## Course Description

What makes numerical computing different from the computing you've done before? How do you know if you can trust your answers? Using a combination of math and computer science, we will answer these questions through the study of several applications in science, engineering, medicine and business. The numerical topics to be covered include numerical integration and differentiation, solving linear and non-linear equations, ordinary differential equations.

## Prerequisites

V22.0102 (Intro. to Computer Science II)

V63.0140 (Calculus I, and preferably Calculus II)

V63.0140 (Linear Algebra)

## Course Work

The course will include written and programming assignments (in matlab and/or other (compiled) languages), in-class tests, and possibly a course final project. You will not need a laptop in-class; in fact I ask all students to close their laptops at the start of each class. Class participation and attendance will count.

## Course Textbook

The course will use a draft of "A First Course on Numerical Methods", by Uri Ascher and Chen Greif. It is available on a password protected website at Click Here

## Class Mailing List

All students should register with the class mailing list, which should be used for all questions and technical discussions concerning the course and the homeworks. To subscribe to the class mailing list, there is a web based interface at http://cs.nyu.edu/mailman/listinfo/v22_0421_001_sp11

Class Date | Subject | Corresponding Text Reading |
---|---|---|

Jan. 25 | Course Introduction what is numerical computing; types of errors | Chap. 1 |

Jan. 27 | Snow Day - Class Cancelled | |

Feb. 1 | Floating Point Number Representation | Chap. 2 |

Feb. 3 | (cont.) | |

Feb. 8 | Non-linear Equations | Chap. 3 (skip fixed pt. iteration) |

Feb. 10 | (cont.) | |

Feb. 15 | Systems of Linear Equations | Chap. 4 and 5 |

Feb. 17 | cont. - (Gauss Elim.) | |

Feb. 22 | cont. (LU factorization ) | |

Feb. 24 | cont. (pivoting, stability ) | |

March 1 | matrix and vector norms, error bounds | |

March 3 | Cholesky factorization, SPD matrices | |

March 8 | Review | |

March 10 | Midterm | |

March 15 | Spring Break | |

March 17 | Spring Break | |

March 22 | Interpolation and Approximation | Chap. 10 |

March 24 | Lagrange and Newton form of interp. | |

March 29 | Divided differences (short class) | |

March 31 | Poly. interpolation error estimates | |

April 5 | Splines | Chap. 11 |

April 7 | Richardson Extrapolation | p. 440 neighborhood |

April 12 | Numerical Quadrature | Chap. 15 |

April 14 | Composite Rules, Errors, Corrected Trap. Rule | |

April 19 | Adaptive Quadrature, Richardson extrap. for unknown p | |

April 21 | 2 point Guass quadrature | |

April 26 | Some performance issues in Scientific Computing | |

April 28 | Intro. to Shared memory programming using OpenMP | |

May 3 | Least Squares | pp. 153-163 (skip p. 159 formulas) |

May 5 | More OpenMP, Amdahl's Law, Review | |

May 12 | Final Exam 10:-11:50 AM |

- Assigned Feb. 1, Due Feb. 8. Homework 1
- Assigned Feb. 10, Due Feb. 17. Programming Homework 2
- Assigned Feb. 15, Due Feb. 17. Written Assignment 2
- Assigned Feb. 24, Due Mar. 3. Homework 3
- Assigned March 24, Due Mar. 31. Homework 4 hw4a.dat hw4b.dat hw4c.dat
- Assigned April 5, Due April 12. Homework 5
- Assigned April 19, Due April 26. Homework 6
- Assigned April 28, Due May 5. Homework 7

- Compute a derivative deriv.m
- Newton iteration example

newtonSetup.m

newtonStep.m

f.m - Lagrange polynomial example
polyEx.m

- Error polynomial, Runge example
runge.m ,
psi.m

- sum1.c timing.c timing.h
sum1.c ,
timing.c
timing.h

compile line: gcc -O2 sum1.c timing.c -lm -lrt -o xsum1 - serialmat.c serialmat.c ,