Math 373 - Numerical Analysis I
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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.
Fall 2018 Schedule
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. Some prior programming experience is desirable, but not essential.
Programming
Part of the course involves computer implementation of the algorithms discussed, and therefore some prior programming experience is desirable, although not essential. The computer assignments will be fairly short, and although a computer language is not taught in the course, a description of Matlab commands that can be used to write the programs and examples of their use will be provided on the course webpage.
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