Spring 17: MATH-UA 0252-001: Numerical Analysis
Instructor:
Georg Stadler, Warner Weaver Hall Office #1111
Lectures: Tuesday and Thursday 12:30-13:45pm, class starts on 1/24
Location: Warren Weaver Hall #317
Office Hours: Wed. 10am-noon or by appointment-please email.
Recitation: Friday 12:30-13:45pm, TA: Ana Perez-Gea, WWH 101
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.
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 |
|---|---|---|---|---|
| 1/24 | fixed point iteration | 1.1, 1.2 | Slides (PDF), Notes (PDF) | |
| 1/26 | stable fixed points, convergence speed | 1.2 | Notes (PDF) | |
| 1/31 | Newton's method | 1.4 | Notes (PDF) | fixed point example |
| 2/2 | Secant, bisection, global, Newton in 2D | 1.5-1.7 | Notes (PDF), Global_plot (PNG) | global behavior script |
| 2/7 | Gaussian elimination | 2.1,2.2 | Notes (PDF), Timing plot (PDF) | Timing script |
| 2/9 | *** snow day *** | |||
| 2/14 | LU factorization, pivoting | 2.3-2.5 | Notes (PDF) | |
| 2/16 | computatioal work, forw/back subst. | 2.5,2.6 | Notes (PDF) | |
| 2/21 | conditioning, vector and matrix norms | 2.7 | Notes (PDF) | example from class |
| 2/23 | conditioning, least squares | 2.7,2.9 | Notes (PDF), Matrix norm illustration (PDF) | |
| 2/28 | least squares, QR | 2.9 | ||
| 3/2 | eigenvalues intro, power method, inverse iterations, Gerschgorin | 5.1,5.2,5.8,Deuflhard/Hohmann 5.2 | ||
| 3/7 | summary of QR, power method and Google, inverse iterations | Notes (PDF) Wired article on Google, paper1, paper2, SIREV paper | ||
| 3/21 | Householder for tridiagonalization | 5.5 | Notes (PDF) | |
| 3/23 | Givens/plane rotations, QR for eigenvalues | 5.3,5.7 | Notes (PDF) | orthogonalization example, QR for eigenvalues example |
| 3/28 | Remarks around QR, Lagrange interpolation | 6.1,6.2 | Notes (PDF) | |
| 3/30 | Lagrande, Hermite interpolation, convergence | 6.2-6.4 | Notes (PDF) | Interpolation example, Runge phenomenon |
| 4/4 | Newton-Cotes quadrature | 7.1-7.4 | Notes (PDF) | |
| 4/6 | Composite quadrature formulas, inner product spaces | 7.5, 9.1-9.2 | Notes (PDF) | |
| 4/11 | orthogonal polynomials | 9.2-9.4 | Notes (PDF) | l2 polynomial approx. |
| 4/13 | orthogonal polynomials, intro to Gauss quadrature | 9.4, 10 | Notes (PDF) | |
| 4/18 | Gauss quadrature | 10 | Notes (PDF) | |
| 4/20 | Intro to initial value problems | 12.1,12.2 | Notes (PDF) | |
| 4/25 | Euler's method | 12.2 | Notes (PDF) | Euler example |
| 4/27 | Trapezoidal rule, Runge Kutta | 12.4, 12.5 | Notes (PDF) | Trapezoidal IVP solver |
| 5/2 | classic RK4, multistep methods | 12.5,12.6 | Notes (PDF) | Runge-Kutta IVP solver |
Homework assignments:
*) Assignment 1: [ PDF, TEX ], due Feb 9.
*) Assignment 2: [ PDF, TEX ], due Feb 23.
*) Assignment 3: [ PDF, TEX ], due March 9.
4) Assignment 4: [ PDF, TEX ], due March 30.
5) Assignment 5: [ PDF, TEX ], due April 13.
6) Assignment 6: [ PDF, TEX ], due April 25.
7) Assignment 7: [ PDF, TEX ], due May 4.