Numerical Analysis 1
Fall 2025
Scores
Project
Here are the project options. The project is to be all your own work, and is due Tuesday, Dec 2.
Homework
Homework assignments now including Homework 10.
Homework 1 solutions | Homework 2 solutions | Homework 3 solutions | Homework 4 solutions | Homework 5 solutions | Homework 6 solutions | Homework 7 solutions | Homework 8 solutions | Homework 9 solutions
Lecture board photos and screenshots
Day 01, Aug 26: Outline, photos and screenshots. What is numerical analysis? What is this course about? Machine numbers.
Day 02, Aug 28. More detail about floating-point machine numbers, and starting to think about machine arithmetic.
Day 03, Sep 2. Relative error in floating point arithmetics, and some remedies.
Day 04, Sep 4. Roundoff error bound. Root-finding 1D: bisection, functional iteration.
Day 05, Sep 9. Conditions for convergence of functional iteration to a fixed point, convergence with order q.
Day 06, Sep 11. Newton failure. Secant method. Stopping criteria. Linear systems.
Day 07, Sep 16. Implementation of GE and BS. Speed of computer arithmetic. Operation count for GE.
Day 08, Sep 18. Vectorization. GE with partial pivoting. Round-off in GE. Bound on change in solution when problem perturbed.
Day 09, Sep 23. GE as LU factorization. Overdetermined systems and QR factorization.
Day 10, Sep 25. QR factorization cont'd, implementation. Application of QR.
Day 11, Sep 30. Exam 1
Day 12, Oct 2. Concluding notes on QR. Ch 4. Polynomial approximation: Weierstrass theorem, Bernstein polynomials.
Day 13, Oct 7. Polynomial interpolation, using Lagrange and monomial bases. (Jupyter notebook)
Day 14, Oct 9. Error bound for polynomial interpolation. Piecewise polynomial interpolation (linear and cubic).
Day 15, Oct 16. Cubic spline interpolation. Bezier cubic curves.
REMOTE FROM DAY 16 ON
Day 16, Oct 21. Notes and illustrations, Jupyter notebook Best trigonometric polynomial approximation. Trigonometric interpolation.
Day 17, Oct 23. Exam protocol guide. Notes and illustrations: pre-class version, annotated version. Recording of piano note, Jupyter notebook.
Day 18, Oct 28. Notes and illustrations. Fast Fourier Transform (FFT). Estimating derivatives. (Jupyter notebooks: fft, symbolic differentiation and finite difference error.
Day 19, Oct 30: Notes and illustrations, FD approx error, cont'd. Forward and reverse mode AD. Jupyter notebook.
Day 20 = Day -9, Nov 4: Notes and illustrations. Reverse-mode AD. Quadrature.
Day 21, Nov 6: Exam 2. One single-sided handwritten page of notes is allowed. No other resources.
Day 22 = Day -7, Nov 11: Notes and illustrations. Gaussian quadrature. Adaptive quadrature. Jupyter notebook.
Day 23, Nov 13: Notes and illustrations. Ch 8: solving systems of nonlinear equations - multi-D Newton. Jupyter notebook:.
Day 24, Nov 18: Notes and illustrations. Ch 8, cont'd.
Day 25, Nov 20: Notes and illustrations. Ch 8, cont'd: homotopy. Ch 9 Optimization in 1D.
Day 26, Nov 25: Notes and illustrations. Ch 9 Optimization in several variables. Individual frames of downhill simplex success and failure.
Day 27, Dec 2
Day 28, Dec 4
Dec 11, Final Exam