Rutgers Math 373 – Numerical Analysis

Current Semester

History and philosophy of the course

Separate sub-sections follow giving the catalog description, relation with other courses, prerequisites, and programming requirements.

Catalog Description

01:640:373-374. NUMERICAL ANALYSIS I,II (3,3)
Prerequisites: CALC4 and familiarity with a computer language. Credit not given for both these courses and 01:198:323,324.
An analysis of numerical methods for the solution of linear and nonlinear equations, approximation of functions, numerical differentiation and integration, and the numerical solution of initial and boundary value problems for ordinary differential equations.
 

373 versus 374

The catalog description treats this a single two semester course with no fixed division of topics between the two parts. This allows some flexibility in organizing the course to follow the presentation in the textbook.  One approach is to put things dealing with functions of one variable in the first semester, with multivariable methods in the second semester.  In particular, techniques of numerical linear algebra are more likely to appear in the second semester, and the solution of differential equations in the first. The page for the current course should be consulted for a syllabus.
 

640:373 versus 198:323

The needs of the subject tends to blur the distinction between Mathematics and Computer Science.  It is not unusual for the same textbook to be used in the two courses.  Neither course is a collection of Numerical Recipes, although it is likely that programming considerations and questions of machine implementation would be more at home in a Computer Science course, while questions of the existence of solutions or the theoretical basis for error estimates are more suitable for a Mathematics course.
 

Prerequisites

Since the numerical solution of differential equations is a major topic in Math 373, prior exposure to the topic in a CALC4 course is essential. That course uses linear algebra, which is also used in other topics contained in Math 373 such as interpolation. The brief treatment of linear algebra in Math 244 will probably suffice for Math 373, but a course equivalent of Math 250 is strongly recommended for Math 374.
 

Programming

We prefer students who are able to implement the algorithms on a computer, but have no specific requirement. There are many different ways to coax useful answers from a computer, and we don't want to limit the students to one particular one. For more than a decade, a pocket calculator has been adequate for most of the methods in 373, although the programming languages of calculators are often so low-level as to be tedious. The textbook fits our approach to the course well because it describes all algorithms in a pseudocode that is easily implemented in the reader's favorite computing environment. Many of the algorithms allow elegant formulation in a spreadsheet, and systems like Maple allow answers to be computed to an accuracy that has no practical interest, but tests the limits of our theoretical results.

Previous semester resources


Comments on this page should be sent to: R.T. Bumby
Last updated: Aug. 29, 2003

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This material is posted by the faculty of the Mathematics Department at Rutgers New Brunswick for informational purposes. While we try to maintain it, information may not be current or may not apply to individual sections. The authority for content, textbook, syllabus, and grading policy lies with the current instructor.

Information posted prior to the beginning of the semester is frequently tentative, or based on previous semesters. Textbooks should not be purchased until confirmed with the instructor. For generally reliable textbook information—with the exception of sections with an alphabetic code like H1 or T1, and topics courses (197,395,495)—see the textbook lists for the appropriate terms: Fall orWinter, Summer.