| Week | Lecture | Subject | reading | Week0 | Lecture1 (9/28) | General course overview, Background for programming projects. | 1.1 |
| Week1 | Lecture2 (10/1) | Computer representation of numbers. Limitations imposed by floating point representation. | 1.2 |
| Lecture3 (10/3) | Errors in floating point arithmetic computations | 1.2 | |
| Lecture4 (10/5) | Introduction to the solution of nonlinear equations.The bisection method. | 2.1 | |
| Week2 | Lecture5 (10/8) | Convergence estimates for the bisection method. Errors and residuals. | 2.1 |
| Lecture6 (10/10) | The fixed point iteration1 | 2.2 | |
| Lecture7 (10/12) | The fixed point iteration2 | 2.3 | |
| Week3 | Lecture8 (10/15) | The Newton-Raphson method. | 2.3 |
| Lecture9 (10/17) | The secant method. The method of false position. Rates of convergence. | 2.3, 2.4 | |
| Lecture10 (10/19) | Error analysis for Newton-Raphson and the secant method. | 2.4 | |
| Week 4 | Lecture11 (10/22) | Multiple roots of a function. Comparison of iterative methods. Global convergence properties. | 2.4 |
| Lecture12 (10/24) | Polynomial Interpolation. Method of undetermined coefficients. (Vandermonde matrix.) | 3.1 | |
| Lecture13 (10/26) | Newton Divided differences. | 3.3 | |
| Week5 | Lecture14 (10/29) | Lagrange Interpolation Formula. Interpolant existence and uniqueness. | 3.1 |
| Lecture15 (10/31) | Polynomial interpolation error estimates. (Error estimate for equispaced nodes*.) | 3.1, 3.2 | |
| Lecture16 (11/2) | Runge phenomenon. Neville's method. | 3.2 | |
| Week6 | Lecture17 (11/5) | Midterm | |
| Lecture18 (11/7) | Numerical differentiation. | 4.1 | |
| Lecture19 (11/9) | Error estimates for numerical differentiation formula. Asymptotic error expansions for numerical differentiation. | 4.1 | |
| Week7 | Lecture20 (11/12) | Veterans Day holiday | |
| Lecture21 (11/14) | Richardson extrapolation | 4.2 | |
| Lecture22 (11/16) | Numerical integration. Newton-Cotes formulas. | 4.3 | |
| Week8 | Lecture23 (11/19) | Composite integration formulas. Numerical integration error estimates. (Aitken estimation of rates of convergence.) | 4.3, 4.4 |
| Lecture24 (11/21) | Composite integration formulas.Gauss quadrature. | 4.4, 4.7 | |
| Lecture25 (11/23) | Thanksgiving holiday | ||
| Week9 | Lecture26 (11/26) | Gauss quadrature., derivation of 2 and 3 point formulas. Error estimates. | 4.7 |
| Lecture27 (11/28) | Solving linear systems of equations. Review of Gaussian elimination. | 6.1, 6.5 | |
| Lecture28 (11/30) | Equivalence of Gaussian elimination and LU factorization. | 6.5 | |
| Week10 | Lecture29 (12/3) | Construction of the LU factorization. Pivoting. Use of the LU factorization.Operation counts for Gaussian elimination (LU factorization). | 6.2, 6.6 |
| Lecture30 (12/5) | (Special type of matrices. Band solvers, Choleski factorization.) | 6.6 | |
| Lecture31 (12/7) | Review | ||
| Final | 12/11 (Thesday) | 8:00AM-11:00AM at TBA |