Fall 2006 Numerical Analysis I Math 507
Mackey Reading

For homework assignments, go to http://homepages.wmich.edu/~mackey/Teaching/507/hw.html

Read the text regularly. Before you come to class, read the material that was covered in the previous class, then read the material that is scheduled to be covered. Prepare questions that you have on the material that you have read.

Section 1.1
  1. Suppose (-1, 0) and (8, -10) are two points on the graph of a polynomial.
    • What does the intermediate value theorem say in this situation?
    • What does the mean value theorem say in this situation?
  2. Read and understand Rolle's Theorem
  3. Read Taylor's Theorem (p.6).
    Follow Example 1.
    Construct the first 4 nonzero terms in the Taylor series for the functions sin(x), cos(x) and e^x.
    Alternate form of Taylor's Theorem (p. 10)
Section 1.2
  1. Orders of convergence
  2. Big O notation
Section 2.1
  1. Binary and decimal number systems
  2. Normalized scientific notation
  3. Rounding
  4. Single and double precision
  5. IEEE Arithmetic: Zero, Infinity, NaN (p. 42)
  6. Machine epsilon
  7. Chapter 4, p. 37-40 of the Matlab Guide by Higham and Higham.
  8. Handout on Floating Point Numbers
Section 2.2
  1. Absolute and relative errors
  2. Theorem 1 on loss of precision in subtraction (p. 57)
  3. Rewriting expressions to avoid loss of precision
Section 2.3
  1. Numerical Instability
  2. Computing roots of polynomials
    • how sensitive are roots to errors in the coefficients of the polynomial?
    • understand derivation at the bottom half of p. 67
    • Example 2 on p. 68
Niloufer Mackey
Last modified: Thu Sep 14 17:02:23 EDT 2006

[ home ]    [ Math 507 ]    [ classes ]   [ selected papers ]   [ selected links ]