The University of Massachusetts Boston

Department of Mathematics

MA425: Numerical Analysis, Fall 2013

Instructor: Prof. Alfred Noël

Office : 3-175 Science Building

Phone : (617)-287-6458

Email : anoel@math.umb.edu

Url : http://www.math.umb.edu/~anoel

Time: Tuesday, Thursday 2:00 PM – 3:15 PM

Room: M02-0417

Conference Hours: Tuesday, Thursday 12:00 PM – 1:30 PM

Course Description:

This course introduces students to the formulation, the evaluation and the construction of rigorous mathematical software. Most problems in science and engineering require a strong understanding of various numerical schemes that are suitable for modern computing machines. The main goal of the course is to emphasize mathematical and software engineering methods that will allow students to fully participate at all levels of algorithm design and implementation.

The topics to be covered include: fundamental principles of digital computing and the implications for algorithm accuracy and stability, error propagation and stability, the solution of systems of linear equations, including direct and iterative techniques, roots of equations and systems of equations, numerical interpolation, matrix decompositions, least-Square methods, Monte Carlo Simulation, Trigonometric Interpolation, Fast Fourier Transform and error and convergence analysis.

Prerequisite: MA 141, MA 260 or Instructor’s permission.

Software: Most of the implementation will be done in MATLAB. Homework assignment must be compiled using a version of TeX or LaTeX.

Text: Numerical Analysis 2^nd Edition by Timothy Sauer. ISBN 978-0321-7

Material to be covered:

The following chapters will be covered: Chapters : 0, 1, 2, 3, 4 Sections: 9.1, 9.2, 10.1, 10.2, 11.1, 11.2 and Chapter 12 if time permits.

Students are expected to quickly familiarize themselves with the basics of MATLAB

Click here to find your homework assignment.

MATLAB Tutorial Resources:

http://www.mathworks.com/academia/student_center/tutorials/launchpad.html

Matlab tutorial - University of Florida

http://www.math.utah.edu/lab/ms/matlab/matlab.html

Assessment: There will be weekly homework assignments, a midterm exam and a cumulative final exam. The homework assignments will deal with the theoretical part of the material and will include some small computational and programming exercises.

Grading Procedures:

Homework 50%: Midterm 20% Tuesday October 29, 2010: Final 30%

STUDENTS ARE RESPONSIBLE FOR MATERIAL COVERED IN CLASS.