Approximation Theory (MAE585)

Undergraduate Courses Outlines - Department of Mathematics

General

School	School of Science
Academic Unit	Department of Mathematics
Level of Studies	Undergraduate
Course Code	ΜΑΕ645
Semester	6
Course Title	Approximation Theory
Independent Teaching Activities	Lectures (Weekly Teaching Hours: 3, Credits: 6)
Course Type	Special Background
Prerequisite Courses	-
Language of Instruction and Examinations	Greek
Is the Course Offered to Erasmus Students	Yes (in English)
Course Website (URL)	-

Learning Outcomes

Learning outcomes

After successful end of this course, students will be able to: understand the basic theory of approximation in spaces of functions, be aware and apply the taught methods for best uniform polynomial approximation, least squares polynomial approximation of functions defined in an interval (continues case), as well as of functions defined in a set of points (discrete case), be aware and apply the taught methods for cubic splines polynomial interpolation, implement the above methods with programs on the computer.

General Competences

Search for, analysis and synthesis of data and information, with the use of the necessary technology Adapting to new situations Criticism and self-criticism Production of free, creative and inductive thinking

Syllabus

Introduction to Approximation Theory in Spaces of Functions (Existence - Uniqueness). Polynomial Approximation of Functions: Weierstrass Theorem. Best Uniform Approximation. Least Squares Approximation. Hermite Polynomial Interpolation. Cubic Splines Polynomial Interpolation.

Teaching and Learning Methods - Evaluation

Delivery	In the class
Use of Information and Communications Technology	-
Teaching Methods	Activity Semester Workload Lectures 39 Study and analysis of bibliografy 104 Exercises-Homeworks 33 Course total 150
Student Performance Evaluation	Written examination

Attached Bibliography

See Eudoxus. Additionally:

• "Approximation Theory". Noutsos D., University of Ioannina.