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

ΜΑΕ585

Semester

5

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) See eCourse, the Learning Management System maintained by the University of Ioannina.

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 the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:

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