 The Complete Research Material is averagely 52 pages long and it is in Ms Word Format, it has 15 Chapters.
 Major Attributes are Abstract, All Chapters, Figures, Appendix, References.
 Study Level: BTech, BSc, BEng, BA, HND, ND or NCE.
 Full Access Fee: ₦4,000
Get the complete project »
CHAPTER ONE
1.0 INTRODUCTION
1.1 BACKGROUND OF STUDY
The Laplace transform is a widely used integral transform with many applications in physics and engineering. Denoted ℓ {f(t)}= dt, it is a linear operator of a function f(t) with a real argument t (t ≥ 0) that transforms it to a function F(s) with a complex argument s. This transformation is essentially bijective for the majority of practical uses; the respective pairs of f(t) and F(s) are matched in tables. The Laplace transform has the useful property that many relationships and operations over the originals f(t) correspond to simpler relationships and operations over the images F(s). It is named after PierreSimon Laplace, who introduced the transform in his work on probability theory. The Laplace transform is related to the Fourier transform, but whereas the Fourier transform expresses a function or signal as a series of modes of vibration (frequencies), the Laplace transform resolves a function into its moments. Like the Fourier transform, the Laplace transform is used for solving differential and integral equations. In physics and engineering it is used for analysis of linear timeinvariant systems such as electrical circuits, harmonic oscillators, optical devices, and mechanical systems. In such analyses, the Laplace transform is often interpreted as a transformation from the timedomain, in which inputs and outputs are functions of time, to the frequencydomain, where the same inputs and outputs are functions of complex angular frequency, in radians per unit time. Given a simple mathematical or functional description of an input or output to a system, the Laplace transform provides an alternative functional description that often simplifies the process of analyzing the behavior of the system, or in synthesizing a new system based on a set of specifications.
On the other hand Partial differential equations (PDEs) provide a quantitative description for many central models in physical, biological, and social sciences. The description is furnished in terms of unknown functions of two or more independent variables, and the relation between partial derivatives with respect to those variables. A PDE is said to be nonlinear if the relations between the unknown functions and their partial derivatives involved in the equation are nonlinear. Despite the apparent simplicity of the underlying differential relations, nonlinear PDEs govern a vast array of complex phenomena of motion, reaction, diffusion, equilibrium, conservation, and more. Due to their pivotal role in science and engineering, PDEs are studied extensively by specialists and practitioners. Indeed, these studies found their way into many entries throughout the scientific literature. They reflect a rich development of mathematical theories and analytical techniques to solve PDEs and illuminate the phenomena they govern. Yet, analytical theories provide only a limited account for the array of complex phenomena governed by nonlinear PDEs.
Over the past sixty years, scientific computation has emerged as the most versatile tool to complement theory and experiments. Modern numerical methods, in particular those for solving nonlinear PDEs, are at the heart of many of these advanced scientific computations. Indeed, numerical computations have not only joined experiment and theory as one of the fundamental tools of investigation, but they have also altered the kind of experiments performed and have expanded the scope of theory. This interplay between computation, theory, and experiments was envisioned by John von Neumann, who in 1949 wrote “the entire computing machine is merely one component of a greater whole, namely, of the unity formed by the computing machine, the mathematical problems that go with it, and the type of planning which is called by both” (Perthame, B., 2007).
1.2 STATEMENT OF THE PROBLEM
The study will try to apply Laplace transform in solving the partial differential equation = sinxsiny; with initial conditions U(x,0) = 1 + cosx, Uy(0,y) = 2siny and also the PDE + + u = 6y with initial conditions U(x,0) = 1, u(0,y) = y, Uy(0,y) = 0 in the second derivatives.
1.3 AIM AND OBJECTIVES OF STUDY
The main aim of the research work is assess the application of Laplace transform in solving partial differential equation in the second derivative. Other specific objectives of the study are:
1. to determine the exact solution of the problems stated above
2. to determine whether PDEs can be verified using substitutions
3. to determine whether any particular solution of PDEs can solve a nonhomogenous problem
4. to investigate on the factors affecting the use of Laplace transform in solving differential equation
1.4 RESEARCH QUESTIONS
The study came up with research questions so as to ascertain the above stated objectives of the study. The research questions for the study are:
1. What is the exact solution of the problems stated above?
2. Can PDEs be verified using substitutions?
3. Can any particular solution of PDEs solve a nonhomogenous problem?
4. What are the factors affecting the use of Laplace transform in solving differential equation?
1.5 SIGNIFICANCE OF STUDY
The study onthe application of Laplace transform in solving partial differential equation in the second derivative will be of immense benefit to the mathematics department as the study will serve as a repository of information to other researchers and students that wishes to carry out similar research on the above topic because the study will educate the students and researchers on how to apply Laplace transforms to PDEs in the second derivatives. Finally the study will contribute to the body of existing literature and knowledge in this field of study and provide a basis for further research
1.6 SCOPE OF STUDY
The study onthe application of Laplace transform in solving partial differential equation in the second derivative will be limited to second order PDEs. The study will cover on how to apply Laplace transforms to PDEs in the second derivatives.
1.7 DEFINITION OF TERMS
PDEs: is a differential equation that contains unknown multivariable functions and their partial derivatives
You either get what you want or your money back. T&C Apply
You can find more project topics easily, just search

SIMILAR MATHEMATICS EDUCATION FINAL YEAR PROJECT RESEARCH TOPICS

1. IMPACT OF MATHEMATICS LABORATORY USE FOR EFFECTIVES TEACHING AND LEARNING OF MATHEMATICS IN JUNIOR SECONDARY SCHOOL
» CHAPTER ONE INTRODUCTION 1.1 Background to the study Education is the totality of life experiences that people acquire and which enable them to cope w...Continue Reading »Item Type & Format: Project Material  Ms Word  85 pages  Instant Download  Chapter 15  MATHEMATICS EDUCATION DEPARTMENT

2. AN ANALYSIS OF FEMALE STUDENTS PERFORMANCE IN MATHEMATICS IN SECONDARY SCHOOLS IN SOKOTO METROPOLIS
» ABSTRACT This study assessed the performance of female students in mathematics in secondary schools in Sokoto metropolis. The population of the study ...Continue Reading »Item Type & Format: Project Material  Ms Word  52 pages  Instant Download  Chapter 15  MATHEMATICS EDUCATION DEPARTMENT

3. FACTORS INFLUENCING THE ATTITUDE OF SECONDARY SCHOOL STUDENTS TOWARDS THE STUDY OF MATHEMATICS
» CHAPTER ONE INTRODUCTION We are living in a world that is rapidly progressing scientifically and technologically. The economic well being of any devel...Continue Reading »Item Type & Format: Project Material  Ms Word  77 pages  Instant Download  Chapter 15  MATHEMATICS EDUCATION DEPARTMENT

4. DIFFERENTIATION AND ITS APPLICATION
» CHAPTER ONE 1.1. INTRODUCTION From the beginning of time man has been interested in the rate at which physical and non physical things change. Astrono...Continue Reading »Item Type & Format: Project Material  Ms Word  78 pages  Instant Download  Chapter 15  MATHEMATICS EDUCATION DEPARTMENT

5. EFFECTS OF TEACHING METHODS, GENDER AND SCHOOL LOCATION ON THE PERFORMANCE OF SECONDARY SCHOOL STUDENTS IN MATHEMATIC: IN KANO STATE
» CHAPTER ONE INTRODUCTION 1.1 Background to the study Mathematics being the pivot at which all the sciences are turning and the remarkable role it play...Continue Reading »Item Type & Format: Project Material  Ms Word  67 pages  Instant Download  Chapter 15  MATHEMATICS EDUCATION DEPARTMENT

6. A COMPARATIVE STUDY BETWEEN MALE AND FEMALE STUDENTS’ PERFORMANCE IN SENIOR SECONDARY SCHOOL MATHEMATICS
» ABSTRACT This study was designed to diagnose students’ performance in Mathematics in senior secondary school in Katsina Metropolis. The study ce...Continue Reading »Item Type & Format: Project Material  Ms Word  85 pages  Instant Download  Chapter 15  MATHEMATICS EDUCATION DEPARTMENT

7. A COMPARATIVE ANALYSIS BETWEEN STUDENT’S COMPETENCE IN MATH AND THEIR PERFORMANCE IN PHYSICS (A CASE STUDY OF SS2 STUDENTS)
» CHAPTER ONE 1.0 INTRODUCTION 1.1 BACKGROUND OF STUDY Competence is defined as capability to apply or use a set of related knowledge, skill and attitud...Continue Reading »Item Type & Format: Project Material  Ms Word  52 pages  Instant Download  Chapter 15  MATHEMATICS EDUCATION DEPARTMENT

8. ASSESSMENT AND FACTORS RESPONSIBLE FOR MASS FAILURE OF MATHEMATICS IN JUNIOR SECONDARY SCHOOL CERTIFICATE EXAMINATION IN KADUNA NORTH L.G.A KADUNA ST...
» CHAPTER ONE INTRODUCTION 1.1 Background of the Study For Nigeria to realize her dream in the development of Junior Secondary Schools, the students of ...Continue Reading »Item Type & Format: Project Material  Ms Word  52 pages  Instant Download  Chapter 15  MATHEMATICS EDUCATION DEPARTMENT