MATH 471

Numerical Analysis I




This course is addressed to senior and graduate students of Sciences and Engineering. Its objectives are to introduce the students to some of the more important topics of Numerical Linear Algebra including aspects of the theory by which its algorithms may be analyzed and to high-quality Numerical Software of Linear Algebra.

The core topics are Direct Methods for Solving Linear Systems, Conditioning and Perturbation, Iterative Techniques for Solving Linear Systems, the Linear Least-Squares Problem and the Matrix Eigenvalue Problem. The treatment of these topics is balanced with respect to theory and computations and it is firm and rigorous. Hence, it calls for a good coverage of some elements of Floating-Point Round-Off Analysis, a study of rudiments of Matrix Theory and a brief review of selected topics from Linear Algebra as bases.

The objectives are consistent with the course description (Undergraduate Bulletin, 2001-03) and they are certainly within the reach of a good student a student who had done good on the Prerequisites (Math 280 and Math 321 or SE 301), who has good recollection of the materials covered there and who is willing to do good and serious work.

Forward Outlook: Math 471 (Numerical Analysis I) and Math 472 (Numerical Analysis II) form a total package that contains standard topics of numerical analysis. Thus, for further study in this field, the next recommended course is Math 472.


(A copy of the syllabus is attached.)



M. Sarhan

Course Instructor

MATH 471

Semester II, 2003-04 (032)

Submitted: January 2004


MATH 471

Numerical Analysis I

Semester II, 2003-04(032)


To the Student



Math 471 is a rigorous course in Numerical Linear Algebra. The student is assumed to have had introductory courses in linear algebra and numerical analysis such as Math 280 and Math 321 or SE 301. He should be able to do programming in FORTRAN.

A copy of the course syllabus is attached to this prelude. It clearly indicates what is to be covered, the references and the rate of coverage. A copy of the list of Supplementary References (SR) and a copy of the course objectives are also attached.

Each lecture is an integral part of the course. Some lectures contain supplementary material. Thus, good notes of lectures must be taken.

There certainly will be reading and studying assignments and homework and programming assignments. A deadline will be specified for each assignment and it must be normally met by all students. Reading and studying assignments may contain material that is not covered in class; such assignments should be taken very seriously. All assignments that are required for submission must be done strictly in clear, clean and neat form. A certain format will be explained in class.

Students should be ready and able to do some simple programming in FORTRAN by the end of the second week of classes. Proficiency in programming is expected at a later stage.

With respect to grading, the general outline of the course is as follows: There will be a Midterm exam (25%), Prefinal (15%) and Final (10%) exams. Each exam will be based largely on all new material covered in the lectures preceding it. All exams will be both computational and theoretical in nature. Homework and programming assignments will count as 50% of the total grade.

It is likely that Help Sessions will be scheduled. Such sessions are meant to remedy deficient background and to assist in learning new materials.

Homepages and e-mail will certainly facilitate contacts. Details are given below. Effective use of all recourses is certainly encouraged.

I wish you a productive and a rewarding experience and I look forward to having a pleasant semester with all of you.




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Dr. Mahmoud Sarhan


Math 471(032)