# Applied Mathematics Ι

 Title Εφαρμοσμένα Μαθηματικά Ι / Applied Mathematics Ι Code 013 Faculty Engineering School Electrical and Computer Engineering Cycle / Level 1st / Undergraduate Teaching Period Winter Coordinator Nikolaos Atreas Common No Status Active Course ID 600000961

### Programme of Study: Electrical and Computer Engineering

Registered students: 454
OrientationAttendance TypeSemesterYearECTS
CORECompulsory Course327

 Academic Year 2022 – 2023 Class Period Winter Faculty Instructors Weekly Hours 6 Class ID 600218049
Course Type 2021
General Foundation
Course Type 2016-2020
• Background
Course Type 2011-2015
General Foundation
Mode of Delivery
• Face to face
Digital Course Content
Language of Instruction
• Greek (Instruction, Examination)
Prerequisites
General Prerequisites
Calculus and multivariable Calculus, Linear Algebra and Analytic Geometry.
Learning Outcomes
Upon completion of the course the students should be able to: 1. Solve linear differential equations of second or higher order and systems of 1st order linear differential equations. 2. Use Laplace transform (its properties and properties of inverse Laplace transform) for solving physical problems, e.g. circuits. 3. Perform calculations with complex numbers and use elementary complex functions as a tool of geometric transformations. Also, use complex integration as a tool for qualitative study of two dimensional vector fields (circulation-flux, complex potential). Finally, uo use complex analysis techniques as a tool in signal processing and PDE’s. 4. Use methods of Fourier Analysis (Fourier series and Fourier integrals) for solving two dimensional Dirichlet's prolem inside a rectangular, or a disk or in the upper half plane, or one dimensional heat and wave equations by applying the method of separation of variables.
General Competences
• Apply knowledge in practice
• Retrieve, analyse and synthesise data and information, with the use of necessary technologies
• Work autonomously
• Work in teams
• Work in an interdisciplinary team
• Advance free, creative and causative thinking
Course Content (Syllabus)
Linear differential equations of second and higher order: definitions and solutions. A short introduction to non linear differential equations. Systems of differential equations. Applications. Laplace transform and inverse Laplace transforms. Properties and applications. Elements of complex analysis: complex derivative and integration, Cauchy’s theorem and Cauchy’σ integral formula, Laurent series, residuals, harmonic functions. A short introduction to Fourier Analysis: Fourier series and Fourier integral. A short introduction to partial differential equations. The method of separation of variables. Two dimensional Dirichlet problem iside a rectangular, disk, or upper half plane. One dimensional heat and wave equations.
Keywords
Differential equations, Laplace transform, complex numbers, Fourier Analysis, method of separation of variables.
Educational Material Types
• Notes
• Book
Course Organization
Lectures782.6
Exams30.1
Other / Others792.6
Total2107
Student Assessment
Description
Final exam (duration: 2,5-3 h).
Student Assessment methods
• Written Exam with Problem Solving (Formative, Summative)
• Written examination
Bibliography
Course Bibliography (Eudoxus)
1. Ν. Μυλωνάς και Χ. Σχοινάς, Διαφορικές Εξισώσεις, Μετασχηματισμοί και Μιγαδικές Συναρτήσεις. 2. Κ. Σεραφειμίδης, Διαφορικές Εξισώσεις.
Last Update
19-10-2022