# Schedule of MATH/CSE 455 Lectures

Items flagged in yellow are tentative.

1 8/27/97 introduction to numerical analysis
divide and average algorithm
read Ch. 1; review Taylor's theorem
2 8/29/97 introduction to course hardware and software
matlab; creating and compiling a Fortran program; an unstable recursion
review Taylor's theorem again
3 9/3/97 mathematical preliminaries
discussion of the unstable recursion and remedies; Mean Value Theorem; Integral Mean Value Theorem; Taylor polynomials
and again!
4 9/5/97 Taylor's Theorem with remainder
application to forward and divided difference approximations of the derivative
read Ch. 2; HW 1 due
5 9/8/97 rates of convergence
big O and little o; nested multiplication

6 9/10/97 floating point number systems, IEEE arithmetic
base; mantissa; exponent; normalization

7 9/12/97 Lab 1: Errors in finite precision arithmetic
8 9/15/97 floating point arithmetic
catastrophic cancellation

9 9/17/97 errors and error propagation
stability and conditioning
Lab 1 due; read Ch. 3.1-3.4
10 9/19/97 Lab 2: Stability, cancellation, and conditioning problems with polynomials
11 9/22/97 the bisection method and Newton's method
bracketing intervals; rate of convergence for bisection; local quadratic convergence for Newton, proof; global convergence and divergence for Newton

12 9/24/97 the secant method
local superlinear convergence

13 9/26/97 Lab 3: Root-finding routines
hybrid secant/bisection routines

14 9/29/97 Newton's method for systems
systems of n equations in n unknowns; linearization of systems

15 10/1/97 Fixed point interation
relation between fixed points and roots; existence of fixed points; contractions; fixed point iteration
Lab 3 due; read Ch. 4.1-4.4
16 10/3/97 Lab 4: Fixed points and fixed point iteration
17 10/6/97 review of matrix algebra, introduction to linear systems Homework 2 due
18 10/8/97 Gaussian elimination
19 10/10/97 Exam 1 (in 115 McAllister)
20 10/13/97 LU decomposition
21 10/15/97 Cholesky decomposition
22 10/17/97 Lab 5: Operation Counts for Gaussian Elimination and Introduction to Conditioning of Linear Systems
23 10/20/97 pivoting, scaling, algorithmic aspects 5 minute quiz
24 10/22/97 norms and condition numbers Lab 5 due, 5 minute quiz
25 10/24/97 Lab 6: Tridiagonal matrices
26 10/27/97 applications of condition numbers read Ch. 6.1 through Thm. 8 (you can skip the Meray example)
27 10/29/97 introduction to polynomial interpolation Homework 3 due
28 10/31/97 Lab 7: The Lagrange Interpolating Polynomial read Ch. 6.2 through Thm. 4
29 11/3/97 Newton's formula for LIP
30 11/5/97 more on divided differences, error in Lagrange interpolation read Ch. 6.3
31 11/7/97 Lab 8: The Chebyshev Points
32 11/10/97 Hermite Interpolation read Ch. 6.4 up to, but not including, tension splines
33 11/12/97 piecewise polynomial interpolation Homework 4 and Lab 8 due
34 11/14/97 Lab 9: Cubic Spline Interpolation
35 11/17/97 more on splines
36 11/19/97 adaptive interpolation; numerical differentiation
37 11/21/97 Exam 2 (in 115 McAllister) read Ch. 7.1-7.3, 7.5
38 11/24/97 trapezoidal rule
39 12/1/97 Simpson's rule and other Newton-Cotes rules
40 12/3/97 error expansions and Richardson extrapolation
41 12/5/97 Lab 10: Quadrature rules with uniform spacing, regular and singular integrands
42 12/8/97 Gaussian quadrature Homework 5 due
43 12/10/97 complements on numerical quadrature