Computer Science 362

NUMERICAL ALGORITHMS

Instructor: Nicholas Harkiolakis

E-mail: nhark@laverne.edu.gr Message phone: 6233307

Course Description:

Provides a foundation in modern numerical-approximation techniques along with explanations of how, why, and when the techniques can be expected to work. Use real life problems from areas such as engineering, computer science, biology, and physics to show how numerical methods can be applied. Lab included.

Course Objectives:

To identify the type of problems that require numerical techniques for their solution and see examples of error propagation that can occur when numerical methods are applied. To accurately approximate the solutions of problems that cannot be solved exactly and learn techniques for estimating bounds for the error in the approximations.

Syllabus/Course Topics:

Introduction. Mathematical preliminaries.

Solutions of equations in one variable.

Solutions of linear systems of equations. Direct methods. Iterative techniques.

Solutions of nonlinear systems of equations. Optimization.

Interpolation and approximation techniques and theory.

Differentiation and integration. Initial value and boundary value problems.

Partial differential equations.

Introduction to advanced topics: Simulated annealing, genetics algorithms, DNA computing, neural networks.

Computer Lab work:

A hands on course: Programming with Pascal, C, C++.

Course Organization:

All the theory of CMPS 362 course is combined with the development of computer programs.

Grade Assessment:

Class attendance and participation: 10%

Weakly homework: 50%

Presentation: 20%

2 hour final exam: 20%

Textbook:

Burden, L.R., Faires, J.D., Numerical Analysis, 6^th Edition, Brooks/Cole, 1997.