Scientific Computing (MAE848A)

Undergraduate Courses Outlines - Department of Mathematics

General

School	School of Science
Academic Unit	Department of Mathematics
Level of Studies	Undergraduate
Course Code	MAE848
Semester	8
Course Title	Scientific Computing
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	In most scientific disciplines, the integration of computers has defined new directions to perform research and has offered unprecedented potential to solve complicated problems. Combined with theory and experimentation, computational analysis is nowadays considered an integral part of science and research. The main objective of the course is to familiarize the student with computational techniques that find application in the solution of ordinary and partial differential equations. In the context of this laboratory course, the student will gain access to the programming languages Matlab/Octave and Python, which are widely used to perform scientific calculations. Computational methods to be developed and implemented in PCs will significantly increase the skills and prospects of integrating graduates into the modern scientific and work environment. Starting from the mathematical modeling of problems of Mechanics and Applied Mathematics in general, and by synthesizing information from numerical analysis and numerical solution of ordinary and partial differential equations, students will acquire crucial knowledge in solving mathematical problems by computational means. <br\> Specifically, the objectives of the course are: Familiarity with the Matlab/Octave and Python programming languages to implement numerical methods, solve mathematical problems and graphically design the numerical results Apply numerical derivation using the Finite Difference method Analysis of the numerical schemes resulting from the Finite Difference method Solving ordinary differential equations using one-step and multi-step methods Solving parabolic and elliptic Partial Differential Equations with the Finite Difference Method Theoretical analysis of the Finite Element method Solving parabolic and elliptic Partial Differential Equations with the Finite Element method.
General Competences	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

Initial Value Problems
Boundary Value Problems
Finite Difference method
Equations of Difference
Shooting methods and Method of undetermined coefficients
One-step Methods (Euler, Taylor, Runge-Kutta)
Multi-step Methods (Adams-Bashforth, Adams-Moulton, Predictor-Corrector)
Finite Element Method (Galerkin).

Teaching and Learning Methods - Evaluation

Delivery

In the laboratory

Use of Information and Communications Technology

Use of scientific computing software packages

Teaching Methods

Activity	Semester Workload
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. Additionally:

Numerical Methods for Ordinary Differential Equations, 2 Edition, G.D. Akrivis, V.A. Dougalis, 2012 (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).
The Mathematical Theory of Finite Element Method, S. C. Brenner, L. R. Scott, Springer-Verlag, New York, 2008.
Automated Solution of Differential Equations by the Finite Element Method, A. Logg, K.-A. Mardal, G. N. Wells, Springer-Verlag Berlin Heidelberg, 2012.