Abstract

A differential equation is a mathematical equation for an unknown function of one or several variables that relates the values of the function itself and its derivatives of various orders. Differential equations play a prominent role in engineering, physics, economics, and other disciplines. Hence, the research work is focusing on developing a software for computation of newton methods using visual basic 6.0

CHAPTER ONE

INTRODUCTION

1.1    Background of the Study
Differential equations arise in many areas of science and technology, specifically whenever a deterministic relation involving some continuously varying quantities (modeled by functions) and their rates of change in space and/or time (expressed as derivatives) is known or postulated. This is illustrated in classical mechanics, where the motion of a body is described by its position and velocity as the time value varies. Newton’s laws allow one (given the position, velocity, acceleration and various forces acting on the body) to express these variables dynamically as a differential equation for the unknown position of the body as a function of time. In some cases, this differential equation (called an equation of motion) may be solved explicitly.
An example of modelling a real world problem using differential equations is the determination of the velocity of a ball falling through the air, considering only gravity and air resistance. The ball’s acceleration towards the ground is the acceleration due to gravity minus the deceleration due to air resistance. Gravity is considered constant, and air resistance may be modeled as proportional to the ball’s velocity. This means that the ball’s acceleration, which is a derivative of its velocity, depends on the velocity. Finding the velocity as a function of time involves solving a differential equation.
Differential equations are mathematically studied from several different perspectives, mostly concerned with their solutions —the set of functions that satisfy the equation. Only the simplest differential equations admit solutions given by explicit formulas; however, some properties of solutions of a given differential equation may be determined without finding their exact form. If a self-contained formula for the solution is not available, the solution may be numerically approximated using computers. The theory of dynamical systems puts emphasis on qualitative analysis of systems described by differential equations, while many numerical methods have been developed to determine solutions with a given degree of accuracy.

1.2    Statement of the Problem
Solving mathematical equations are not always easy. Students are becoming too lazy over using their brain to do some mathematical calculations hence the need for an equation solver to compute mathematical equations.

1.3   Purpose of the Project
The purpose of this project is to develop automated differential equation solver using Newton’s method.

1.4    Objectives of the Project
The project will achieve the following:
1.      Create a program environment for maths computations
2.      Generate computation report.

1.5    Justification of the Project
The new system will help students to solve mathematical equations easily and learn more and faster.

1.6    Scope of the Study
The system is limited to differential equations.
1.7    Limitation of Study
During the process of this research work some drawbacks were encountered while trying to get adequate needed data and information.
And secondly, time and financial constraints which had great influence to this work.
1.8    Methodology
The methodology used in this project was basically oral interview. Oral interview was carried out with the staff of the company and some relevant information related to the topic was gathered. Some documents was also sourced from the internet.

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Thursday, 23 February 2017

DIFFERENTIAL EQUATION SOLVER

Abstract

INTRODUCTION

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