ABSTRACT
This research work focuses on the application of matrix in solutions of some physical problems in science and engineering which arise in every human endeavor. This project work attempt to present some physical problems from the selected field (aspect) mentioned, so as to find the solution of the problems. The problems include; using matrix in the process of encrypting and decrypting data in this information age, solving electric circuit problem, balancing a complex chemical equation which is a difficult task for student offering chemistry, modelling of traffic flow to aid free flow, solving problem of forces acting on a truss, and modelling of electric network.
TABLE OF CONTENT
CHAPTER ONE
1.0 INTRODUCTION
1.1 Background of Study
1.2 Statement of the Problem
1.3 Aim and Objectives of the Study
1.3.1 Aim of the Study
1.3.2 Objectives of the Study
1.4 Methodology
1.5 Scope and limitation of Study
1.5.1 Scope of the Study
1.5.2 Limitation of the Study
1.6 Significance of the Study
1.7 Definition of Terms
CHAPTER TWO
2.0 LITERATURE REVIEW
2.1 Introduction
2.2 Direct Methods
2.2.1 Gaussian Elimination Method
2.2.2 Pivotal Strategy
2.2.3 Gauss-Jordan Elimination method
2.2.4 LU Factorisation
2.2.5 Matrix Inversion
2.3 Indirect Method
2.3.1 Jacobi Iteration Method
2.3.2 Gauss-Seidel Method
CHAPTER THREE
3.0 MATERIALS AND METHODS
3.1 Introduction
3.2 Application of Matrix in Solution of Physical Problem
3.3 Engineering
3.3.1 Cryptography
3.3.2 Civil Engineering
3.3.3 Electrical Engineering
3.4 Science
3.4.1 Balancing a Chemical Equation
3.4.2 Modelling of Flow
CHAPTER FOUR
4.0 RESULTS
4.1 Introduction
4.2 Engineering
4.2.1 Cryptography
4.2.2 Civil Engineering
4.2.3 Electrical Engineering
4.3 Science
4.3.1 Balancing a Chemical Equation
4.3.2 Modelling of Flow
CHAPTER FIVE
5.0 DISCUSSION OF RESULTS, CONCLUSION AND RECOMMENDATION 48
5.1 Discussion of Results
5.2 Conclusion
5.3 Recommendation
REFERENCE
LIST OF FIGURE
Figure
3.1 Forces acting on a truss
3.2 Electric Network
3.3 Electric Circuit
3.4 Traffic Flow
CHAPTER ONE
1.0 INTRODUCTION
1.1 Background of Study
Mathematics is being used in general in almost all aspect of human life. Mathematicians seek out patterns and formulate new conjectures. Therefore mathematical models and method have been used in different areas, such as science, technology, social and management science and arts.
Several problems can be transformed into mathematical form, and its application in the real world cannot be over emphasized. Mathematical modelling in general is been used in areas such as systems of linear differential equation, interpolation polynomials, to describe the behavior of a system, population, linear programming and systems of linear equations.
A huge amount of computer time is spent for carrying out matrix computations for solving linear systems, which is the backbone of many science and engineering problems. The connection between digital computation and matrices is obvious. Since many engineering problems are linear, and since digital computers with finite memory can manipulate only finite sets of numbers, the solution of linear problems by digital computation usually involves matrix.
Almost every physical situation can be captured by the help of a mathematical equation (whether differential equation or a linear equation). If physical problems are transformed into mathematical model with help of differential equation, it may be solved by any appropriate method depending on the nature of the differential equation. Something similar (but somewhat slightly different) happen when a physical problem is translated into a system of linear equations. That is, it can be solved by any of the available methods of solving system of linear equations. We observed here that the field of applied mathematics was generally introduced during 19th century by some famous mathematicians.
This project work did not mean to present all the methods of solving a system of linear equation, but it aim at presenting some selected method called matrix methods of solving system of linear equations the linear equations will be transformed into matrix and the solution can be obtained with the used of some properties of matrix.In the project work therefore we are going to consider some specific areas where matrix are applied, they include solutions of problems in science, and engineering though its application covers other aspect such as social science, management science and financial areas.
The work is divided into five chapters as follows:
Chapter one is an introductory part that contains basic definitions and operations of the tools used in the entire project work.
Chapter two is the literature review. We discuss two method of solving systems of linear equations using matrices: viz direct (exact) method and indirect (iterated) method.
In chapter three, we present a number of various areas where matrix can be applied under the field of science and engineering.
In chapter four, we try to discuss the result of our matrix application obtained in chapter three using various matrix method of solution.
Chapter five comprises of the discussion of results, conclusion and recommendations.
1.2 Statement of the Problem