FACULTY

APPLIED TECHNOLOGIES

DEPARTMENT

AIRCRAFT TECHNOLOGY ENGINEERING

LEVEL OF STUDIES

UNDERGRADUATE

MODULE CODE

AE1210T

SEMESTER OF STUDIES

2^ND

MODULE TITLE

ΜΑTHEMATICS II

INDEPENDENT TEACHING ACTIVITIES

TEACHING HOURS PER WEEK

CREDIT UNITS

Lectures

3

3

Practice

1

2

COURSE TYPE

General Background

PRE-REQUIRED COURSES

TEACHING AND EXAMINATION LANGUAGE

GREEK

THE COURSE IS OFFERED TO ERASMUS STUDENTS

COURSE WEBPAGE  (URL)

Learning Objectives

After successfully completing the course, students should be able to analyze the basic concepts of differential equations and differential and integral calculus of multivariable functions. They should also be able to apply the principles for the solution of differential equations and infinitensimal calculus of multivariable functions  for the soulution of practical problems that arise during the repair and maintenance procedures of aircraft parts.

General Skills

Search, analysis and combination of data and information, with the use of the necessary technologies.

Unit 1: Introduction to differential equations

             Generation of differential equation. Solution of differentia equation. Separation variable differential equations.

             Homogeneus first order differential equation

Unti 2: First order differential equations

             Linear first order differential equations. Bernoulli and Ricatti's differential equations. Exact first order

             differential equation. First order differential equation reducible to exact. Clairaut and Lagrange's differential

             equations

Unit 3: Higher order differential equations

             Linear second order differential equations with random continuous function coefficient. Linear second order

             differential equations with constant coefficients. Applications of second order differential equations. Higher

              order differential equations. Linear differential systems.  

Unit 4: Laplace Transformation

Definition of Laplace transformation, Fundamental properties, Inverse Laplace transformation, Application of Laplace transformation for the solution of differential equations and differential systems. 

Unit 5: Introduction to infinitesimal calculus of multivariable functions 

              Continuity, derivative and real function differential of multivariable functions. Partial derivatives and their

              geometric interpretation

Unit 6: Derivatives of multivariable functions

              Total differential. Partial derivatives and complex function differential, Complecated functions and Jacobians,

              Derivative and direction

Unit 7: Double integral:

             Double integral, examples and applications of double integrals in aircraft technology

Unit 8: Multiple integrals

              Triple and multiple integrals and  applications in aircraft technology

TEACHING METHOD

Face to face

USE OF INFRORMATION AND COMMUNICATION TECHNOLOGIES

•  Use of Internet

•  Learning procedure through e-class support

TEACHING ORGANIZATION

STUDENT EVALUATION

·                     Written examination in the scheduled examination periods including theory questions, comprehension questions, multiple choice and  problem solving.

-Suggested Bibliography :

·           Αναστασάτος, Κικίλιας κλπ, Διαφορικές εξισώσεις, Εκδόσεις Δηρός, 2002.

·           Κικίλιας, Κουρής κλπ, Συντηρήσεις πολλών μεταβλητών, Εκδόσεις Δηρός, 2002.

·           Δημητρακούδης,  Κωστάκης κ.λπ., Μαθηματικά ΙΙ, Εκδόσεις Δίφρος, 1999.

·           Κωστάκης, Κικίλιας, Συναρτήσεις πολλών μεταβλητών, Εκδόσεις Μακεδονικές, 1994.

·           Tom Apostol, Διαφορικός και Ολοκληρωτικός Λογισμός (CALCULUS), Τόμος ΙΙ, Εκδόσεις Ατλαντίς, 1962.

·           Α. Παπαϊωάννου, Διαφορικές Εξισώσεις, τεύχος Α, Μακεδονικές Εκδόσεις, 1992.

·           Paul Davis, Differential Equations, Modeling with Matlab Prentice Hall, 1999

·           Kent R. Nagle, et al Fundamentals of Differential Equations, 1999

·           R. Bronson, Modern Introductory Differential Equations, Schaum's Outline Series 

·           R. C. McLann, Introduction to Ordinary Differential Equations, Harcourt Brace Jovanovich Inc.

·           Erwin Kreyszig , Advanced Engineering Mathematics, John Wiley & Sons, 8th Edition, October 1998.

·           Stroud, Engineering Mathematics, The MacMillan Press, 1999.