FACULTY

APPLIED TECHNOLOGIES

DEPARTMENT

AIRCRAFT TECHNOLOGY ENGINEERING

LEVEL OF STUDIES

UNDERGRADUATE

MODULE CODE

AE1110T

SEMESTER OF STUDIES

1^ST

MODULE TITLE

MATHEMATICS I

INDEPENDENT TEACHING ACTIVITIES

TEACHING HOURS
PER WEEK

CREDITS

Lectures

3

3

Practice

1

2

COURSE TYPE

General Background

PRE-REQUIRED COURSES:

LANGUAGE OF TEACHING and EXAMINATION  :

GREEK

THE COURSE ID OFFERED TO ERASMUS

COURSE WEBPAGE (URL)

Learning Objectives

After successfully completing the course, students should be able to analyze the fundamental principles of linear algebra, differential and integral calculus and complex numbers and apply the mathematical principles for the solution of practical problems that arise during the maintenance and construction of aircraft parts. 

General Skills

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

1^st Unit: Introduction to basic knowledge of Arithmetics, Algebra, Geometry.

              Calculation of simple algebraic expressions, linear equations, trigonometry

2^nd Unit: Elements of Linear Algebra

Determinants.Determinants of order 2 and 3.  SARRUS Law. Generalization, determinant of order n. Properties of determinants. Linear systems. Solutions of general linear systems. Homogeneus linear systems.

3^rd Unit: Differential calculus

Functions. Types of functions. Periodic functions.  Graphical representation and diagram functions 

4^th Unit: Sequenses – Variable thresholds

Sequenses. Variable threshold. Theorems concerning infinitesimals and quantities having infinity as threshold. Theorems concerning constant threshold quantities.  Threshold theorem. Function threshold. Single side threshold  and  side threshold.

5^th Unit: Continuity

Local continuity. Total continuity. Basic theorems. Function continuity. Monotonic function. Inverse function.  Cyclic or trigonometric functions and their inversions. Exponential functions. Hyperbolic functions.

6^th Unit: Derivative Ι

Derivative geometric interpretation. Kinematic derivative. Differentiation rules. Derivative of constant function. Force derivative with exponent  ν ε Ν. Sum derivative. Product derivative. Quotient derivative. Τrigonometric function derivative.  Complex function derivative. Complex exponential form functions. Inverse function derivative.

7^th Unit: Function differential – Derivative applications

Funtion differential of higher order. Differential product of two functions. Differential of complex function. Differential of standard functions. Monotonic function criteria. Maximums and minimums.  1^st criterion of extreme values. Concave and convex functions.  Carvature criteria.  2^nd criterion of extreme values.  Endpoints.  Asymptotes in function diagrams.  Undefined forms. Rule de l’ Hospital.

Unit 8:  Integral Calculus

Definite integral. Geometrical interpretation of the definite integral. Applications of the definite integral. Properties of the definite integral. Mean value theorem. Split integrals. Calculation of definite integral.  Fundamental theorem of integral calculus.  Indefinite integral. Properties of the indefinite integral. Similarities and differences between definite and indefinite integral.

9^th Unit: Generalized integrals

Single-ended generalized integrals. Double ended generalized integrals. Generalized integrals with non continous function. 

10^th Unit: Applications of integral calculus

Applications of the indefinite integral. Applications of the definite integral. Flat shapes areas. Arc length of a flat curve.  Solid object volume. 

11^th Unit: Methods of Integration

Integration by parts. Integration by substitution. Ιntegration by factors. Ιntegration by degradation. Integration of the explicit function analyzed by partial fractions.  Integration of implicit functions.  Integration of exponential functions.  Integration of trigonometrical functions. Applications of definite integrals.

12^th Unit: Complex numbers

Definition of complex numbers, complex numbers equality, complex numbers calculations,  complex conjugates. Equality of complex numbers in trigonometrical form, calculations of complex numbers in trigonometrical form, complex numbers roots.  Applications of complex numbers.

TEACHING METHOD

Face to face

USE OF INFORMATION AND COMMUNICATION TECHNOLOGY

•  Use of Internet

•  Support of learning process through the use of e-class platform

TEACHING ORGANIZATION

STUDENT EVALUATION

Written examination in the scheduled examination periods that includes theory questions, comprehension questions, multiple choice problems, and problem solutions.

Suggested Bibliography :

•              Λαμπίρης, Κουρής, Αναστασάτος κ.λ.π, Μαθηματικά Ι, Εκδόσεις Δίφρος, 1999 .

•              Κικίλια, Κουρή κλπ, Διαφορικός και Ολοκληρωτικός Λογισμός, Εκδόσεις Δηρός, 2002.

•              Δημητροκούδη κλπ, Γραμμική Άλγεβρα, Εκδόσεις Δηρός, 2002.

•              Tom Apostol, Διαφορικός και Ολοκληρωτικός Λογισμός (CALCULUS), τόμος Ι, Εκδόσεις Ατλαντίς, 1962.

•              Ralph, Palmer. Agnew, Analytical Geometry and Calculus with vectors (Calculus), McGraw-Hill, 1962.

•              Applied Linear Algebra, Ben Nobles Prentice Hall, 1969.