Day 
Section 
Description 
1. 
1.1 
Numbers, evaluation of expressions, and automatic differentiation. 
2. 
1.1 
Explanation of software for automatic differentiation (excerpts from
Rigorous
Global Search: Continuous Problems, Chapter 2.) 
3. 
1.2 
Floating point numbers, roundoff error. 
4. 
1.3 
numerical stability. 
5. 
1.4 
Error propagation and condition numbers. 
6. 
1.5 
Interval arithmetic. 
7. 
1.5 
Interval evaluation of expressions; software tools (excerpts from Rigorous
Global Search: Continuous Problems, Chapter 2.) 
8. 
2.1 
Gaussian elimination. 
9. 
2.1 
More on Gaussian elimination. 
10. 
2.2 
Structured systems of equations 
11. 
2.3 
Rounding error analysis for Gaussian elimination; pivoting 
12. 
2.4 
Vector and matrix norms 
13. 
2.4 
More on vector and matrix norms 
14. 
2.5 
Condition numbers 
15. 
2.7 
Error bounds for linear systems 
16. 
3.1 
Polynomial interpolation 
17. 
3.1 
More on polynomial interpolation. 
18. 
3.2 
Numerical differentiation. 
19 
3.3 
Cubic splines. 
20. 
3.4 
Approximation by splines 
21. 
3.5 
Radial basis functions 
22. 
5.1 
The secant method; linear, quadratic, and superlinear convergence 
23. 
5.25.3 
Bisection methods and bisection methods for eigenvalue problems 
24. 
5.4 
Convergence order 
25. 
5.5 
Error analysis; interval Newton method 
26. 
5.7 
Newton's method 
27. 

Line searches: supplement 
28. 
6.1 
Systems of nonlinear equations: preliminaries. 
29. 
6.2 
Theory of Newton's method. 
30. 
6.3 
Error analysis for the multivariate Newton's method; interval Newton
method; supplement with section 1.5 of Rigorous
Global Search: Continuous Problems. 
31. 
6.4 
Other methods 
32. 
4.1 
Quadrature formula theory 
33. 
4.2 
Gaussian quadrature 
35. 
4.3 
The trapezoidal rule and extrapolation. Supplement: The trapezoidal
rule for periodic functions. 
36. 
4.4 
Adaptive integration. 
37. 
Ch. 6 
Time permitting, additional topics will be covered. The plan
for next semester is to cover optimization, ordinary and partial differential
equations. (There are 41 meeting periods in the fall semester.) 