Η αξία των μαθηματικών και οι εφαρμογές τους στα μηχανικά προβλήματα

Abstract

The general conviction of Mathematics is that it bridges all the sciences together and leads them to higher levels. It is the motivating force that launches mind to the infinite universe, as well as the source of Logic and Coherence that maintains them in balance. A lot of students, inspired by the beneficial spirit of the era, prefer the mechanical memorization and basic appliance of the various formulas and laws, instead of further searching for the aspiring idea behind the reasoning, which is what actually constitutes the greatness of Mathematics. Students tend not to give the appropriate importance that Mathematics deserves and it is considered that this attitude prevents them from developing an important tool that will be critical for their successful scientific process. The main objective in thisis diploma thesis is the investigation of the various mathematical disciplines that an engineer encounters during his education, and it’s aiming to prove the dependence between the two sciences in the global extent of the knowledge and progress. The first part contains the most important chapters of mathematics, and more particularly the mathematical topics that the Course Curriculum of Civil Engineering contains. There will be a historical retrospect in every one of these chapters, revealing the beauty and the power of the human mind and how it managed to conceive the various ideas. A quote of some appliances in the field of Civil Engineering will be attached as well. Distinctly, we’ll analyse the following chapters: Functions, Differential and Integral Calculus, Series, Linear Algebra, Differential Equations and Statistics. In the second part, there will be an introduction of some Civil Engineering issues, involving extensive mathematical applications. We will in particular focus on spring problems and oscillations. The third part, which constitutes the most substantial part of the diploma thesis, is reviewing an important problem of physics and mechanics, starting from its primitive origins in Ancient Greece and reaching the approaches of Kepler, Newton and Einstein. We shall study the planet orbits and motions which start from mathematics, continues to a stream of thematic areas and states their conclusion. Finally, the whole research leads fluently to the conclusion that, the importance Engineering students should place in mathematics is primarily significant. It is not exaggerating to claim that it constitutes at least half part of our science. However the most fascinating conclusion is that the mere mechanical use of mathematics is not beneficial in the evolution of science. It is the full comprehension and knowledge of the evolutionary way that offers the tools to the aspirant and restless mind to develop and lead the science further.