problems: #1, 8, 9

4.3 Estimating Derivatives.
-First-Derivative Formulas via Taylor Series
-Review problems:#1, 3, 8.

5.2 Trapezoid rule.
-Description 
-Uniform spacing, Error Analysis  and Recursive Trapezoid Formula
-Review problems : #1, 2, 3, 5, 7

5.3 Romberg Algorithm.  
-Description, Algorithm
Review problems : #1, 5, 11.

5.5 Gaussian quadrature formulas.
-Description, Gaussian Nodes and Weights, Legendre Polynomials
-Review problems : #1, 2a,  5, 12

6.1 Naive Gaussian Elimination.
-Algorithm
-Long operation Count
-Review problems :  #1, 7a, 7b 

6.3 Tri-diagonal and banded systems.
-Tridiagonal systems (algorithm)
-Banded systems -definition
-Review problems: #2a, 3, CP16 page 281 

6.4 LU-Factorization.
-Numerical Example
-LU-Factorization theorem and algorithm
-Solving Linear Systems using LU factorization
-Review problems: # 1, 6a, 8

7.1 First degree and second degree splines. 
-Definitions
-First degree spline accuracy theorem
-Review problems: # 1, 9, 20
 
7.2 Natural cubic splines.
-Definitions for cubic spline and natural cubic spline.
-Review problems: # 1, 9, 12, 14 

8.1 Taylor series methods for ODEs. 
-Taylor series method of higher order (algorithms).
-Review problems: # 10, 11a, 12, CP8
  
8.2 Runge Kutta methods. 
-Runge Kutta method of order 2 
-Review problems: #3, 4