| Week 1 covers Lectures 1 and 2. |
| 1 | Course overview, Newton's method for root-finding | |
| 2 | Floating-point arithmetic | |
| Week 2 covers Lectures 3–5. |
| 3 | Floating-point summation and backwards stability | |
| 4 | Norms on vector spaces | |
| 5 | Condition numbers | Problem set 1 due |
| Week 3 covers Lectures 6–8. |
| 6 | Numerical methods for ordinary differential equations | |
| 7 | The SVD, its applications, and condition numbers | |
| 8 | Linear regression and the generalized SVD | |
| Week 4 covers Lectures 9–11. |
| 9 | Solving the normal equations by QR and Gram-Schmidt | |
| 10 | Modified Gram-Schmidt and Householder QR | |
| 11 | Matrix operations, caches, and blocking | Problem set 2 due |
| Week 5 covers Lectures 12–14. |
| 12 | Cache-oblivious algorithms and spatial locality | |
| 13 | LU factorization and partial pivoting | |
| 14 | Cholesky factorization and other specialized solvers. Eigenproblems and Schur factorizations | |
| Week 6 covers Lectures 15–17. |
| 15 | Eigensolver algorithms: Companion matrices, ill-conditioning, and Hessenberg factorization | |
| 16 | The power method and the QR algorithm | |
| 17 | Shifted QR and Rayleigh quotients | Problem set 3 due |
| Week 7 covers Lectures 18–20. |
| 18 | Krylov methods and the Arnoldi algorithm | |
| 19 | Arnoldi and Lanczos with restarting | |
| 20 | The GMRES algorithm and convergence of GMRES and Arnoldi | Final project proposal due |
| Week 8 covers Lectures 21–23. |
| 21 | Preconditioning techniques. The conjugate-gradient method | |
| 22 | Convergence of conjugate gradient | |
| 23 | Biconjugate gradient algorithms | Problem set 4 due |
| Week 9 covers Lectures 24–26. |
| 24 | Sparse-direct solvers | |
| 25 | Overview of optimization algorithms | Take-home midterm exam due before Lec #25 |
| 26 | Adjoint methods | |
| Week 10 covers Lectures 27 and 28. |
| 27 | Adjoint methods for eigenproblems and recurrence relations | |
| 28 | Trust-regions methods and the CCSA algorithm | |
| Week 11 covers Lectures 29–31. |
| 29 | Lagrange dual problems | |
| 30 | Quasi-Newton methods and the BFGS algorithm | |
| 31 | Derivation of the BFGS update | |
| Week 12 covers Lectures 32–34. |
| 32 | Derivative-free optimization by linear and quadratic approximations | |
| 33 | Numerical integration and the convergence of the trapezoidal rule | |
| 34 | Clenshaw-Curtis quadrature | |
| Week 13 covers Lectures 35–37. |
| 35 | Chebyshev approximation | |
| 36 | Integration with weight functions, and Gaussian quadrature | |
| 37 | Adaptive and multidimensional quadrature | |
| Week 14 covers Lectures 38 and 39. |
| 38 | The discrete Fourier transform (DFT) and FFT algorithms | |
| 39 | FFT algorithms and FFTW | Final project due at the end of term |
