Teaching / Course archive
Math 578: Fall 2020
Numerical analysis
Course Record
Overview
Graduate numerical analysis course on linear systems, eigenproblems, least squares problems, nonlinear systems, approximation, and numerical integration of initial value problems.
Python was used as the official programming language for computational work.
Schedule and Topics
Topic List
- Direct methods for linear systems: LU and QR factorization, conditioning, and stability
- Iterative methods for linear systems: Jacobi, Gauss-Seidel, SOR, steepest descent, conjugate gradients, and preconditioning
- Eigenproblems: Hessenberg form, QR algorithm, and Jacobi method
- Least squares problems: normal equations, QR factorization, and SVD
- Nonlinear systems and optimization: gradient descent, fixed point iteration, Newton-Raphson and variants
- Approximation of functions: interpolation, least squares approximation, uniform approximation, polynomial and trigonometric functions
- Initial value problems: Runge-Kutta methods, consistency, stability, convergence, stiffness, and adaptivity
Books and Related Pages
Books
- Alfio Quarteroni, Riccardo Sacco, and Fausto Saleri, Numerical mathematics. Springer.
- Endre Suli and David Mayers, An introduction to numerical analysis. Cambridge University.
- Lloyd N. Trefethen and David Bau III, Numerical linear algebra. SIAM.
- Germund Dahlquist and Ake Bjorck, Numerical methods. Dover.
- Eugene Isaacson and Herbert B. Keller, Analysis of numerical methods. Dover.
Related Course Pages
Assignments and Projects
Assignments and Exams
- Analytical and computational homework assignments.
- Course project involving an advanced topic, implementation, experimentation, report writing, and a presentation.
Archive Note
The Fall 2020 archive preserves the public course outline and topic list; lecture media were hosted inside the course management system and are not included.