SCHOOL

ENGINEERING

ACADEMIC UNIT

ELECTRICAL AND COMPUTER ENGINEERING

LEVEL OF STUDIES

Undergraduate

COURSE CODE

ECE_Υ321

SEMESTER

Third

COURSE TITLE

PARTIAL DIFFERENTIAL EQUATIONS AND TRANSFORMATIONS

INDEPENDENT TEACHING ACTIVITIES
if credits are awarded for separate components of the course, e.g. lectures, laboratory exercises, etc. If the credits are awarded for the whole of the course, give the weekly teaching hours and the total credits

WEEKLY TEACHING HOURS

CREDITS

Lectures and laboratory exercises

4+1

6

Add rows if necessary. The organisation of teaching and the teaching methods used are described in detail at (d).

COURSE TYPE

general background,
special background, specialised general knowledge, skills development

General background, Skills development

PREREQUISITE COURSES:

The courses: “Multivariable Calculus & Vector Analysis” (ECE_Y212) και “Ordinary Differential Equations and Complex Analysis» (ECE_Y214).

LANGUAGE OF INSTRUCTION and EXAMINATIONS:

Greek

IS THE COURSE OFFERED TO ERASMUS STUDENTS

YES

COURSE WEBSITE (URL)

Learning outcomes

The course learning outcomes, specific knowledge, skills and competences of an appropriate level, which the students will acquire with the successful completion of the  course are described.

Consult Appendix A

·    Description of the level of learning outcomes for each qualifications cycle, according to the Qualifications Framework of the European Higher Education Area

·    Descriptors for Levels 6, 7 & 8 of the European Qualifications Framework for Lifelong Learning and Appendix B

·    Guidelines for writing Learning Outcomes

This course is one of the basic courses of Applied Mathematics taught in the Department, since the knowledge and the skills developed herein are necessary in subsequent specialization courses in electrical and computer engineering, and in general they contribute to building a complete background for Engineering. Thus the intended learning outcomes are the following:

1.  Familiarisation with the basic special functions and integral transformations used in Αpplied Sciences, as well as with the different kinds, forms and mathematical techniques of partial differential equations (PDEs) encountered in the literature.

2.  Knowledge of the origin, the mathematical properties and the use of special functions and transforms in order to solve differential and integral equations and systems.

3.  Knowledge of basic solution techniques as regards PDEs, especially of linear and quasi-linear forms, as well as of the respective boundary and initial value problems encountered in mechanics and physics.

By the end of the course the students will be able to:

·    Treat mathematically the relevant problems and understand the form, as well as the practical use of the solutions with respect to the physical background of the considered problem.

·    Retrieve theory and solution methodologies in the relevant bibliography.

·    Apply the proper technique, in order to handle unfamiliar problems.

General Competences

Taking into consideration the general competences that the degree-holder must acquire (as these appear in the Diploma Supplement and appear below), at which of the following does the course aim?

Search for, analysis and synthesis of data and information, with the use of the necessary technology

Adapting to new situations

Decision-making

Working independently

Team work

Working in an international environment

Working in an interdisciplinary environment

Production of new research ideas

Project planning and management

Respect for difference and multiculturalism

Respect for the natural environment

Showing social, professional and ethical responsibility and sensitivity to gender issues

Criticism and self-criticism

Production of free, creative and inductive thinking

……

Others…

…….

·    Working independently

·    Team work

·    Working in an interdisciplinary environment

- Special functions: Gamma, Error, Bessel, Legendre polynomials, generating functions.

- Laplace transformation: Step function, impulse function. Convolution theorem. Application to differential and integrodifferential equations.

- Boundary value problems: Eigenvalues, eigenfunctions. Regural Sturm-Liouville problem.

- Fourier series, Fourier transformation.

- Partial differential equations (PDEs): Basic concepts.

- PDEs of the first order: Linear and quasi-linear equations. Method of characteristics. Gauchy initial value problem.

- PDEs of the second order. Classification. Gauchy problem. Normal forms.

- Boundary value problems: Method of separation of variables. One-dimensional hyperbolic and parabolic homogeneous equations (wave eqn., diffusion eqn.). D’Alembert solution of the wave equation. Non homogeneous equations. Two-dimensional homogeneous equations (wave eqn., diffusion eqn., Laplace eqn.) in Cartesian and polar coordinates. Helmholtz and Poisson equations in Cartesian and polar coordinates.

- Application of Fourier transform to PDEs.

DELIVERY
Face-to-face, Distance learning, etc.

Face-to-face

USE OF INFORMATION AND COMMUNICATIONS TECHNOLOGY
Use of ICT in teaching, laboratory education, communication with students

Support of the learning process by e-class

TEACHING METHODS

The manner and methods of teaching are described in detail.

Lectures, seminars, laboratory practice, fieldwork, study and analysis of bibliography, tutorials, placements, clinical practice, art workshop, interactive teaching, educational visits, project, essay writing, artistic creativity, etc.

The student's study hours for each learning activity are given as well as the hours of non-directed study according to the principles of the ECTS

STUDENT PERFORMANCE EVALUATION

Description of the evaluation procedure

Language of evaluation, methods of evaluation, summative or conclusive, multiple choice questionnaires, short-answer questions, open-ended questions, problem solving, written work, essay/report, oral examination, public presentation, laboratory work, clinical examination of patient, art interpretation, other

Specifically-defined evaluation criteria are given, and if and where they are accessible to students.

Final written examinations with problem solving

- Suggested bibliography:

·        MATHEMATICAL METHODS FOR SCIENTISTS AND ENGINEERS: PARTIAL DIFFERENTIAL EQUATIONS, FOURIER SERIES & BOUNDARY VALUE PROBLEMS, COMPLEX FUNCTIONS, P.M. Hatzikonstantinou, Gotsis Publications, 2017, Patras (in Greek).

·        ADVANCED MATHEMATICS, E. Kreyszig, Tziolas Publications, 2018, Thessaloniki (in Greek).

·       PARTIAL DIFFERENTIAL EQUATIONS AND COMPLEX FUNCTIONS, N.M. Stavrakakis, Tsotras Publications, 2016, Athens (in Greek).