1 Riemann Integration 2 1.1 Partitions and Riemann sums . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.1.1 Definition (Partition P of size > 0) . . . . . . . . . . . . . . . . . . . . 2 1.1.2 Definition (Selection of evaluations points zi) . . . . . . . . . . . . . . . . 2 1.1.3 Definition (Riemann sum for the function f(x)) . . . . . . . . . . . . . . 2 1.1.4 Definition (Integrability of the function f(x)) . . . . . . . . . . . . . . . 2 1.1.5 Definition (Notation for integrab...
I can still remember my expression and feeling when we were asked to show that sup(A + B) = sup(A) + sup(B). It was an herculean task because the concept was too difficult to grasp with the use of approximation property until I discovered an easy route. In a bid to restrict my papers to just few pages, I will focus more on examples than theorems.
Linear programming is a mathematical tool that is used to maximize or minimize a function when constraints are linear. In this project, we considered some examples and applications of linear programming problems. TABLE OF CONTENTS Title page Certification Dedication Acknowledgements Abstract Table of Contents List of Tables�...
ABSTRACT In the period of the 1970’s, Agriculture was the main stay of the Nigeria economy. The oil boom of 1970’s brought about a gradual shift from agriculture to crude oil making Nigeria to depend heavily on petroleum as main source of foreign exchange earnings. Agriculture sector which use to be the back bone of the economy was rendered competitive over time. The crux of this study is to analyze the revenue generated from selected non-oil produce in Nigeria. Dat...
In Financial Institutions such as banks and other firms, we face financial risk which emanates from different source. Credit Risk as one of the prominent risk, had been found to reduce the efficiency of banks and other financial firms, hence, the research to model the risk . In this project, several models used to evaluate credit risk, including their drawbacks, frame works and strengths are reviewed.
ABSTRACT In this paper we introduce, numerical study of some iterative methods for solving non linear equations. Many iterative methods for solving algebraic and transcendental equations are presented by the different formulae. Using bisection method, false position method, secant method and the Newton’s iterative method and their results are compared. The bisection, Regular Falsi, Newton-Raphson and secant method were applied to a single variable function over the interval [0,1]. Numerical...
In this research work, we have reviewed and studied two disease models: a disease model with logistic recruitment rate with and without incubation period and a disease model with linear recruitment rate with and without incubation period. The existence and stability or otherwise of the equilibrium states of the models were studied; also numerical experiments were conducted using a written computer program in MATLAB function ode45; for which table of parameter values were generated using sec...
Abstract: Soft set theory initiated by Molodtsov is an important mathematical tool that deals with uncertainties about imprecision and vagueness. Research on soft ideals of ring has been carried out by other researchers. In this paper, we discuss on some properties of soft ring ideals and idealistic soft ring. We state and prove some important theorems and propositions on soft ring ideals and idealistic of soft ring that has not been studied by other researchers.
Abstract: In this paper, we presented the differential forms method which is used in the linearization of second order non-linear differential equations. The differential forms used here is limited to 2-forms with their respective operations. After presentation of the method, an example is used to illustrate the procedure of the linearization problem. Keywords Linearization, Differential forms, Differential Equations, Second Order
Abstract The fundamental idea of the project is to provide basic and concrete concepts of the fuzzy set theory, and thus focused on easy illustrations of the basic concepts. There are numerous examples and figures to help readers to understand. It tries to explain the emergence of fuzzy sets from historical perspective. Looking back to the history of sciences, it seems that fuzzy sets were bound to appear at some point in the 20th century. Indeed, Zadeh's works have cristalized and popularize...
This work considers the direct solution of general third order ordinary differential equation. The method is derived by collocating and interpolating the approximate solution in power series. A single hybrid three-step method is developed. Taylor series is used to generate the independent solution at selected grid and off grid points. The order, zero stability and convergence of the method were established. The developed method is then applied to solve some initial value problems of third ord...
ABSTRACT This project studied the relevance of Mathematics as a core subject in senior secondary schools in Nsukka Local Government Area of Enugu State. The following research questions were posed to help the researchers in conducting this research: what are the benefits of teaching Mathematics in schools? Are adequate instructional materials used in the study of the subject? Are teachers encouraged to teach the subject matter? Is Mathematics relevant to other subjects? The information fo...
INTRODUCTION The 21st century requires equipping children with basic education in literacy and numeracy, as the more advanced completes skills needed for living that can serve as the foundation of life, enabling the children to adapt and change life abetting to life changing circumstances. Basic education remains the most important factor that enables the very process in enhancing knowledge, skills and attitudes needed for societal and national growth of any country of the world. Learning is...
Abstract This study investigates the Effect of Computer- Instructional Package (COMPUTER INSTRUCTIONAL PACKAGE) on the Performance of Senior Secondary Students in Quadratic Equation in Bida Educational Zone of Niger State, Nigeria. The study examined the significant of performances of students thought using computer instructional package andLecture method. The sample consisted of 120 senior secondary school students drawn from four secondary schools. Stratified random sampling was used to se...
ABSTRACT This study proposes and analyzes a non-linear mathematical model for the dynamics of HIV/AIDS with treatment and vertical transmission. The equilibrium points of the model system are found and their stability is investigated. The model exhibits two equilibria namely, the disease-free and the endemic equilibrium. It is found that if the basic reproduction number R0 1, the disease-free equilibrium is always locally asymptotically stable and in such a case the endemic equilibrium doe...