20462 Numerical Analysis I 1

Credits: 4 intermediate credits in Mathematics or in Computer Science

Prerequisites: none

Required: One of the following: Introduction to Computer Science Using Java, Introduction to Computer Science Using Java I, Fundamentals of Programming with Java; one of the following: Linear Algebra I, Linear Algebra for Natural Science Students; one of the following: Infinitesimal Calculus I, Differential and Integral Calculus I; and one of the following: Infinitesimal Calculus II, Differential and Integral Calculus II

The course, based on Numerical Analysis (8th ed.), by R.L. Burden and J.D. Faires (Brooks/Cole, 2005), was developed by Tamir Tassa and Mireille Avigal.

Numerical analysis is one of the fundamental domains of applied Mathematics. It deals with efficient methods for the approximate solution of numerical problems of continuous Mathematics, including the estimation of the error in such approximate computations. A discussion of a particular problem includes the design of an approximation method, its implementation, typically by a computer program, estimating its computational efficiency (time and memory complexities), and proving theorems regarding the magnitude of the error of the approximation. Hence, even though it is a mathematical subject, numerical analysis may be viewed as an interdisciplinary area that also belongs to Computer Science.

The course combines theory and implementation. Students are required to program some of the algorithms covered in the course.

Topics: Solutions of equations in one variable; Interpolation and polynomial approximation; Numerical differentiation and integration; Introduction to approximation theory; Numerical methods for systems of linear equations.

1There is some overlap in the content of this and other courses. For details, see Overlapping Courses.