Course number: | MATH-UA 252.001 |

Semester: | Spring 2018 |

Time & Location: | Tues & Thurs, 12:30pm - 1:45pm in CIWW 101 |

Instructor: | Mike O'Neil (oneil@cims.nyu.edu) |

Office hours: | Tues, 2:30pm - 4:30pm in CIWW 1119 |

Recitation: | Fri, 12:30pm - 1:45pm in CIWW 101 |

Recitation Instructor: | Mu-Hua Chien (mhc431@nyu.edu) |

Office hours: | Wed, 9:50am - 10:50am in CIWW 505 |

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.

Various other documents and course schedule will be posted to this website.

The textbook for the course is *An Introduction to
Numerical Analysis*, Suli and Mayers, Cambridge
University Press,
2003. PDF available via NYU. Supplemental
texts and references will be suggested along the way.

Relevant code examples will be posted on gitlab.com/oneilm/na18.

Important information for the course will appear on the Piazza page.

- Assignment 1: [ .pdf, .tex ], due Feb 8.
- Assignment 2: [ .pdf, .tex ], due Feb 22.
- Assignment 3: [ .pdf, .tex ], due Mar 8.
- Assignment 4: [ .pdf, .tex ], due April 5.
- Assignment 5: [ .pdf, .tex ], due April 19.
- Assignment 6: [ .pdf, .tex ], due May 3.

Below is an updated list of lecture topics along with any documents that were distributed, or relevant code.

Date | Topics | Materials |
---|---|---|

January 23 | Overview, bisection and secant methods | Trefethen,
1992 Suli & Mayers, Sec 1.1, 1.5-1.6 Lecture notes |

January 25 | Newton's method | Suli & Mayers, Sec 1.4 Lecture notes |

January 30 | Fixed points, contractions | Suli & Mayers, Sec 1.2 Lecture notes |

February 1 | Stability and convergence of fixed points | Suli & Mayers, Sec 1.2 Lecture notes |

February 6 | Fixed points, floating point arithmetic | Lecture notes |

February 8 | Gaussian elimination, computational cost | Suli & Mayers, Sec 2.1-2.2 Lecture notes |

February 13 | LU factorization, pivoting | Suli & Mayers, Sec 2.3-2.6 Lecture notes |

February 15 | Vector and matrix norms | Suli & Mayers, Sec 2.7 Lecture notes |

February 20 | Condition numbers | Suli & Mayers, Sec 2.7 Lecture notes |

February 22 | Condition number of a matrix | Suli & Mayers, Sec 2.7 Lecture notes |

February 27 | The SVD | Suli & Mayers, Sec 2.7, 2.10 Lecture notes |

March 1 | Least squares | Suli & Mayers, Sec 2.9 Lecture notes |

March 6 | Review for midterm | Review topics |

March 8 | Midterm | |

March 13 | Spring Break | |

March 15 | Spring Break | |

March 20 | Eigenvalues: Motivation | Lecture notes |

March 22 | Eigenvalues: Power method | Suli & Mayers, Sec 5.4 Lecture notes |

March 27 | Eigenvalues: Inverse power method | Suli & Mayers, Sec 5.8 Lecture notes |

March 29 | Eigenvalues: Jacobi's Method | Suli & Mayers, Sec 5.3 Lecture notes |

April 3 | Polynomial interpolation: Lagrange form | Suli & Mayers, Sec 6.1-6.3 Lecture notes |

April 5 | Polynomial interpolation: Barycentric forms, Runge effect | Lecture
notes Berrut and Trefethen, 2004 |

April 10 | Function approximation: Infinity-norm | Suli & Mayers, Chap 8 Lecture notes |

April 12 | Function approximation: 2-norm, orthogonal polynomials | Suli & Mayers, Chap 9 Lecture notes |

April 17 | Numerical Integration: Newton-Cotes | Suli & Mayers, Sec 7.1-7.4 Lecture notes |

April 19 | Numerical Integration: Euler-Maclaurin, Gaussian Quadrature | Suli & Mayers, Sec 7.5-7.6, 10.1-10.4 Lecture notes |

April 24 | ODEs: Initial value problems, finite differences | Suli & Mayers, Sec 12.1-12.2 Lecture notes |

April 26 | ODEs: Richardson extrapolation, Local & global error | Suli & Mayers, Sec 7.7, 12.2-12.3 Lecture notes |

May 1 | ODEs: Implicit schemes, stiff equations | Suli & Mayers, Sec 12.3-12.4, 12.8, 12.11 Lecture notes |

May 3 | ODEs: Stiff equations, stability | Suli & Mayers, Sec 12.11 Lecture notes |

May 10 | Final Exam: 12:00pm-1:50pm, CIWW 101 | Review topics |