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