Primjena diferencijalnog i integralnog računa u ekonomiji i fizici

master's thesis

• Author: Kristijan Galić
• Mentor: Željka Milin Šipuš (mentor)
• Committee member: Željka Milin Šipuš (predsjednik povjerenstva)
• Committee member: Franka Miriam Brückler (član povjerenstva)
• Committee member: Pavle Goldstein (član povjerenstva)
• Committee member: Sanja Varošanec (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2020-09-29, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

Osim strogoga formiranja pojmova derivacije i integrala, važno je razumjeti i ulogu i korištenje, odnosno svrhu tih pojmova izvan matematičkoga konteksta. U ovome radu dajemo im značenje u područjima fizike i ekonomije. Matematičko uvođenje tih pojmova primjereno je učenicima četvrtoga razreda gimnazije te prvoj godini tehničkih fakulteta. U prvome poglavlju upoznali smo se s interpretacijom derivacije, kako fizikalnom tako i geometrijskom. Upoznali smo se s definicijom derivacije te s osnovnim pravilima deriviranja. Spomenuli smo metode deriviranja implicitnih te parametarski zadanih funkcija. Pomoću par kratkih primjera upoznali smo se s derivacijom u kontekstu te smo na kraju pomoću ekonomskog i fizikalnog modela predstavili derivaciju u “svakodnevnom životu“. U drugome poglavlju upoznali smo se s integralima, kako određenim tako i neodređenim integralima. Pokazali smo kako se uvode određeni i neodređeni integral u nastavu. Potom smo uveli osnovni teorem diferencijalnog i integralnog računa koji je poveznica između derivacije i integrala te samim time jedan od najbitnijih teorema u matematici. Nakon toga pomoću par kratkih primjera predstavili smo integral u kontekstu, te smo na kraju pomoću par zadataka iz područja ekonomije i fizike predstavili upotrebu integrala u “svakodnevnom životu“.

Abstract (english)

In addition to the strict formation of the concepts of derivation and integration it is important to understand their role and purpose outside of the mathematical context. In this paper we give them meaning in the fields of physics and ecnonomics. The mathematical introduction of these concepts is appropriate for students in the fourth grade of high schoold and the first year of technical faculties. In the first chapter we are introduced to the interpretation of derivation, both physical and geometric. We got acquainted with the definition of derivation and the basic rules of derivation. We mentioned methods of deriving implicit and parametrically given functions. With the help of few short examples, we were introduced to derivation in context and finally, using an economic and physical model we presented derivation in „everyday life“. In the second chapter, we are introduced to integrals, both definite and indefinite. We have shown how definite and indefinite integrals are introduced in teaching. Then we introduced the basic theorem of differential and integral calculus, which is the connection between the derivative and the integral, and thus one of the most important theorems in mathematics. After that, with the help of few short examples, we presented integral in the context, and finally, with the help of few examples from the field of economics and physics we presented the use of integrals in „everyday life“.

• Keywords: derivacija; integral; derivacija u “svakodnevnom životu“
• Keywords (english): derivation; integration; derivation in „everyday life“
• Language: croatian
• URN:NBN: urn:nbn:hr:217:647108
• Study programme: Title: Mathematics Education; specializations in: Mathematics Education; Course: Mathematics Education; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra edukacije matematike (magistar/magistra edukacije matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2020-12-10 13:53:13