| Class | Date | Topic | Reading | Assigned | Due |
|---|---|---|---|---|---|
| 1 | 9/27 | Preliminaries - Sources of error - Floating point - Well-posedness | Heath, Chapter 1 | ||
| 2 | 10/2 | Solving linear systems - Existence and Uniqueness of solutions | Heath, Chapter 2 | HW1 | |
| 3 | 10/4 | Vector and Matrix Norms - Sensitivity and conditioning | Heath, Chapter 2 | ||
| 4 | 10/9 | Matrix condition number - Solving linear systems - SPD systems - Cholesky factorization | Heath, Sections 2.3.3, 2.3.4, 2.4.7, 2.5 | HW1 | |
| 5 | 10/11 | Orthogonality - Projectors - SVD - Overdetermined systems | Heath Sections 3.1, 3.2, 3.6 | HW2 | |
| 6 | 10/16 | no class | |||
| 7 | 10/18 | Least squares and QR decomposition | Heath Sections 3.4, 3.5 | HW2 | |
| 8 | 10/23 | Eigenvalues and eigenvectors | Heath Sections 4.1, 4.2, 4.4, 4.5.1, 4.5.2, 4.5.4, 4.5.5 | ||
| 9 | 10/25 | Nonlinear Equations | Heath Sections 5.1-5.5.3 | ||
| 10 | 10/30 | Nonlinear Equations (cont.) | Heath Sections 5.5.4, 5.5.7, 5.6.1-5.6.3 | ||
| 11 | 11/1 | no class | |||
| 12 | 11/6 | Midterm 1 | |||
| 13 | 11/8 | Optimization - unconstrained - one-dimensional | Heath Sections 6.1, 6.2.2., 6.3, 6.4.1, 6.4.3 | HW4 | |
| 14 | 11/13 | Optimization - multi-dimensional | Heath Sections, 6.5.2-6.5.6 | ||
| 15 | 11/15 | Conjugate Gradients | An Introduction to the Conjugate Gradient Method Without the Agonizing Pain by Jonathan Richard Shewchuk | HW4 | |
| 16 | 11/20 | Polynomial Interpolation | Heath, Sections 7.3.1-7.3.3, 7.4 | ||
| 17 | 11/22 | no class | |||
| 18 | 11/27 | Numerical Integration and Differentiation | Heath Sections 8.1, 8.2, 8.3.1, 8.3.3, 8.3.6, 8.4.3, 8.4.4, 8.6.1, 8.7 | HW5 | |
| 19 | 11/29 | Numerical ODEs | Heath Sections 9.1-9.3.2 | ||
| 20 | 12/4 | Midterm 2 | HW5 | ||
| 21 | 12/6 | Review | |||
| 22 | TBA | Final |