6213 Programming Techniques
2nd Semester RSGE
Τομέας: Τοπογραφίας
ECTS : 5
Language : el
Learning Outcomes : Upon successful completion of the course, the student will be able to develop the following skills: • To develop code • To formulate problems algorithmically • To solve geoinformatics problems • Understanding the importance of automation in future work as a Rural & Surveying Engineer. • To distinguish the special requirements of different geoinformatics application conditions.
Repetition from the Course of the Programming introduction.
Recursion.
Data structures
Classes, objects
Constructors, destructors.
Class inheritance
Operators
List, trees.
6178 Projective Geometry
2nd Semester RSGE
ECTS : 4
Language : el
Learning Outcomes : Upon successful completion of the course, students will be able to: • possess mathematical knowledge in the field of projective geometry. They will thus be able to sharpen their mathematical thinking at a theoretical level and enrich their geometric background, through the acquisition of advanced geometric knowledge beyond classical Euclidean geometry. • be able to understand the connection between mathematical knowledge of projective geometry on the one hand and representations of technical drawings and objects in space in general on the other. • be able to understand the application of the above knowledge for handling various technical issues related to the science of surveying via computer. • have the ability to mathematically analyze and describe existing topographic problems, propose their mathematical solutions, conduct their mathematical investigation, transfer the results to colleagues, predict the results of their actions without constructing true models for experimentation and perform correct actions to create designs corresponding to real objects with specific mathematical properties. • have the ability to undertake future postgraduate studies in subjects of the surveying field or related fields, where a solid geometric foundation is essential.
Course description: Projective line, projective plane, projective space, ideal points. Duality, ratios, harmonic quadruples, conic sections, projective transformations, holologies,Theorems ofDesargues,Brianchon and Pascal. Homogeneous cordinates.
6143 Geodesy I (Introduction to Geodesy)
2nd Semester RSGE
ECTS : 5
Language : el
Learning Outcomes : • Has understood basic concepts of space and Geodesy. • Uses appropriate mathematical relationships for calculating the position of points on the Physical Earth Surface in three dimensions. • Search, analysis and synthesis of data and information, using the necessary technologies • Exercise critical and self-critical thinking • Promotion of free, creative and inductive thinking • Uses modern instruments for measuring angles, lengths and determining elevation differences • Knows the basic operating principles of instruments used in geodetic works (total station and digital level) • Knows the basic principles of measurement methods and performs measurements (angles, lengths, elevation differences).
Introduction - Background - Definitions. Earth - Structure and basic movements. Shape and size of the earth. Reference surfaces, Geoid, ellipsoid of revolution - sphere - plane. Basic definitions - units. Measurements (of lengths, angles, height differences). Methods of surveying. Mean value - variability of measured quantities. Weighted and unweighted observations. Fundamental Geodetic problems. Geodetic calculations in the plane - basic problems - area - transformations - coordinate systems in the plane. Sphere geometry & arc calculations.
6042 Probability Theory and Statistics
2nd Semester RSGE
ECTS : 5
Language : el
Learning Outcomes : Upon successful completion of the course, the student acquires the following skills: • they will be able to solve problems in the field of Probabilities • they will be able to analyze data • use statistical techniques to draw useful conclusions for a given population based on a sample from that population • apply general statistical methods to data from the science of Surveying Engineers. Upon successful completion of the course, the student acquires the following abilities: • Search, analyze and synthesize data and information, using the necessary technologies • Decision making • Autonomous work • Teamwork Search, analysis and synthesis of data and information, using the necessary technologies Decision making Autonomous work Teamwork Work in an international environment Work in an interdisciplinary environment.
Descriptive Statistics, Probability: definitions and axioms, conditional probability, independent events, law of total probability, Bayes’ theorem, combinatorics.
Random variables: basic discrete and continuous univariate distributions, exponential family of distributions, mean and variance of random variables.
Multivariate distributions: marginal distributions, independence of random variables.
Central limit theorem.
Estimation: method of maximum likelihood, moment estimators. Applications.
Confidence intervals: for the mean and variance of one population, for the difference of the means of two populations, for the ratio of the variances of two populations. Approximate confidence intervals.
Hypothesis testing: for the mean and variance of one population, inference for two populations. X^2 tests.
Correlation. Simple linear regression, introduction to the linear model.Multiple linear regression. Estimation of parameters and properties of the estimators. Applications.
6032 Cartography I (General Cartography)
2nd Semester RSGE
ECTS : 5
Language : el
Learning Outcomes : • Understand the concept of the map, its characteristics and functions • Recognize and utilize topographic and nautical charts • Choose to use the sphere or the ellipsoid depending on the map scale • Recognize the characteristics of geographical and Cartesian coordinates, the geographical grid and the square grid • Understand the necessity of cartographic representations and the deformations they cause • Analyze the geometric and descriptive characteristics of spatial elements • Know the characteristics of point, line and area symbols and choose the appropriate symbology for each spatial element • Use visual variables and utilize color in cartographic symbology • Have knowledge of the basic principles and concepts of relief representation on maps • Understand the basic principles, concepts and techniques of cartographic generalization • Place nomenclature on the map based on the principles of typography/lettering and good cartographic practices and conventions in relation to geographical names • Know the principles and techniques of map design and especially the creation of the map s architecture and the basic elements of a map (e.g. title, grid, graticule, legend, etc.) • Be informed about cartographic specifications, standardization and copyright of cartographic products • Understand the modern principles governing map production and reproduction and the new perspectives offered by modern technology.
Introduction to Cartography – The role of maps
• The shape and the size of the Earth - Cartographic projections
• Scale, reference and coordinate systems
• Relief representation
• Spatial data feature analysis and basic processing
• Cartographic symbolization
• Color theory and color models
• Use of color
• Cartographic Generalization
• Map design
• Map composition
• Typography and lettering
• Map production and map reproduction
• New perspectives in Cartography offered by modern technology
6009 Physics I (Mechanics)
2nd Semester RSGE
ECTS : 4
Language : el
Learning Outcomes : The purpose of the course is for students to understand basic concepts of Physics (Mechanics), which will be particularly useful in their studies and in their future professional career. Upon successful completion of the course, the student: develops skills and is able to • understand basic concepts of Physics (Mechanics), so that they can use them in subsequent courses. • better and more deeply understand the operation of devices and instruments used by rural and surveying engineers, and on the one hand use them more correctly and efficiently, and on the other hand propose possible improvements. • process experimental data and draw useful conclusions from experimental measurements.
The content of the course, according to the curriculum of the School of Surveyors, includes the following sections:
Kinematics and dynamics of the material point: Study of motion in one and more dimensions, Newton s laws, kinetic and dynamic energy, principle of conservation of energy, momentum, principle of conservation of momentum, collisions.
Solid body kinematics & dynamics: study of rotational motion, moment of inertia, moment of force, angular momentum, principle of conservation of angular momentum, equilibrium conditions, elasticity.
Gravity and central forces: Law of universal attraction, study of motion in gravitational field, Kepler s laws, study of satellite motion, escape velocity, black holes.
Mechanical oscillations: Simple harmonic oscillation, oscillation with damping, forced oscillation, resonance, coupling of oscillators.
Introduction to wave theory: General characteristics of waves, wave equation, types of waves.
Introduction to relativistic mechanics: Relativity of tautochronism, relativity of length and time, energy and momentum in special relativity, applications.
6004 Differential Equations
2nd Semester RSGE
ECTS : 4
Language : el
Learning Outcomes : Upon successful completion of the course, the student will be able to: • know the process of modeling simple mechanical systems for formulating an ordinary differential equation and initial conditions. • know and apply solution methods for linear and nonlinear ordinary differential equations of 1st order of various types. • know solution methods for homogeneous and non-homogeneous ordinary linear differential equations of 2nd order with constant coefficients and apply these to solving mechanical-electrical oscillation problems. • solve ordinary linear differential equations of 2nd order with non-constant coefficients using the power series method. Recognize Bessel and Legendre differential equations and recall their solutions. solve linear systems with constant coefficients. • solve initial value problems of 2nd order ordinary differential equations using the Laplace transform method. • understand the introductory basic concepts of partial differential equations and apply the method of separation of variables to the three basic partial differential equations.
The differential equations describe a broad range of phenomena and processes in technological, physical, biological, and financial sciences. The aim of this course is to provide the basic knowledge for the comprehension of the differential equations as well as their basic solution methods and techniques.
Skills:
Upon successfully completion of the course, the student should be in position to
• formulate a mathematical model for simple mechanical systems, i.e., to account for the right ordinary differential equation as well as for the appropriate initial conditions that accompany it.
• apply the taught solution methods to linear and non-linear ordinary differential equations of first order.
• apply the solution methods to homogeneous and non-homogeneous ordinary differential equations of second order with constant coefficients and to apply them to the solution of mechanical and electrical vibration problems.
• solve linear systems of differential equations with constant coefficients.
• solve initial value problems for second order differential equations using the Laplace transform method.
• apprehend the fundamental notions of partial differential equations and to apply the variables’ separation method to the three basic partial differential equations of mathematical physics.