Fall 18: MATH-UA 0252-001: Numerical Analysis
Instructor:
Georg Stadler, Warner Weaver Hall Office #1111
Lectures: Tuesday and Thursday 11:00-12:15pm, class starts on September 6
Location: Warren Weaver Hall #312
Office Hours: Wed. 10-11:30am or by appointment-please email.
Recitation: Friday 11:00-12:15pm, WWH #201, TA: Karina Koval
If you email me about the class, please start your subject line with [NA], or use this link.
We will use Piazza for communication and organization. If you are registered for this class you will receive an invitation to join the course on Piazza at the beginning of the semester. Otherwise please email me and I will add you.
Content:
We will cover classical topics in Numerical Analysis: The solution of linear and nonlinear equations, conditioning, least squares, numerical computation of eigenvalues, interpolation, quadrature, and numerical methods for ODEs. The course will have a focus on the analysis of numerical methods, but also require you to use numerical software (Matlab, Python, or Julia). If you are not familiar with any of these tools, the recitation will give an introduction to Matlab during the first weeks. Additionally, I recommend to work through one of the books listed below before the course starts or in the first weeks of the semester.
Grading policy:
30% Homework, 10% Quizzes, 25% Midterm, 35% Final.
Literature:
Endre Suli and David Mayers (2003): An Introduction to Numerical Analysis. Cambridge University Press, 2003. PDF available from campus
Further reading:
Ridgeway Scott (2011): Numerical Analysis, Princeton University Press.
Gander, W., Gander, M.J., & Kwok, F. (2014). Scientific Computing - An Introduction Using Maple and MATLAB. Texts in Computation Science and Engineering [Series, Vol. 11]. New York, NY: Springer-Verlag.
Moler, C: (2004) Numerical Computing with Matlab, SIAM.
Classes and Material:
| Date | Topics | Book Sections | Slides and notes | Code Examples |
|---|---|---|---|---|
| 9/6 | fixed point iteration | 1.1, 1.2 | Slides (PDF), Notes (PDF) | |
| 9/11 | fixed point convergence | 1.2, 1.3 | Notes (PDF) | fixed point example (.m) |
| 9/13 | stability of fixed points, Newton method | 1.4 | Notes (PDF) | Newton method example (.m) |
| 9/18 | Newton convergence proof, secant, bisection, global behavior of Newton | 1.5-1.7 | Notes (PDF) | Newton ex1 (.m), Newton ex2 (.m), Newton ex3 (.m), global Newton behavior plot (.png) |
| 9/20 | Gaussian elimination | 2.1,2.2 | Notes (PDF) | timings of LA operations (.m) |
| 9/25 | LU factorization, pivoting | 2.3,2.4 | Notes (PDF) | |
| 9/27 | pivoting, computational work | 2.6 | Notes (PDF) | |
| 10/2 | computer number representation, conditioning | 2.7 and notes | Notes (PDF) | |
| 10/4 | vector and matrix norms | 2.7 | Notes (PDF) | |
| 10/9 | **no class (fake Tuesday)** | |||
| 10/11 | condition numbers | 2.7 | Notes (PDF) | |
| 10/16 | least squares | 2.8 | Notes (PDF) | |
| 10/18 | eigenvalues, Gershgorin, power method | 5.1,5.2,4.4 | Notes (PDF) | |
| 10/23 | power method, revision | Notes (PDF) | ||
| 10/25 | **midterm** | |||
| 10/30 | inverse iteration, Householder | 5.8,5.5 | Notes (PDF) | |
| 11/1 | Householder, Givens | 5.6 | Notes (PDF) | orthogonalization.m |
| 11/6 | QR factorization, QR algorithm | 5.7,5.3 (only first 2 pages) | Notes (PDF) | |
| 11/8 | QR alg, Lagrange interpolation | 6.1,6.2 | Notes (PDF) | |
| 11/13 | Hermite interpolation, convergence | 6.2,6.3,6.4 | Notes (PDF) | Interpolation, Runge phenomenon(.m) |
| 11/15 | Newton-Cotes quadrature | 7.1-7.4 | Notes (PDF) | |
| 11/20 | Composite quadrature | 7.5 | Notes (PDF) | |
| 11/27 | inner product spaces, orthogonal polynomials | 9.1-9.4 | Notes (PDF) | 2-norm approximation (.m) |
| 11/29 | orthogonal polynomials, quadrature | 10 | Notes (PDF) | |
| 12/4 | Gauss quadrature | 10 | Notes (PDF) | |
| 12/6 | IVPs, Euler's method | 12.1-12.2 | Notes (PDF) | |
| 12/11 | Trapezoidal rule, implicit Euler | 12.4 | Notes (PDF) | ODE-Euler(.m), ODE-trapezoidal(.m) |
| 12/13 | Runge-Kutta | 12.5 | Notes (PDF) |
Homework assignments:
*) Assignment 1: [ PDF, TEX and figure for TEX file], due Sep 25.
*) Assignment 2: [ PDF, TEX], due Oct 11.
*) Assignment 3: [ PDF, TEX], due Oct 23.
*) Assignment 4: [ PDF, TEX], due Nov 8.
*) Assignment 5: [ PDF, TEX], due Nov 20.
*) Assignment 6: [ PDF, TEX, figure for TEX file], due Dec 6.
*) Assignment 7: [ PDF, TEX ], due Dec 13.
*) Final, Dec 18.