V22.0421-001

Numerical Computing

Tues/Thurs 11:00 a.m.-12:15 p.m.

Warren Weaver Hall, Room 317

Prof. Marsha Berger

Office: WWH 1120


Basic Course Information:

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

Lectures/Corresponding Text Chapters

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

Homework/Programming Assignments:

Matlab and C Programs

Matlab Tutorials

You can find many on the web. A few short ones to get started are: