Review for the FINAL EXAM 

Sections 11, Monday, December 14, 2009, 10:30 AM -12:30 PM in EWING 209!

Section 13, Friday, December 18, 2009, 10:30 AM -12:30 PM in EWING 209!


Review the (non MATLAB) problems from Homework 1-7.


CHAPTER 1, Solving Equations. Sections 1.1, 1.2 and  1.4 and 1.5.1 
-Bisection method, Bisection Theorem:  |xc-r|<(b-a)/2^(n+1).
-Fixed point iteration, Fixed-Point Theorem
-Newton Raphson Method and N-R Theorem. N-R iteration function.
-Rate of convergence for N-R iteration  
-Secant Method
-Review problems:
1.1 #  2, 4, 6. 
1.2 # 3, 4, 16.
1.4 # 2, 6, 8, 10, 12 
1.5 # 1a

CHAPTER 2, Systems of Linear equations . Sections: 2.1, 2.2, 2.4, 2.5 

- Naive Gaussian Elimination (GE) 
- Triangular Systems (TS). 
 -Know  how to solve by hand and how to write   algorithms for GE and TS.
 -Iterative methodes
 -Jacobi and Gauss-Seidel Iteration, algorithms. 
 -Diagonally dominant matrices: 
 -Convergence of Jacobi and Gauss-Seidel Iteration 
 -Review problems:
2.1 #  2, 3, 4a. 
2.2 # 2a, 4a, 7
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


-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 
Gaussian Quadratures

-Review problems:
5.1: # 5, 7, 15
5.2: 2, 3a, 7, 9, 10, Example 5.6, page 257
5.5: 1b, 2b, 4d, 5d, 9

Chapter 6, ODEs, Sections 6.1-6.4
-Euler, Heun's (trapezoid), and Runge-Kutta (order 4) methods and the estimates for the  global error. 
-Theorem 6.2 page 291
-Systems of of ODEs
-Higher order Differential Equations and reduction to first order systems of DE. 
- Know how to write MATLAB implementation of vector functions needed for solving  a first order systems. 

-Review problems:
6.1: # 5b, 7, 12
6.2: # 4b
6.3: # 3, 5a,b
6.4: # 3b, 6