#### Research Papers/Topics in Mathematics

##### Discrete time mathematical SIR model for disease transmission

ABSTRACT: Infectious  disease  has  become  a  source  of  fear  and  superstition  since  the first  ages  of  human  civilization.  In  this  study,  we  consider  the  Discrete  SIR  model for  disease  transmission  to  explain  the  use  of  this  model  and  also  show  significant explanation  as  regard  the  model.  We  discuss  the  mathematics  behind  the  model and  various  tools  for  judging  effectiveness  of  policies  ...

70 PAGES (12993 WORDS)
##### THE ADAMS-BASHFORTH ITERATIVE SCHEME FOR INITIAL VALUE PROBLEMS

ABSTRACTIn this project work, we studied the Adams-Bashforth scheme for solving initial value problems. We gave an indebt explanation on the Adam-Bashforth scheme, its consistency, stability, and convergence, the two and three step methods were also derived. Numerical solutions were obtained using four (4) examples.TABLE OF CONTENTS Cover page                                 i         &nbs...

74 PAGES (12325 WORDS)
##### SPECTRAL METHOD SOLUTION OF VOLTERRA INTEGRAL EQUATIONS VIA THIRD KIND CHEBYSHEV

Contents1 General Introduction 11.1 Background of Study . . . . . . . . . .11.2 Integral Equation . . . . . . . . . .......21.2.1 Fredholm integral equation . . .31.2.2 Volterra integral equation . . . . 41.3 Polynomials . . . . . . . . . . . . . . . . . 41.4 Orthogonal Polynomials . . . . . . .51.5 Chebyshev Polynomials . . . . . . . 61.5.1 Chebyshev polynomial of the first kind Tr(x) . . . . . 61.5.2 Chebyshev polynomial of second kind Ur(x) . . . . . 61.5.3 Chebyshev polynomials of third-k...

52 PAGES (6290 WORDS)
##### Systematic study of z transform and its analysis on Discrete Time Systems

ABSTRACTIn this project work, we have established a systematic study of z transform and its analysis on Discrete Time (DT) systems. The researcher also deal with Linear Time Invariant (LTI) system and Difference Equation as examples of DT systems. The right and left shift was use as a method of solution of the z transform to linear difference equation.CHAPTER 1          &nb...

78 PAGES (19906 WORDS)
##### The relationships between students’ attitude towards mathematics and their performance in mathematics

It is said that mathematics is the gate and key of the sciences. According to the famous philosopher Kant, “A science is exact only in so far as it employs mathematics”. So all scientific education which does not commence with mathematics is said to be defective at its foundation, In fact it has formed the basis for the evolution of scientific development all over. Taking into cognizance, the usefulness, relevance and importance of mathematics, like bringing positive changes to the scient...

60 PAGES (10501 WORDS)
##### A Survey of Linear Programming Concepts

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        &nb...

83 PAGES (12878 WORDS)
##### TIME SERIES ANALYSIS ON SOME SELECTED NON OIL PRODUCE IN NIGERIA (A CASE STUDY OF CASH CROPS & LIVESTOCK)

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 Nig...

70 PAGES (9565 WORDS)
##### Credit Risk Models

In Financial Institutions such as banks and other firms, we face financial risk whichemanates from different source. Credit Risk as one of the prominent risk, had beenfound to reduce the efficiency of banks and other financial firms, hence, the researchto model the risk .In this project, several models used to evaluate credit risk, including their drawbacks,frame works and strengths are reviewed.

41 PAGES (7570 WORDS)
##### APPLICATION OF NUMERICAL ANALYSIS TO ALGEBRAIC AND TRANSCENDENTAL EQUATIONS

ABSTRACTIn 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 ...

50 PAGES (6680 WORDS)
##### THE ROLE OF INCUBATION PERIOD IN A DISEASE MODEL WITH LOGISTIC AND LINEAR RECRUITMENT RATES

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 us...

68 PAGES (13742 WORDS)
##### A Study of the Fundamentals of Fuzzy Set

AbstractThe 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 popularized...

40 PAGES (7053 WORDS)
##### RELEVANCE OF MATHEMATICS AS A CORE SUBJECT IN SENIOR SECONDARY SCHOOLS IN NSUKKA LOCAL GOVERNMENT AREA OF ENUGU STATE

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? ...

38 PAGES (7329 WORDS)
##### MATHEMATICAL MODELING OF THE EFFECT OF IRRESPONSIBLE IMMIGRANT ON THE TRANSMISSION DYNAMICS OF HIV

ABSTRACTThis project proposes a non – linear mathematical model to study the effect of irresponsible infected immigrants on the spread of HIV/AIDS in a heterogeneous population with a constant recruitment of susceptible. The equilibrium points, stability analysis and numerical simulation on the model are presented. It is realised that at the disease – free equilibrium, the model is stable when the basic reproduction number R0<1 and unstable otherwise. The Routh – Hurwi...

39 PAGES (5554 WORDS)
##### Mathematical Modelling Of Hiv/Aids Dynamics With Treatment And Vertical Transmission

ABSTRACTThis study proposes and analyzes a non-linear mathematical model for the dynamicsof HIV/AIDS with treatment and vertical transmission. The equilibrium points of themodel system are found and their stability is investigated.The model exhibits two equilibria namely, the disease-free and the endemicequilibrium. It is found that if the basic reproduction number R0 1, the disease-freeequilibrium is always locally asymptotically stable and in such a case the endemicequilibrium does not e...

91 PAGES (19877 WORDS)