| 1 | Introduction, Examples, Matrix-Vector and Matrix-Matrix Products | |
| 2 | Orthogonal Matrices, Norms of Matrices | |
| 3 | The Singular Value Decomposition | |
| 4 | QR Factorization | |
| 5 | Givens Rotations and Householder Reflections | Homework 1 due |
| 6 | Least Squares Problems | |
| 7 | Floating Point Arithmetic | Homework 2 due |
| 8 | Conditioning and Stability | |
| 9 | Stability of Givens Rotations and Backward Substitution | Homework 3 due |
| 10 | Stability of Least Squares Problems | |
| 11 | Gaussian Elimination | |
| 12 | Cholesky Factorization | Homework 4 due |
| 13 | Eigenvalue Problems | |
| 14 | Hessenberg Reduction | Homework 5 due |
| 15 | QR Algorithm | |
| 16 | Midterm | Homework 6 due |
| 17 | Stability of the QR Algorithm; Jacobi | |
| 18 | Bisection, Divide and Conquer | |
| 19 | SVD Algorithms | |
| 20 | Iterative Algorithms, Arnoldi | Homework 7 due |
| 21 | Lanczos, GMRES | |
| 22 | Conjugate Gradients | Homework 8 due |
| 23 | Solutions to Ordinary Differential Equations | |
| 24 | Runge Kutta Methods | Homework 9 due |
| 25 | Solutions to Stiff ODEs - I | |
| 26 | Solutions to Stiff ODEs - II | Homework 10 due |