20900 Numerical Analysis II 1

Credits: 4 advanced credits in Mathematics or in Computer Science

Prerequisites: Students must fulfill all English requirements and take bibliographic instruction in the Library.

Required: Numerical Analysis I and one of the following: Ordinary Differential Equations I or Introduction to Ordinary Differential Equations

The course, which is mostly 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.

The course is a sequel to Numerical Analysis I. It deals with topics in numerical linear algebra that were not covered in Numerical Analysis I, numerical solution of nonlinear systems of equations, and numerical solution of ordinary differential equations.

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

Topics: Iterative methods for the solution of linear systems of equations, approximating eigenvalues, SVD (Singular Value Decomposition), numerical solutions of nonlinear systems of equations, numerical solution of initial value and boundary value problems for ordinary differential equations.

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