Integration theory and an introduction to generalized ordinary differential equations

• Grant number: 18/05030-9
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: July 01, 2018
• End date: June 30, 2019
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Marta Cilene Gadotti
• Grantee: Marcelo Petrini Vallerini Filho
• Host Institution: Instituto de Geociências e Ciências Exatas (IGCE). Universidade Estadual Paulista (UNESP). Campus de Rio Claro. Rio Claro , SP, Brazil

Abstract

Derivative and integral are the fundamental notions of calculus and there are a variety of integrals, developed over the years, for different purposes. It is also known that the Riemann integrable function class is very restricted and does not have good convergence properties. Thus, this project has the objective of presenting important results on the Integration Theory involving other types of integrals, such as that of Perron, in addition, show that it is possible to generalize the concept of ordinary differential equation (ODE) and consequently perform some applications involving the study of physical problems models by EDO or EDP. In this current work plan applications of the Theory of Integration were added, especially in the area of Mathematical Physics and the theoretical part related to the Lebesgue integral was reduced. (AU)