Assistant Professor of Mathematics at IUBAT-International University of Business Agriculture and Technology. Phone: +8801710507576 Address: B-82/1 Jaleswer, Savar, Dhaka, Bangladesh.
The rationale for the inclusion of the course The course provides the necessary knowledge and ski... more The rationale for the inclusion of the course The course provides the necessary knowledge and skill in getting proper knowledge about numerical methods. Also, the application of numerical methods in different Engineering sections. Semester Spring 2023 Status Non-Core Level Under Graduate Credit Value/Hours 3 Prerequisites (if any) MAT 147 (Applied Calculus) Consultation Hours 11:45 AM-12:45 PM (Saturday & Sunday) Total Student Learning Time (SLT)
The course provides necessary knowledge and skill in empirical research a prerequisite to underta... more The course provides necessary knowledge and skill in empirical research a prerequisite to undertaking many technical and engineering problem analyzing. Semester Spring 2023 Status Non-Core Level Under Graduate Credit Value/Hours 3 Pre-requisites(if any) MAT 147 (Applied Calculus) Consultation Hours 11:45 AM-12:45 PM (Saturday & Sunday) Total Student Learning Time (SLT)
With uncertainty on the parameters, a linear system of equations plays an important role in Econo... more With uncertainty on the parameters, a linear system of equations plays an important role in Economics and Finance. In Economics, linear systems of equations with uncertainty on parameters are widely used due to some imprecise data on the relation of a linear system of equations. In this paper, a detailed study of solution technique of system of fuzzy linear equations has been done. Appropriate applications have been also given to illustrate the technique. Before starting the main discussion, we have reviewed basic definitions and results of the fuzzy set theory. Then we have discussed the method to solve the system of fuzzy linear equations. Finally, we have presented some applications of the method for three different types of example.
In the paper some aspects of Riemannian manifolds, pseudo-Riemannian manifolds, Lorentz manifolds... more In the paper some aspects of Riemannian manifolds, pseudo-Riemannian manifolds, Lorentz manifolds, Riemannian metrics, affine connections, parallel transport, curvature tensors, torsion tensors, killing vector fields, conformal killing vector fields are focused. The purpose of this paper is to develop the theory of manifolds equipped with Riemannian metric. I have developed some theorems on torsion and Riemannian curvature tensors using affine connection. A Theorem 1.20 named "Fundamental Theorem of Pseudo-Riemannian Geometry" has been established on Riemannian geometry using tensors with metric. The main tools used in the theorem of pseudo Riemannian are tensors fields defined on a Riemannian manifold.
The system of linear equations plays a vital role in real life problems such as optimization, eco... more The system of linear equations plays a vital role in real life problems such as optimization, economics, and engineering. The parameters of the system of linear equations are modeled by taking the experimental or observation data. So the parameters of the system actually contain uncertainty rather than the crisp one. The uncertainties may be considered in term of interval or fuzzy numbers. In this paper, a detailed study of three solution techniques namely Classical Method, Extension Principle method and α-cuts and interval Arithmetic Method to solve the system of fuzzy linear equations has been done. Appropriate applications are given to illustrate each technique. Then we discuss the comparison of the different methods numerically and graphically.
We design a new numerical method which is the advanced version of the Regula-Falsi [1] method whe... more We design a new numerical method which is the advanced version of the Regula-Falsi [1] method where the bisection technique [2] is used. We briefly discuss these two methods with their respective graphs. We provide an algorithm along with the graphical representation of our proposed method. Finally, we compare our proposed method with some basic iterative methods using a data table.
There are many equations in mathematics which are used in our practical life. Burger's equation i... more There are many equations in mathematics which are used in our practical life. Burger's equation is one of them which is a good simplification of Navier-Stokes equation where the velocity is one spatial dimension and the external force is neglected in absence of pressure gradient. This equation is used to analyze traffic congestion and acoustics. It occurs in various areas of applied mathematics, such as modeling of various problems in fluid dynamics and traffic flow etc. Due to the complexity of the analytical solutio n, one needs to use numerical methods to solve this equation. For this we investigate finite difference method for Burger's equation and present an explicit central difference scheme. We implement the numerical by computer programming for artificial initial and boundary data and verify the qualitative behavior of the numerical solution of burger's equation.
With uncertainty on the parameters, a linear system of equations plays an important role in Econo... more With uncertainty on the parameters, a linear system of equations plays an important role in Economics and Finance. In Economics, linear systems of equations with uncertainty on parameters are widely used due to some imprecise data on the relation of a linear system of equations. In this paper, a detailed study of solution technique of system of fuzzy linear equations has been done. Appropriate applications have been also given to illustrate the technique. Before starting the main discussion, we have reviewed basic definitions and results of the fuzzy set theory. Then we have discussed the method to solve the system of fuzzy linear equations. Finally, we have presented some applications of the method for three different types of example.
In this paper some important aspects of tensor algebra, tensor product, exterior algebra, symmetr... more In this paper some important aspects of tensor algebra, tensor product, exterior algebra, symmetric algebra, module of section, graded algebra, vector subbundles are studied. The purpose of this paper is to develop the theories which are based on multi-linear algebra and tensors with vector bundles of manifolds. A Theorem 1.34. is established by using sections and fibrewise orthogonal sections of an application of Gran-Schmidt.
The system of linear equations plays a vital role in real life problems such as optimization, eco... more The system of linear equations plays a vital role in real life problems such as optimization, economics, and engineering. The parameters of the system of linear equations are modeled by taking the experimental or observation data. So the parameters of the system actually contain uncertainty rather than the crisp one. The uncertainties may be considered in term of interval or fuzzy numbers. In this paper, a detailed study of three solution techniques namely Classical Method, Extension Principle method and α-cuts and interval Arithmetic Method to solve the system of fuzzy linear equations has been done. Appropriate applications are given to illustrate each technique. Then we discuss the comparison of the different methods numerically and graphically.
There are many equations in mathematics which are used in our practical life. Burger's equation i... more There are many equations in mathematics which are used in our practical life. Burger's equation is one of them which is a good simplification of Navier-Stokes equation where the velocity is one spatial dimension and the external force is neglected in absence of pressure gradient. This equation is used to analyze traffic congestion and acoustics. It occurs in various areas of applied mathematics, such as modeling of various problems in fluid dynamics and traffic flow etc. Due to the complexity of the analytical solutio n, one needs to use numerical methods to solve this equation. For this we investigate finite difference method for Burger's equation and present an explicit central difference scheme. We implement the numerical by computer programming for artificial initial and boundary data and verify the qualitative behavior of the numerical solution of burger's equation.
In the paper some aspects of Riemannian manifolds, pseudo-Riemannian manifolds, Lorentz manifolds... more In the paper some aspects of Riemannian manifolds, pseudo-Riemannian manifolds, Lorentz manifolds, Riemannian metrics, affine connections, parallel transport, curvature tensors, torsion tensors, killing vector fields, conformal killing vector fields are focused. The purpose of this paper is to develop the theory of manifolds equipped with Riemannian metric. I have developed some theorems on torsion and Riemannian curvature tensors using affine connection. A Theorem 1.20 named "Fundamental Theorem of Pseudo-Riemannian Geometry" has been established on Riemannian geometry using tensors with metric. The main tools used in the theorem of pseudo Riemannian are tensors fields defined on a Riemannian manifold.
Linear algebra has in recent years become an essential part of the mathemtical background require... more Linear algebra has in recent years become an essential part of the mathemtical background required by
The rationale for the inclusion of the course The course provides the necessary knowledge and ski... more The rationale for the inclusion of the course The course provides the necessary knowledge and skill in getting proper knowledge about numerical methods. Also, the application of numerical methods in different Engineering sections. Semester Spring 2023 Status Non-Core Level Under Graduate Credit Value/Hours 3 Prerequisites (if any) MAT 147 (Applied Calculus) Consultation Hours 11:45 AM-12:45 PM (Saturday & Sunday) Total Student Learning Time (SLT)
The course provides necessary knowledge and skill in empirical research a prerequisite to underta... more The course provides necessary knowledge and skill in empirical research a prerequisite to undertaking many technical and engineering problem analyzing. Semester Spring 2023 Status Non-Core Level Under Graduate Credit Value/Hours 3 Pre-requisites(if any) MAT 147 (Applied Calculus) Consultation Hours 11:45 AM-12:45 PM (Saturday & Sunday) Total Student Learning Time (SLT)
With uncertainty on the parameters, a linear system of equations plays an important role in Econo... more With uncertainty on the parameters, a linear system of equations plays an important role in Economics and Finance. In Economics, linear systems of equations with uncertainty on parameters are widely used due to some imprecise data on the relation of a linear system of equations. In this paper, a detailed study of solution technique of system of fuzzy linear equations has been done. Appropriate applications have been also given to illustrate the technique. Before starting the main discussion, we have reviewed basic definitions and results of the fuzzy set theory. Then we have discussed the method to solve the system of fuzzy linear equations. Finally, we have presented some applications of the method for three different types of example.
In the paper some aspects of Riemannian manifolds, pseudo-Riemannian manifolds, Lorentz manifolds... more In the paper some aspects of Riemannian manifolds, pseudo-Riemannian manifolds, Lorentz manifolds, Riemannian metrics, affine connections, parallel transport, curvature tensors, torsion tensors, killing vector fields, conformal killing vector fields are focused. The purpose of this paper is to develop the theory of manifolds equipped with Riemannian metric. I have developed some theorems on torsion and Riemannian curvature tensors using affine connection. A Theorem 1.20 named "Fundamental Theorem of Pseudo-Riemannian Geometry" has been established on Riemannian geometry using tensors with metric. The main tools used in the theorem of pseudo Riemannian are tensors fields defined on a Riemannian manifold.
The system of linear equations plays a vital role in real life problems such as optimization, eco... more The system of linear equations plays a vital role in real life problems such as optimization, economics, and engineering. The parameters of the system of linear equations are modeled by taking the experimental or observation data. So the parameters of the system actually contain uncertainty rather than the crisp one. The uncertainties may be considered in term of interval or fuzzy numbers. In this paper, a detailed study of three solution techniques namely Classical Method, Extension Principle method and α-cuts and interval Arithmetic Method to solve the system of fuzzy linear equations has been done. Appropriate applications are given to illustrate each technique. Then we discuss the comparison of the different methods numerically and graphically.
We design a new numerical method which is the advanced version of the Regula-Falsi [1] method whe... more We design a new numerical method which is the advanced version of the Regula-Falsi [1] method where the bisection technique [2] is used. We briefly discuss these two methods with their respective graphs. We provide an algorithm along with the graphical representation of our proposed method. Finally, we compare our proposed method with some basic iterative methods using a data table.
There are many equations in mathematics which are used in our practical life. Burger's equation i... more There are many equations in mathematics which are used in our practical life. Burger's equation is one of them which is a good simplification of Navier-Stokes equation where the velocity is one spatial dimension and the external force is neglected in absence of pressure gradient. This equation is used to analyze traffic congestion and acoustics. It occurs in various areas of applied mathematics, such as modeling of various problems in fluid dynamics and traffic flow etc. Due to the complexity of the analytical solutio n, one needs to use numerical methods to solve this equation. For this we investigate finite difference method for Burger's equation and present an explicit central difference scheme. We implement the numerical by computer programming for artificial initial and boundary data and verify the qualitative behavior of the numerical solution of burger's equation.
With uncertainty on the parameters, a linear system of equations plays an important role in Econo... more With uncertainty on the parameters, a linear system of equations plays an important role in Economics and Finance. In Economics, linear systems of equations with uncertainty on parameters are widely used due to some imprecise data on the relation of a linear system of equations. In this paper, a detailed study of solution technique of system of fuzzy linear equations has been done. Appropriate applications have been also given to illustrate the technique. Before starting the main discussion, we have reviewed basic definitions and results of the fuzzy set theory. Then we have discussed the method to solve the system of fuzzy linear equations. Finally, we have presented some applications of the method for three different types of example.
In this paper some important aspects of tensor algebra, tensor product, exterior algebra, symmetr... more In this paper some important aspects of tensor algebra, tensor product, exterior algebra, symmetric algebra, module of section, graded algebra, vector subbundles are studied. The purpose of this paper is to develop the theories which are based on multi-linear algebra and tensors with vector bundles of manifolds. A Theorem 1.34. is established by using sections and fibrewise orthogonal sections of an application of Gran-Schmidt.
The system of linear equations plays a vital role in real life problems such as optimization, eco... more The system of linear equations plays a vital role in real life problems such as optimization, economics, and engineering. The parameters of the system of linear equations are modeled by taking the experimental or observation data. So the parameters of the system actually contain uncertainty rather than the crisp one. The uncertainties may be considered in term of interval or fuzzy numbers. In this paper, a detailed study of three solution techniques namely Classical Method, Extension Principle method and α-cuts and interval Arithmetic Method to solve the system of fuzzy linear equations has been done. Appropriate applications are given to illustrate each technique. Then we discuss the comparison of the different methods numerically and graphically.
There are many equations in mathematics which are used in our practical life. Burger's equation i... more There are many equations in mathematics which are used in our practical life. Burger's equation is one of them which is a good simplification of Navier-Stokes equation where the velocity is one spatial dimension and the external force is neglected in absence of pressure gradient. This equation is used to analyze traffic congestion and acoustics. It occurs in various areas of applied mathematics, such as modeling of various problems in fluid dynamics and traffic flow etc. Due to the complexity of the analytical solutio n, one needs to use numerical methods to solve this equation. For this we investigate finite difference method for Burger's equation and present an explicit central difference scheme. We implement the numerical by computer programming for artificial initial and boundary data and verify the qualitative behavior of the numerical solution of burger's equation.
In the paper some aspects of Riemannian manifolds, pseudo-Riemannian manifolds, Lorentz manifolds... more In the paper some aspects of Riemannian manifolds, pseudo-Riemannian manifolds, Lorentz manifolds, Riemannian metrics, affine connections, parallel transport, curvature tensors, torsion tensors, killing vector fields, conformal killing vector fields are focused. The purpose of this paper is to develop the theory of manifolds equipped with Riemannian metric. I have developed some theorems on torsion and Riemannian curvature tensors using affine connection. A Theorem 1.20 named "Fundamental Theorem of Pseudo-Riemannian Geometry" has been established on Riemannian geometry using tensors with metric. The main tools used in the theorem of pseudo Riemannian are tensors fields defined on a Riemannian manifold.
Linear algebra has in recent years become an essential part of the mathemtical background require... more Linear algebra has in recent years become an essential part of the mathemtical background required by
Multi-linear Algebras and Tensors with Vector Bundles of Manifolds, 2014
− In this paper some important aspects of tensor algebra, tensor product, exterior algebra, symme... more − In this paper some important aspects of tensor algebra, tensor product, exterior algebra, symmetric algebra, module of section, graded algebra, vector subbundles are studied. The purpose of this paper is to develop the theories which are based on multi-linear algebra and tensors with vector bundles of manifolds. A Theorem 1.34. is established by using sections and fibrewise orthogonal sections of an application of Gran-Schmidt.
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