Approximation Theory (MAE585)

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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.