# DIFFERENTIAL EQUATIONS (MATHEMATICS III) Title ΔΙΑΦΟΡΙΚΕΣ ΕΞΙΣΩΣΕΙΣ (ΜΑΘΗΜΑΤΙΚΑ ΙΙΙ) / DIFFERENTIAL EQUATIONS (MATHEMATICS III) Code 111 Faculty Engineering School Mechanical Engineering Cycle / Level 1st / Undergraduate Teaching Period Winter Coordinator Vasileios Rothos Common Yes Status Active Course ID 20000475

### Programme of Study: UPS of School of Mechanical Engineering

Registered students: 264
OrientationAttendance TypeSemesterYearECTS
CoreCompulsory Course326

 Academic Year 2021 – 2022 Class Period Winter Faculty Instructors Vasileios Rothos 5hrs Instructors from Other Categories Weekly Hours 5 Class ID 600192491
Course Type 2016-2020
• Background
• General Knowledge
Course Type 2011-2015
General Foundation
Mode of Delivery
• Face to face
Erasmus
The course is also offered to exchange programme students.
Language of Instruction
• Greek (Instruction, Examination)
• English (Examination)
Prerequisites
Required Courses
• 102 PHYSICS
• 101 CALCULUS I (MATHEMATICS I)
• 106 CALCULUS II (MATHEMATICS II)
General Prerequisites
Calculus -Linear Algebra
Learning Outcomes
By the end of the course students will be able to: Model a simple physical system to obtain a first order differential equation. Test the plausibility of a solution to a differential equation (DE) which models a physical situation by using reality-check methods such as physical reasoning, looking at the graph of the solution, testing extreme cases, and checking units. Visualize solutions using direction fields and approximate them using Euler's method. Find and classify the critical points of a first order autonomous equation and use them to describe the qualitative behavior and, in particular, the stability of the solutions. The main equations studied in the course are driven first and second order constant coefficient linear ordinary differential equations and 2x2 systems. For these equations students will be able to: Use known DE types to model and understand situations involving exponential growth or decay and second order physical systems such as driven spring-mass systems or LRC circuits. Solve the main equations with various input functions including zero, constants, exponentials, sinusoids, step functions, impulses, and superpositions of these functions. Understand and use fluently the following features of the linear system response: solution, stability, transient, steady-state, amplitude response, phase response, amplitude-phase form, weight and transfer functions, pole diagrams, resonance and practical resonance, fundamental matrix. Use the following techniques to solve the differential equations described above: characteristic equation, exponential response formula, Laplace transform, convolution integrals, Fourier series, complex arithmetic, variation of parameters, elimination and anti-elimination, matrix eigenvalue method. Understand the basic notions of linearity, superposition, and existence and uniqueness of solutions to DE's, and use these concepts in solving linear DE's. Draw and interpret the phase portrait for autonomous 2x2 linear constant coefficient systems. Linearize an autonomous non-linear 2x2 system around its critical points and use this to sketch its phase portrait and, in particular, the stability behavior of the system.
General Competences
• Apply knowledge in practice
• Retrieve, analyse and synthesise data and information, with the use of necessary technologies
Course Content (Syllabus)
Differential Equations: Definition and Properties. DE 1st and higher order linear and nonlinear Systems of Differential Equations. Laplace Transform and Fourier series. Partial Differential Equations, Separation of variables. Boundary Value Problems
Educational Material Types
• Notes
• Slide presentations
• Book
Use of Information and Communication Technologies
Use of ICT
• Use of ICT in Course Teaching
Description
projector and PC
Course Organization
Lectures1003.3
Tutorial401.3
Interactive Teaching in Information Center270.9
Written assigments100.3
Exams30.1
Total1806
Student Assessment
Description
Final Exam 3hrs duration or final coursework and 2 midterm tests
Student Assessment methods
• Written Exam with Multiple Choice Questions (Formative, Summative)
• Written Exam with Short Answer Questions (Formative, Summative)
• Written Exam with Extended Answer Questions (Formative, Summative)
• Written Assignment (Formative, Summative)
• Written Exam with Problem Solving (Formative, Summative)
Bibliography
Course Bibliography (Eudoxus)
Επιλογές Συγγραμμάτων: Βιβλίο : Διαφορικές Εξισώσεις: Συνήθεις και Μερικές. Θεωρία και Εφαρμογές από τη Φύση και τη Ζωή, ΝΙΚΟΛΑΟΣ M. ΣΤΑΥΡΑΚΑΚΗΣ Λεπτομέρειες Ρόθος, Β., Σφυράκης, Χ., 2015. Διαφορικές εξισώσεις. [ηλεκτρ. βιβλ.] Αθήνα:Σύνδεσμος Ελληνικών Ακαδημαϊκών Βιβλιοθηκών. Διαθέσιμο στο: http://hdl.handle.net/11419/3912 Βιβλίο : Διαφορικές Εξισώσεις, Μετασχηματισμοί και Μιγαδικές Συναρτήσεις, Μυλωνάς Νίκος - Σχοινάς Χρήστος Λεπτομέρειες
Last Update
12-01-2022