Riccatijeve diferencialne enačbe : diplomsko delo

Brolih, Anita (author), Razpet, Marko (mentor)

Diplomsko delo obravnava Riccatijeve diferencialne enačbe, ki jih uporabljamo v matematiki in mnogih drugih naravoslovnih vedah. Te enačbe so predstavljene v osnovni in nekaterih specifičnih oblikah ter podkrepljene z raznimi primeri, tako da je obravnavana tema čim bolj jasna in razumljiva. Predstavljene so predvsem Riccatijeve diferencialne enačbe prvega reda, na koncu pa še povezava z linearno diferencialno enačbo drugega reda. V začetku je kot osnova reševanja povzeta obravnava navadnih diferencialnih enačb prvega reda. Definirani so pojmi rešitev ali integral diferencialne enačbe, red diferencialne enačbe in stopnja diferencialne enačbe. Na kratko je opisano tudi življenje Jacopa Francesca Riccatija, avtorja Riccatijevih enačb, in njegov prispevek k reševanju diferencialnih enačb.

• Language: Slovenian
• Keywords: diferencialne enačbe
• Work type: Undergraduate thesis
• Typology: 2.11 - Undergraduate Thesis
• Organization: PEF - Faculty of Education
• Place of publishing: Ljubljana
• Publisher: [A. Brolih]
• Year: 2011
• Number of pages: 47 str.
• PID: 20.500.12556/RUL-68050
• UDC: 517.923(043.2)
• COBISS.SI-ID: 8900425
• Publication date in RUL: 10.07.2015

Secondary language

• Language: English
• Title: Riccati differential equations

Abstract

The intention of this thesis is to present Riccati differential equations, which are used in mathematics and in many other natural sciences. These equations are presented in their basic and in some specific forms and supported with several examples, which make this issue easier to understand. We will introduce mostly Riccati equations of first order and also their correlation with second-order differential equation. At the beginning of solving equations we will sum up the process of solving first-order differential equation and define the concept of the solution or the integral of a differential equation, order of a differential equation and degree of a differential equation. At the end, there is a short description of Jacopo Francesco Riccati’s biography, the author of Riccati equations and his contribution to solving differential equations.