Items flagged in yellow are tentative.
No.  Date  Topics  Comments 

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. 3.13.4 
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: Rootfinding 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. 4.14.4 
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. 7.17.3, 7.5 
38  11/24/97  trapezoidal rule  
39  12/1/97  Simpson's rule and other NewtonCotes 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  
44  12/12/97  Lab 11: Adaptive Quadrature  Lab 10 due 