Browsing by Author "Haque, Md. Abdul"

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Eulerian Method for Third Order Linear Systems
(University of Rajshahi, 2003) Haque, Md. Abdul; Sattar, M. Abdus
In this thesis, we have studied the solutions of the various types of third order linear systems of ordinary differential equations. In chapter I, we have considered the third order linear homogeneous system with constant coefficients and developed Eulerian methods for all possible cases of the characteristic roots of the variational matrix. In chapter 2, we have considered the third order linear nonhomogeneous system with constant coefficients. The method covers all the cases when the roots of the characteristic equation of the corresponding homogeneous linear system are real and distinct, real and equal and complex. In finding particular solutions for the nonhomogeneous system of equations we have used the method of variation of parameters. Finally, we have obtained solutions of this system with the help of Crammer's rule. In chapter 3, we have considered the generalized form of third order linear nonhomogeneous system with constant coefficients. We have extended the Eulerian method and developed new techniques for obtaining solutions of this system. In chapter 4, we have discussed the third order linear nonhomogeneous system with variable coefficients. This problem is very difficult to solve, so we have examined a special case of this problem. By using a suitabletransformation, we have reduced it to a third order linear nonhomogeneous system with constant coefficients and have found solutions by the method of Chapter 2. We have illustrated all the methods by several suitable examples.
Laminar Flow of Incompressible Viscous Newtonian Fluid
(University of Rajshahi, 2009) Haque, Md. Abdul; Rahman, M. Zillur; Alam, M. Shamsul
The thesis entitled "Laminar Flow of Incompressible Viscous Newtonian Fluid" is being presented for the award of the degree of Doctor of Philosophy in Applied Mathematics. It is the outcome of my researches conducted in the Department of Applied Mathematics, University of Rajshahi, Bangladesh. The whole thesis consists of nine chapters. The first chapter is a general introductory chapter, giving the general information about Laminar Flow of Incompressible Viscous Newtonian Fluid. In chapter II, we have described about the basic concepts of incompressible viscous Newtonian fluid. Some fundamental equations are presented in this chapter. In Chapter III a laminar flow of incompressible viscous fluid has been considered. Here two numerical methods for solving boundary layer equation have been discussed; (i) Keller Box scheme, (ii) shooting method. Runge-Kutta method is used to solve the initial value problem. The shooting method is supported by a suitable example. The Chapter IV is divided into two parts. In Part: A an attempt has been made to investigate the velocity profile of unsteady laminar flow of incompressible viscous fluid. The method of separation of variable is used to determine the solutions of the governing differential equations. Time varying pressure gradient is considered for poiseuille flow. The velocity profiles for the various types of flow are shown by the figures. In Part: B a fully developed conducting flow of incompressible viscous Newtonian fluid between two parallel plates under the action of a parallel Lorentz force is considered. Analytic solutions for this type of flow are developed. The velocity profiles are presented in figures. In Chapter V, an attempt has been made to study the flow of a viscous incompressible fluid between two parallel porous plates. In case I, we have considered the flow of conducting fluid between two fixed porous plates in presence of a transverse magnetic field. Small suction and injection are imposed on the plates. The velocity of the fluid has been obtained under the three different cases, when pressure gradient is (i) varying linearly with time (ii) decreasing exponentially with time and (iii) varying periodically with time. In case I I of this chapter an attempt have been made to study the flow of a conducting viscous incompressible fluid between two porous plates in absence of pressure gradient force. One plate is at rest and the other plate is oscillating with a constant frequency. A small suction is imposed on the oscillating plate. A transverse magnetic field is also placed on the fluid. The velocity distribution has been investigated numerically with the help of finite difference method. In Chapter VI the laminar flow of Newtonian conducting fluid produced by a moving plate in presence of transverse magnetic field is investigated. The basic equation governing the motion of such flow is expressed in non-dimensional form. Analytic solution of the governing equation is obtained by Laplace transformation. Numerical solution of the dimensionless equation is also obtained with the help of Crank-Nicholson implicit scheme. Velocity profiles of the corresponding problem are shown in the graphs. The Chapter VII is also divided into two parts. In part: A, the temperature distributions of various types of parallel flow of incompressible viscous fluid have been considered. Temperature distribution near a heated plate is also discussed. Coefficients of heat transfer for various types flow has been investigated. In part: B of this chapter, we have considered unsteady MHD flows of an incompressible viscous fluid past an infinite vertical plate. The uniform flow is subject to a transverse applied magnetic field………………………………
Problems and Prospects of Vocational Education: An Empirical Study in Rajshahi Division, Bangladesh
(University of Rajshahi, 2018) Hossain, Md. Shahadat; Mondal, Md. Nazrul Islam; Haque, Md. Abdul; Banu, Akter
Skilled manpower is essential concomitant of sustainable development for the populous country like Bangladesh. Vocational education (VE) is work-based and training oriented education which is the main tool for skill development.. The VE of Bangladesh suffers from many kinds of challenges, though it focuses some prospects for economic growth by creating skilled manpower. The SSC (Voc) [Secondary School Certificate (Vocational)] is the most widely extended vocational course over the country. The Government of Bangladesh (GOB) has introduced various steps to increase the enrolment in SSC (Voc) course, but till now it does not fulfill the goal. The SSC (Voc) education suffers low enrolment situation due to some challenges. It is a dire need of academic research for in-depth investigation to know the causes of low enrolment and to know the extent in where the SSC (Voc) course is effective. Therefore, an effort has been made to reveal the problems and prospects of VE in context of SSC (Voc). This research is predominantly both quantitative and qualitative in nature (mixed method) where three districts namely Rajshahi, Natore and Bogra of Rajshahi Division, Bangladesh were selected as the study areas. Document analysis, interview, and questionnaire survey methods were used. Relevant policies and reports of various national and international agencies were collected for document analysis. For questionnaire survey, 500 students, 80 Trade instructors, 20 Head teachers/Principals, 51 guardians and 91 social leaders were selected as respondents through random and purposive sampling techniques. For qualitative analysis, 40 respondents (all types) were selected for interview. Univariate, bivariate and multivariate analysis were used to analyze the data for estimating the required indicators and to measure the intensity of the explanatory variables on explained variables. VE course in nearest institutions. Another cause for low enrolment is misconception that only weak student admit in VE and the scope of trade related higher education is limited. Student‟s father‟s education and age and type of respondent of „guardian‟s and social leader‟s‟ were found significant predictors for „less social dignity of vocational profession‟. Student‟s mother‟s education and monthly family income were found significant predictors for „physical work-based job nature of vocational profession‟. Student‟s father‟s education, father‟s occupation and district and age and gender of „guardian‟s and social leader‟s‟ were found significant predictors for „lack of social awareness about VE‟. Student‟s education class, father‟s occupation, district and type of institutions and age and gender of „guardian‟s and social leader‟s‟ were found significant predictors for „lack of proper learning in VE‟. Student‟s age, education class, district and type of institutions and type of respondents of „guardian‟s and social leader‟s‟ were found significant predictors for „comparatively high expense than general education‟. Student‟s father‟s education, mother‟s education, and monthly family income and only age of „guardian‟s and social leader‟s‟ were found significant predictors for „absence of VE course in nearest institutions‟. The VE also suffers from some kinds of negative attitudes like it is work-based and labor oriented education, bear negative social values i.e. some vocational professions are restricted within the caste, and religious and social restriction for girl‟s entrance. The students face negligence and noncooperation for admitting in VE. Most of the Trade instructors, Head teachers/Principals, and guardians and social leaders were agreed with the same. Student‟s father‟s education, father‟s occupation, mother‟s education, district and type of institutions and type of respondent of „guardian‟s and social leader‟s were found significant predictors for „negligence and noncooperation‟. In Bangladesh, status of VE is low quality. Among the Trade instructors, about half of them (56.2%) said that the quality of VE is good, but most of the Head teachers/Principals (85.0%) and „guardians and social leaders‟ (76.1%) did not agree with the same. All categories of respondents were agreed to the causes of low quality of VE are as follows: i) Lack of skilled and trained teacher; ii) Shortage of insufficient classrooms; iii) Lack of labs and instruments; iv) lack of practical expertise of Trade instructors and exercise of students; v) lack of sincerity and regularity of Trade instructors; vi) lack of students own sincerity; vii) lack of guardians consciousness and help; and viii) comparatively weak students admit in VE. Most of the Trade instructors, Head teachers/Principals and „guardians and social leaders‟ were expressed that VE institutions do not have sufficient labs/instruments and other infrastructures. All respondents were agreed that apprenticeship of VE is a must. Almost all Trade instructors said that their salary structure is not sufficient as a teacher. They noted that salary structure is the main constraint to attract competent teacher in VE. For this reason, in spite of existing sufficient VE institutions (Government and Non-government) in Bangladesh, skilled manpower is not increasing enough. Almost all Trade instructors, Head teachers/Principals and „guardians and social leaders‟ were agreed that people have no consciousness about VE. Almost all Head teachers/Principals and „guardians and social leaders‟ were agreed that after completion of SSC (Voc) course, students do not achieve enough knowledge for getting trade jobs. About fifty percent of Trade instructors were agreed the same. Trade instructors were also mentioned that weak merit of students, lack of guardians‟ awareness, weak primary and junior secondary education, lack of skilled teachers and instructors, lack of trade related practical exercise, and absence of helping environment in house are the constraints for student good learning in VE. Almost all respondents thought that child marriage, and some social myths influence girl‟s in VE. Most of the „guardians and social leaders‟ were agreed that religious restrictions are also a cause of low girls‟ entrance. Almost all respondents (all types) were given their opinions that, VE has a great importance for developing a country because of it has a great contribution to become drop-out and weak student as skilled manpower. It also has contribution to reduce unemployment, child labor, child abuse, and to create scopes of self-employment, income generating activities for girls, and to help earning more foreign currency by exporting skilled manpower. By considering the importance of VE, the study revealed that initiatives are to be taken as stimulants to expand VE are as follows: building awareness of people about facilities of VE, taking various steps to reduce negative attitudes towards VE, creating necessary and sufficient scope to admit in VE, taking initiatives for establishing VE institutions by Government and Non-government sectors, creating necessary and sufficient job sectors for VE graduates, giving facilities to make entrepreneur, creating opportunity for higher education in related trades, advertising women empowerment through VE, and establishing VE institutions separately and also attached with general education institutions as a separate unit.