# Applied Mathematics II Title Εφαρμοσμένα Μαθηματικά ΙΙ / Applied Mathematics II Code 055 Faculty Engineering School Electrical and Computer Engineering Cycle / Level 1st / Undergraduate Teaching Period Winter Coordinator Athanasios Kechagias Common No Status Active Course ID 600001004

### Programme of Study: Electrical and Computer Engineering

Registered students: 159
OrientationAttendance TypeSemesterYearECTS
ELECTRICAL ENERGYElective Courses744
ELECTRONICS AND COMPUTER ENGINEERINGElective Courses744
TELECOMMUNICATIONSElective Courses744

 Academic Year 2021 – 2022 Class Period Winter Faculty Instructors Weekly Hours 4 Class ID 600196739
Course Type 2021
Specialization / Direction
Course Type 2016-2020
• Scientific Area
Course Type 2011-2015
Specific Foundation / Core
Mode of Delivery
• Face to face
Digital Course Content
Erasmus
The course is also offered to exchange programme students.
Language of Instruction
• Greek (Instruction, Examination)
• English (Examination)
Prerequisites
General Prerequisites
Calculus I, Linear Algebra, Calculus II, Αpplied Mathematics
Learning Outcomes
At the conclusion of this class the students will be able to do the following. 1. Solve analytically the basic linear partial differential equations: Laplace equation, wave equation, heat equation. 2. Solve the same equations as well as their nonlinear extensions using numerical software (e.g., Matlab) and/or symbolic algebra software (e.g., Maple). 3. Use the PDE formalism in modeling and solving applied problems (e.g. applications to electromagnetic field, image processing, transportation problems etc.). 4. To be able to solve 2nd order linear differential equations by series methods. 5. To know the basic special functions (Bessel, Legendre, Chebyshev). In addition, the students will have a clear intuitive understanding of the physical significance of partial differential equations as well as their connection to systems of algebraic equations.
General Competences
• Retrieve, analyse and synthesise data and information, with the use of necessary technologies
• Work autonomously
• Work in teams
• Advance free, creative and causative thinking
Course Content (Syllabus)
Partial differential equations (PDE's): Laplace equation, heat equation, wave equation. In the first part of this course solution methods will be taught. 1. Separation of variables. 2. Integral transforms (Fourier, Laplace). 3. Solution using symbolic algebra software (computer algebra systems, CAS) e.g. Maple, Mathematica. 4. Solution using numerical methods and introduction to the corrsponding software (e.g. Maple, Mathematica, Matlab PDE Toolbox, MathPDE). In the second part of the course, the students will study and present papers from the current literature, related to the applications of PDE's (e.g., applications to electromagnetic field, image processing, transportation problems, stochastic processes etc.).
Keywords
Partial differential equations (PDE's): Separation of variables, Laplace equation, heat equation, wave equation.
Educational Material Types
• Notes
• Interactive excersises
• Book
Course Organization
Lectures521.7
Project230.8
Exams451.5
Total1204
Student Assessment
Student Assessment methods
• Written Assignment (Formative, Summative)
• Oral Exams (Formative, Summative)
• Report (Formative, Summative)
• Written examination
Bibliography
Course Bibliography (Eudoxus)
1. Σ. Τραχανάς, Μερικές Διαφορικές Εξισώσεις. 2. Γ. Παντελίδης, Δ. Κραβαριτης, Εισαγωγή στις διαφορικές εξισώσεις μερικών παραγώγων