| 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. | 5.2-5.3 | 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.) |