BookPDF Available

Matematika 1

August 2021

Publisher: OFF SET Tuzla
ISBN: 978-9958-31-482-7

Authors:

Samir Karasuljic

University of Tuzla

Sanela Halilović

University of Tuzla

Figures - uploaded by Sanela Halilović

Content may be subject to copyright.

Content uploaded by Samir Karasuljic

Content may be subject to copyright.

A preview of the PDF is not available

Matematika 1-korice

Data

December 2021

Samir Karasuljic · Sanela Halilović

ResearchGate has not been able to resolve any citations for this publication.

Ekonomski fakultet Osijek, R.Hrvatska

Jan 1994

M Crnjac
D Jukić
R Scitovski
Matematika

M. Crnjac, D. Jukić and R. Scitovski. Matematika. Ekonomski fakultet Osijek, R.Hrvatska, 1994. isbn: 953-6073-03-X.

Matematika 1. STUDIO HS Internet d

Jan 2017
978-953

D Jukić
R Scitovski

D. Jukić and R. Scitovski. Matematika 1. STUDIO HS Internet d.o.o., Osijek, R. Hrvatska, 2017. isbn: 978-953-6032-18-1.

Matematika 1. Prehrambeno tehnološki fakultet i Elektrotehnički fakultet Osijek, R. Hrvatska

Jan 1998
953-6032

D Jukić
R Scitovski

D. Jukić and R. Scitovski. Matematika 1. Prehrambeno tehnološki fakultet i Elektrotehnički fakultet Osijek, R. Hrvatska, 1998. isbn: 953-6032-18-X.

Linearna algebra, polinomi, analitička geometrija. Beogradski izdavački zavod

Jan 1973

D S Mitrinović
D Mihailović
P M Vasić

D.S. Mitrinović, D. Mihailović and P.M. Vasić. Linearna algebra, polinomi, analitička geometrija. Beogradski izdavački zavod, Beograd, SFRJ, 1973.

Elementi više matematike I. IP "Nauka

Jan 2002

M P Ušćumlić
P M Miličić

M.P. Ušćumlić and P.M. Miličić. Elementi više matematike I. IP "Nauka", Beograd, Srbija, 2002.

Matematika 1. Tuzla, BiH: IN SCAN d

Jan 2014

R Vugdalić

R. Vugdalić. Matematika 1. Tuzla, BiH: IN SCAN d.o.o., 2014. isbn: 978-9958-894-22-0.

Project

Numerical grids and Applications

Project

Diference schemes for nonlinear singular perturbation problem

Project

Master thesis

The project contains the manuscripts of the students of master studies

Project

Research of new applications of some methods from harmonic and spectral analysis

The goal of our project are: - to find new results about the relations between the generation function of superposition operator and its various (nonlinear) spectra - to find new ways for determin ing the jump of function in the discontinuities of the first kind ... [more]

Data

Full-text available

Matematika 1-korice

December 2021

Preprint

Full-text available

Matematika 1

August 2021

The book was written on the basis of materials that we presented at several faculties, either as lectures or as part of auditory exercises. Aware that there are more books and textbooks in the area in which the topics covered by this book are covered, we tried, based on the mentioned experience, to write a book oriented towards students.

Book

Full-text available

Matematika III za studente mašinstva

December 2016

Article

Full-text available

Nonlinear Spectral Theories and Solvability of Nonlinear Hammerstein Equations

January 2010

Sanela Halilović

We study some possibilities of nonlinear spectral theories for solving nonlinear operator equations. The main aim is to research a spectrum and establish some kind of nonlinear Fredholm alternative for Hammerstein operator KF. It is well-known that the major methods for studying solvability of linear or nonlinear equations in literature are: the variational method, the method of a vector field ... [Show full abstract] rotation and the fixed point methods. "The brachistochrone problem" is usually considered to be the begin-ning of variational calculus and nonlinear analysis. It was first introduced by J. Bernoulli in the 17th century and was first solved by Isaac Newton. An-other method for obtaining existence and uniqueness results has been built on a topological method known as the degree theory, the index theory or rota-tion of the vector fields. The founders of the index theory were: M. Atiyah, R. Bott, F. Hirzebruch and Is. Singer. The first claim, which is an equivalent to the Brouwer fixed-point theorem, was given and proved by H. Poincaré in 1883 and the next by P. Bole in 1904 (the first one-dimensional equivalent is the well-known Bolcano's theorem on the zeros of a continuous function, proved in 1817). In 1909 Brouwer proved the theorem on fixed points in the case of the three-dimensional space. In 1910 Adamar proved a similar statement for an arbitrary finite-dimensional space, by using a Cronecker index. The same statement was proved by Brouwer in 1912 by using simplex approximation and the notion of mapping degree. Although Poincaré and Bole gave direct applications of their results in the theory of differential equations, as well as in spacial and analytical mechanics, 322 Sanela Halilovi since then there have not been serious applications of the Brouwer theorem in the mathematical analysis, except one Shauder's result in 1927 about the existence of solution of elliptic partial equations. The situation reversed when John von Neumann applied this theorem to proving the existence of solution for matrix games. These results, which present a base of the classic game theories, increased the mathematicians´s interest in studying the applications of this theorem in various areas of analysis. Modern research in contractive type conditions started with the Banach fixed point theorem which is one of the classic statements in functional analysis. The following two facts have enabled broad applications of this theorem: 1. solving many kinds of numerical and functional equations can be done by finding fixed points of some mappings; 2. the Banach theorem provides effective calculation (construction) of fixed point and also gives the possibility for estimating error i.e. finding maximal distance from approximative to the accurate solution. Given a Banach space X over the field C and a bounded linear operator A : X → X. If some x 0 = 0 is a fix point of the operator A, i.e. Ax = x has a nontrivial solution x = x 0 , we can also say (∃x = 0)(I − A)x = 0.