Review for the FINAL EXAM (Thursday, December 18, 12:20PM in 107 Wartik).


3.1-3.3 Bisection method, Newton's method, Secant method. 
-Review problems: 
3.1 #2, 4. 
3.2 #6, 7, 9, 10, 23. 
3.3 #2, 4. 
  
3.4
-CMT, fixed points.
-Example 3, page 103,
-Review problems: #2, 4, 26, 28, 40, 41

4.2 LU and Cholesky Factorization
-forward substitution
-back substitution
-Doolittle, Crout, Chollesky factorizations for 3 by 3 matrices.
-Review problems:#1, 20, 28, 30, 31, 36

4.3 
-Basic  Gaussian Elimination.
-Algorithm 
-Operation Counts (ops)
-Tridiagonal system
-Review problems:#1 (No pivoting), 11, 12, 13, 39

6.1
-Newton form and Lagrange forms of the Interpolation Polynomial
-The error in Polynomial Interpolation (Theorem 2). 
-Review problems:#1, 8, 9, 22, 25

6.2
-Divided differences (definition)
-Theorem 1, Theorem 4
-Algorithm for divided differences and finding 
 the Newton form of the Interpolation Polynomial
-Review problems:#4, 5, 22, 23, 24,  26

6.4 
-Spline functions of degree k.
-Cubic splines
-Review problems: See Hw #7 

7.1
-Numerical Differentiation
-Richardson Extrapolation
-Review problems: See Hw #7 

7.2 and 7.3
-Integration via Polynomial interpolation
-Trapezoid rule. The composite trapezoid rule.
-Method of Undetermined Coefficients. General integration formulas. 
-Gaussian Quadrature. Theorem1, page493.
-Review problems: See Hw #8