An unintended consequence of using “research expenditures” as a figure of merit for universities is to reduce the research output per dollar invested by discouraging the diffusion of superior, lower-cost, open-source scientific equipment.

The laws of Physics and some other related courses are generally written as differential equations. Therefore, all of science and engineering use differential equations to some extent. A good knowledge of differential equations will be an integral part of your study in science and/or engineering classes. You can think of mathematics as the language of science, and differential equations are one of the most important parts of this language as far as science and engineering are concerned. De...

Trigonometry (from Greek trigōnon, "triangle" and metron, "measure"[1]) is a branch of mathematics that studies relationships involving lengths and angles of triangles. The field emerged in the Hellenistic world during the 3rd century BC from applications of geometry to astronomical studies.[2] The 3rd-century astronomers first noted that the lengths of the sides of a right-angle triangle and the angles between those sides have fixed relationships: that is, if at least th...

Contents 1 General Introduction 1 1.1 Background of Study . . . . . . . . . .1 1.2 Integral Equation . . . . . . . . . .......2 1.2.1 Fredholm integral equation . . .3 1.2.2 Volterra integral equation . . . . 4 1.3 Polynomials . . . . . . . . . . . . . . . . . 4 1.4 Orthogonal Polynomials . . . . . . .5 1.5 Chebyshev Polynomials . . . . . . . 6 1.5.1 Chebyshev polynomial of the first kind Tr(x) . . . . . 6 1.5.2 Chebyshev polynomial of second kind Ur(x) . . . . . 6 1.5.3 Chebyshev polynomials...

ABSTRACT In 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 �...

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...

An alternate method of absolute value

Research Thesis on Formulation of HAMILTONIAN MECHANICS reconciliation of Classical Mechanics (Langrangian) with Quantum Mechanics (Hamiltonian), smaller infinitesimal particles Einstein's Mechanics. Addendum, Canonical Transformation, Principle of Virtual Work, Harmonic Oscillator and Lemma on Mathematical Method ascertained by PROF. J.C AMAZIGO DEPARTMENT OF MATHEMATICS UNIVERSITY OF NIGERIA NSUKKA.

This research work ‘’THE EFFECT OF ANXIETY ON PERFORMANCE OF STUDENTS IN MATHEMATICS’’ focuses on the relationship between Mathematics anxiety and students performance. A descriptive experimental research design was used to investigate the research questions. The population consisted of 120 pre-service teachers at Adeniran Ogunsanya College of Education, Ojo Local Government, Lagos State. A personal data questionnaire was used to gather demographic and anxiety information about the pa...

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...