Review for MIDTERM EXAM I (Friday, March 17).

CHAPTER 1,  Preliminaries: Sections 1.2, 1.3
-Binary numbers, Binary fractions, Machine numbers, Computer floating point numbers.
-Absolute and relative error, approximation to d significant digits
- Round-off error, loss of significance 
- Review problems:
1.2 #  2, 3, 4a, 6a. 
1.3 # 1, 5, 12. 

CHAPTER 2, Solutions of Nonlinear Equations. Sections 2.1, 2.2 and  2.4  
-Fixed point iteration, Fixed-Point Theorem
-Bisection method of Bolzano, Bisection Theorem 
-Newton Raphson Method and N-R Theorem. N-R iteration function.
- Rate of convergence for N-R iteration (Theorem 2.6) 
-Secant Method
-Review problems:
2.1 #  1a, 4, 6. 
2.2 # 3, 9, 11.
2.4 #4, 5, 8, 11 

CHAPTER 3, Solutions of Linear Systems. Sections: 3.3-3.6 
Triangular Systems, Gaussian Elimination: Know 
how to solve by hand and how to write   algorithms. 
LU factorization. Solve AX=B using a  LU factorization
Computational Complexity (counting  ops)
Jacobi and Gauss-Seidel Iteration, algorithms. Diagonally dominant matrices: 
Convergence of Jacobi and Gauss-Seidel Iteration
Norms on R^n, propertiees. 
-Review problems:

3.3 #  1, 5, 7. 
3.4 # 2, 12.
3. 5 # 1, 5, 6(by hand). 
3.6 #  8(a,b), 11.

Algorithms and Programs:
page 125 # 2
page 125 #3( Write an algorithm or a Matlab  function) which   constructs the matrix L)
page 140 #1
page 166 # 3(i