Course number: | MA-UY 4423 |

Semester: | Spring 2015 |

Time & Location: | Tues & Thurs, 2:00pm - 3:30pm in JABS 673 |

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

Office hours: | Tues & Thurs, 3:30pm - 5:00pm in RH 321F |

This course will serve as an introduction to the topic of numerial analysis for those students interested in gaining some knowledge of the computational aspects of mathematics on modern day computers. This course is intended for students that have completed Calculus II, Ordinary Differential Equations, and (maybe) have some programming experience. Topics covered in this class will include: floating-point arithmetic, numerical integration and differentiation, interpolation, numerical linear algebra, orthogonal polynomials, and solution of ODEs. Time permitting, algorithms used in Monte Carlo methods and optimization will be covered. Programming assignments will be in Matlab.

The course text will be
Greenbaum and Chartier,
*Numerical Methods:
Design, Analysis, and Computer Implementation of
Algorithms*.
Notes covering additional topics in numerical linear algebra will
be provided. Course homework will partially be drawn
from the textbook.

Other textbooks that might serve as useful supplements are:

- Burden and Faires,
*Numerical Analysis* - Suli and Mayers,
*An Introduction to Numerical Analysis* - Stoer and Bulirsch,
*Introduction to Numerical Analysis*(more advanced)

The grades in the course will be determined based on homework, a midterm exam, and a final exam. Details to follow.

Important information, and homework assignments, for the course will appear below as necessary.

- First class on Jan 26
- Homework 1 (due Feb 4)
- Homework 2 (due Feb 11)
- Homework 3 (due Feb 18)
- Homework 4 (due Feb 25)
- Homework 5 (due Mar 3)
- Homework 6 (due Mar 10)
- See last year's lecture notes for help reviewing for the midterm.
- Homework 7 (due Mar 31)
- Homework 8 (due Apr 7)
- Homework 9 (due Apr 14)
- Homework 10 (due Apr 21)
- Homework 11 (due Apr 28)
- The Final Exam is Tuesday May 17th, from 1pm-3pm in room RH315. Only scientific calculators are allowed. No sheet of notes or formulas is allowed.

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

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

Tues. Jan 26 | Introduction & overview | |

Thurs. Jan 28 | Newton, secant method, fixed point | |

Tues. Feb 2 | Multivariate Newton, optimization | newton.pdf |

Thurs. Feb 4 | Floating point arithmetic | |

Tues. Feb 9 | Conditioning and stability | |

Thurs. Feb 11 | LU factorization | |

Tues. Feb 16 | Matrix conditioning | |

Thurs. Feb 18 | Least squares, SVD | |

Tues. Feb 23 | Lagrange interpolation | |

Thurs. Feb 25 | Interpolation error, Chebyshev polynomials | |

Tues. Mar 1 | Splines, numerical differentiation | |

Thurs. Mar 3 | Numerical differentiation, finite differences | |

Tues. Mar 8 | Review for midterm | |

Thurs. Mar 10 | Midterm exam | |

Tues. Mar 15 | No class - spring break | |

Thurs. Mar 17 | No class - spring break | |

Tues. Mar 22 | Richardson extrapolation, trapezoidal rule | |

Thurs. Mar 24 | Gaussian quadrature | integration.pdf |

Tues. Mar 29 | ODE: Euler's method | |

Thurs. Mar 31 | ODE: Trapezoidal method, Heun's method | |

Tues. Apr 5 | ODE: Runge-Kutta methods | |

Thurs. Apr 7 | ODE: Linear difference equations | |

Tues. Apr 12 | ODE: Stability | |

Thurs. Apr 14 | Intro to eigenvalue computation | |

Tues. Apr 19 | Power methods | |

Thurs. Apr 21 | Iterative solvers | iterative.pdf |

Tues. Apr 26 | The FFT | fft.pdf |

Thurs. Apr 28 | The FFT | |

Tues. May 3 | Methods for PDEs | |

Thurs. May 5 | Review for final exam | |

Tues. May 17 | Final exam |