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: 347
Orientation  Attendance Type  Semester  Year  ECTS 

Core  Compulsory Course  3  2  6 
Academic Year  2019 – 2020 
Class Period  Winter 
Faculty Instructors 

Instructors from Other Categories  
Weekly Hours  5 
Class ID  600149859

Type of the Course
 Background
 General Knowledge
Course Category
General Foundation
Mode of Delivery
 Face to face
Digital Course Content
 eStudy Guide https://qa.auth.gr/en/class/1/600149859
 eLearning (Moodle): https://elearning.auth.gr/course/view.php?id=7485
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 realitycheck 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 springmass 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, steadystate, amplitude response, phase response, amplitudephase 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 antielimination, 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 nonlinear 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
 Adapt to new situations
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
Activities  Workload  ECTS  Individual  Teamwork  Erasmus 

Lectures  100  3.3  ✓  
Tutorial  40  1.3  
Interactive Teaching in Information Center  27  0.9  
Written assigments  10  0.3  
Exams  3  0.1  
Total  180  6 
Student Assessment
Description
Final Exam 3hrs duration
Student Assessment methods
 Written Exam with Problem Solving (Formative, Summative)
Bibliography
Course Bibliography (Eudoxus)
Επιλογές Συγγραμμάτων:
Βιβλίο [50847519]: 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 [50655955]: Διαφορικές Εξισώσεις, Μετασχηματισμοί και Μιγαδικές Συναρτήσεις, Μυλωνάς Νίκος  Σχοινάς Χρήστος Λεπτομέρειες
Last Update
09062020