Introduction to Computational Mathematics (MAE742A)

General

School School of Science Department of Mathematics Undergraduate MAE742A 7 Introduction to Computational Mathematics Lectures (Weekly Teaching Hours: 3, Credits: 6) Special Background - Greek Yes (in English) See eCourse, the Learning Management System maintained by the University of Ioannina.

Learning Outcomes

Learning outcomes Science is based on two major pillars, both theoretical and experimental. However, over the last few decades scientific computing has emerged and recognized as the third pillar of science. Now, in most scientific disciplines, theoretical and experimental studies are linked to computer analysis. In order for the graduate student to be able to stand with claims in the modern scientific and work environment, knowledge in computational techniques is considered a necessary qualification. The course aims to introduce the student into the field of computational mathematics, emphasizing the implementation of numerical methods using computers. The student will be able to familiarize himself with Matlab and Python programming languages, the most widespread for performing scientific calculations. Working autonomously and in groups, the student will be required to implement computational methods related to the fields of numerical analysis and numerical linear algebra. Specifically, the objectives of this laboratory course are: Familiarity with Matlab and Python programming languages to implement numerical methods and graphical design of the numerical solutions Implementation of polynomial interpolation and function approximation Apply numerical integration Solving linear and nonlinear equations Solving systems of linear equations Study of direct and iterative methods. The course aims to enable the student to: Search, analyze and synthesize data and information, using the available technologies Work autonomously Work in a team Promote free, creative and inductive thinking

Syllabus

• Vector and matrix definition and calculations
• Basic commands and functions
• Graphic representation of the numerical results
• Polynomial interpolation: Lagrange Method, Newton's Method
• Numerical integration: Simple and generalized types of numerical integration, rectangular rule, trapezoid rule, Simpson rule, Gauss integration
• Numerical solution of non-linear equations: iterative methods, bisection method, fixed point method, Newton's method
• Numerical solution of linear systems - Direct methods: Gauss elimination, LU decomposition.

Teaching and Learning Methods - Evaluation

Delivery

In the laboratory

Use of Information and Communications Technology Use of scientific computing software packages
Teaching Methods
Lectures 39
Study of bibliography 39
Laboratory exercises 39
Home exercises (project) 33
Course total 150
Student Performance Evaluation
• Weekly assignments
• Final project
• Written examination at the end of the semester

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:

• Introduction to Numerical Analysis, G.D. Akrivis, V.A. Dougalis, 2010 (in Greek).
• Numerical Linear Algebra, V. Dougalis, D. Noutsos, A. (in Greek).
• A Primer on Scientific Programming with Python, H. P. Langtangen, Springer-Verlag Berlin Heidelberg, 5 Edition, 2016.
• Programming for Computations- MATLAB/Octave, S. Linge, H. P. Langtangen, Springer International Publishing, 2016 (in Greek).