Skip to main content

SERIES SOLUTION OF ORDINARY DIFFERENTIAL EQUATION  

ATTENTION:

BEFORE YOU READ THE ABSTRACT OR CHAPTER ONE OF THE PROJECT TOPIC BELOW, PLEASE READ THE INFORMATION BELOW.THANK YOU!

 

INFORMATION:

YOU CAN GET THE COMPLETE PROJECT OF THE TOPIC BELOW. THE FULL PROJECT COSTS N5,000 ONLY. THE FULL INFORMATION ON HOW TO PAY AND GET THE COMPLETE PROJECT IS AT THE BOTTOM OF THIS PAGE. OR YOU CAN CALL: 08068231953, 08168759420

 

 

SERIES SOLUTION OF ORDINARY DIFFERENTIAL EQUATION

 

ABSTRACT

An ordinary differential equation (ODE) is a differential equation containing one or more functions of one independent variable and its derivatives. The term ordinary is used in contrast with the term partial differential equation which may be with respect to more than one independent variable. The few non-linear ODEs that can be solved explicitly are generally solved by transforming the equation into an equivalent linear ODE

Some ODEs may be solved explicitly in terms of known functions and integrals. When it is not possible, one may often use the equation for computing the Taylor series of the solutions. For applied problems, one generally uses numerical methods for ordinary differential equations for getting an approximation of the desired solution.

CHAPTER ONE

1.1                                         INTRODUCTION

A differential equation is a mathematical equation that relates some function with its derivatives. In applications, the functions usually represent physical quantities, the derivatives represent their rates of change, and the equation defines a relationship between the two. Because such relations are extremely common, differential equations play a prominent role in many disciplines including engineering, physics, economics, and biology.

In pure mathematics, differential equations are studied from several different perspectives, mostly concerned with their solutions—the set of functions that satisfy the equation. Only the simplest differential equations are solvable 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. In mathematics, there are three different types of differential equation which are:

i.            Ordinary differential equations

ii.           Partial differential equations

iii.         Non-linear differential equations

However, in this work an ordinary differential equation (ODE) is studied which is an equation containing an unknown function of one real or complex variable x, its derivatives, and some given functions of x. The unknown function is generally represented by a variable (often denoted y), which, therefore, depends on x. Thus x is often called the independent variable of the equation. The term "ordinary" is used in contrast with the term partial differential equation, which may be with respect to more than one independent variable.

1.2                             BACKGROUND OF THE STUDY

Ordinary differential equations (ODEs) arise in many contexts of mathematics and science (social as well as natural). Mathematical descriptions of change use differentials and derivatives. Various differentials, derivatives, and functions become related to each other via equations, and thus a differential equation is a result that describes dynamically changing phenomena, evolution, and variation. Often, quantities are defined as the rate of change of other quantities (for example, derivatives of displacement with respect to time), or gradients of quantities, which is how they enter differential equations.

Specific mathematical fields include geometry and analytical mechanics. Scientific fields include much of physics and astronomy (celestial mechanics), meteorology (weather modelling), chemistry (reaction rates),[2] biology (infectious diseases, genetic variation), ecology and population modelling (population competition), economics (stock trends, interest rates and the market equilibrium price changes).

Many mathematicians have studied differential equations and contributed to the field, including Newton, Leibniz, the Bernoulli family, Riccati, Clairaut, d'Alembert, and Euler.

 

1.3                               OBJECTIVE OF THE STUDY

The objective of this work is have a series solution to ordinary differential equation with different formulas.

1.4   APPLICATIONS OF THE STUDY

The study of differential equations is a wide field in pure and applied mathematics, physics, and engineering. All of these disciplines are concerned with the properties of differential equations of various types. Pure mathematics focuses on the existence and uniqueness of solutions, while applied mathematics emphasizes the rigorous justification of the methods for approximating solutions. Differential equations play an important role in modelling virtually every physical, technical, or biological process, from celestial motion, to bridge design, to interactions between neurons. Differential equations such as those used to solve real-life problems may not necessarily be directly solvable, i.e. do not have closed form solutions. Instead, solutions can be approximated using numerical methods.

Many fundamental laws of physics and chemistry can be formulated as differential equations. In biology and economics, differential equations are used to model the behavior of complex systems. The mathematical theory of differential equations first developed together with the sciences where the equations had originated and where the results found application. However, diverse problems, sometimes originating in quite distinct scientific fields, may give rise to identical differential equations. Whenever this happens, mathematical theory behind the equations can be viewed as a unifying principle behind diverse phenomena. As an example, consider the propagation of light and sound in the atmosphere, and of waves on the surface of a pond. All of them may be described by the same second-order partial differential equation, the wave equation, which allows us to think of light and sound as forms of waves, much like familiar waves in the water. Conduction of heat, the theory of which was developed by Joseph Fourier, is governed by another second-order partial differential equation, the heat equation. It turns out that many diffusion processes, while seemingly different, are described by the same equation; the Black–Scholes equation in finance is, for instance, related to the heat equation.

1.5                                   SCOPE OF THE STUDY

In this introductory course on Ordinary Differential Equations, we first provide basic terminologies on the theory of differential equations and then proceed to methods of solving various types of ordinary differential equations. We handle first order differential equations and then second order linear differential equations. We also discuss some related concrete mathematical modeling problems, which can be handled by the methods introduced in this course.

1.6                                 PURPOSE OF THE STUDY

This course is recommended for undergraduate students in mathematics, physics, engineering and the social sciences who want to learn basic concepts and ideas of ordinary differential equations. Learners are required to know usual college level calculus including differential and integral calculus.

HOW TO GET THE FULL PROJECT WORK

 

PLEASE, print the following instructions and information if you will like to order/buy our complete written material(s).

 

HOW TO RECEIVE PROJECT MATERIAL(S)

After paying the appropriate amount (#5,000) into our bank Account below, send the following information to

08068231953 or 08168759420

 

(1)    Your project topics

(2)     Email Address

(3)     Payment Name

(4)    Teller Number

We will send your material(s) after we receive bank alert

 

BANK ACCOUNTS

Account Name: AMUTAH DANIEL CHUKWUDI

Account Number: 0046579864

Bank: GTBank.

 

OR

Account Name: AMUTAH DANIEL CHUKWUDI

Account Number: 2023350498

Bank: UBA.

 

 

 

FOR MORE INFORMATION, CALL:

08068231953 or 08168759420

 

 

AFFILIATE LINKS:

myeasyproject.com.ng

easyprojectmaterials.com

easyprojectmaterials.net.ng

easyprojectsmaterials.net.ng

easyprojectsmaterial.net.ng

easyprojectmaterial.net.ng

projectmaterials.com.ng

googleprojectsng.blogspot.com

myprojectsng.blogspot.com.ng

https://projectmaterialsng.blogspot.com.ng/

https://foreasyprojectmaterials.blogspot.com.ng/

https://mypostumes.blogspot.com.ng/

https://myeasymaterials.blogspot.com.ng/

https://eazyprojectsmaterial.blogspot.com.ng/

https://easzprojectmaterial.blogspot.com.ng/

 

 

 

 


Comments

Popular posts from this blog

AN APPRAISAL OF THE LOAN EVALUATION CRITERIA AND CONTROL TECHNIQUE IN ZENITH BANK

ATTENTION: BEFORE YOU READ THE PROJECT WORK, PLEASE READ THE INFORMATION BELOW. THANK YOU! TO GET THE FULL PROJECT FOR THE TOPIC BELOW PLEASE CALL: 08168759420, 08068231953 TO GET MORE PROJECT TOPICS IN YOUR DEPARTMENT, PLEASE VISIT: www.easyprojectmaterials.com www.easyprojectsolutions.com www.worldofnolimit.com AN APPRAISAL OF THE LOAN EVALUATION CRITERIA AND CONTROL TECHNIQUE IN ZENITH BANK ABSTRACT The role of banks as financial intermediary is crucial to the growth of any society. Primarily, bank supply, such financial services as provision of savings and time deposits, call deposits, working capital and terms l oans, tender and performance bonds documentary collections, fund transfer, foreign exchange transaction, equipment leasing and business advisory services. To the individual and corporate business community, bank loans are a prime source of fun

OWNERSHIP STRUCTURES, CORPORATE GOVERNANCE AND PERFORMANCE OF small MFIs in Nigeria(MSC)

YOU CAN CALL US BACK FOR THE COMPLETE THESIS. WE CAN ALSO HELP YOU WITH CORRECTIONS FROM YOUR SUPERVISOR. PLEASE CALL 08068231953, 08168759420        MSC THESIS TOPIC: OWNERSHIP STRUCTURES, CORPORATE GOVERNANCE AND PERFORMANCE OF small MFIs in Nigeria(MSC)   Abstract The purpose of the study was to examine the relationship between ownership structures, corporate governance and the performance of small MFIs in Nigeria. Interest in this study was as a result of poor performance of these MFIs as indicated in the AMFIU Annual report of 2006. The study therefore sought to determine if this could be attributed to their ownership structures and therefore governance levels.   A cross sectional survey design was used to undertake this study using a sample of 65 MFIs from which responses from 44 MFIs were received; giving a response rate of 67.7%.    Findings of the study reveal that ownership structures and corporate governance are significant predictors of MFI performance accounting for 42.4%

ROLE OF RURAL WOMEN FARMERS ON THE ECONOMIC DEVELOPMENT OF EDO STATE

ATTENTION: BEFORE YOU READ THE PROJECT WORK, PLEASE READ THE INFORMATION BELOW. THANK YOU! TO GET THE FULL PROJECT FOR THE TOPIC BELOW PLEASE CALL: 08168759420, 08068231953 TO GET MORE PROJECT TOPICS IN YOUR DEPARTMENT, PLEASE VISIT: www.easyprojectmaterials.com www.easyprojectsolutions.com www.worldofnolimit.com ROLE OF RURAL WOMEN FARMERS ON THE ECONOMIC DEVELOPMENT OF EDO STATE ABSTRACT The role of rural women farmers in the economic development of Egor Local Government Area in Edo State cannot be over emphasized. There is basicall y no aspect of economic development in Edo State that one cannot find women. A review of feminist literature, indicate that there is now a demand for re-orientation of research and change in methodological procedures used for complication of national statistics so as to reflect accurately the position of women and their la