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Course Credit: 4

It is an excellent introductory combined course on theory of relativity and cosmology. This is a module principally on Einstein's general theory of relativity, a relativistic theory of gravitation which explains gravitational effects as coming from the curvature of space-time. It provides a comprehensive introduction to material which is currently the subject of enthusiastic study from the theoretical and experimental standpoints. In addition, in order to understand the general theory fully, some familiarity with tensor calculus is required. This will involve some self-study material at the start of the module. The rest of the course will be devoted to a detailed investigation of the theory itself together with applications to classical black holes and cosmology.

Course Credit: 4

The objective of this course is to introduce the concept of space-time, the theory of special relativity and some preliminary ideas from general relativity, cosmology and the mathematical model of the expanding universe. The aim of studying cosmology is to construct mathematical models of the universe.

Course Credit: 4

Hydrology treats the flow of water on and below the surface of the Earth. It involves mainly water quality and treats river flood forecasting and ground water flow to wells. It also treats soil deposition, stream erosion and sediment transport. Bangladesh is a riverine country. We have many international and national rivers. Mathematical Hydrology deals with the occurrence, movement, and storage of water in the earth system. So hydrology is a very important subject for our country. The objectives of this course are to give a clear concept to students about use of Hydrology in science and water engineering fields. This course will help the student to identify surface flow, river flow, flood forecasting, measure soil erosion, channel erosion by using different kind of conceptual, mathematical and hydrodynamic.

Course Credit: 4

It is an excellent introductory combined course of Finite Element Method (FEM) and Finite Difference Method (FDM). The approaches of this course are motivated by two primary considerations: audience and pedagogy. Regarding audience, the purpose is to make the method understandable and usable to people in all fields of engineering and physical sciences. Regarding pedagogy, the purpose is to make the technical derivations and explanations as lucid and as simple as possible, without being simplistic. FEM is a general and powerful numerical method, applicable to a broad variety of mathematical problems that arise in almost all areas of science and engineering. FDM is introduced in this course to solve partial differential equations approximately. To apply the FDM, all derivatives in a differential equation are replaced by approximating difference quotients. Both FEM and FDM procedure reduce the ordinary and partial differential equation problems to the system of algebraic equations.

Course Credit: 4

Magnetic fields are of vital importance in astrophysics and geophysics, playing crucial roles in the dynamics of galaxies, stars (including star formation) and planets (including the Earth). Magneto-hydrodynamics (MHD) is concerned with understanding the nature of fluid flows in the presence of magnetic fields. It therefore combines electromagnetic theory with fluid dynamics. This course gives a basic introduction to MHD, detailing how magnetic fields can have significant effects on the nature of fluid flows (including the important topic of plasma confinement in fusion devices) and how fluid flows can self-consistently lead to the generation of magnetic fields via dynamo action (which is believed to be important for the maintenance of the magnetic field of both the Earth and Sun).

Course Credit: 4

This course is an introduction to the beautiful theory of Riemannian Geometry, a subject with no lack of interesting examples. The core of this course will be an introduction to Riemannian geometry - the study of Riemannian metrics on abstract manifolds. This is a classical subject, but is required knowledge for research in diverse areas of modern mathematics. We will try to present the material in order to prepare for the study of some of the other geometric structures one can put on manifolds. They are indeed the key to a good understanding of it and will therefore play a major role throughout the course.

Course Credit: 4

Derivative securities (such as options) depend on the values of primary securities (such as stock or bond prices). During the last thirty years trading in derivative securities have undergone a tremendous development and nowadays derivative securities are traded on markets all over the world in large numbers. The purpose of the course is to exhibit basic features of advanced financial derivatives, starting with basic model specifications, introducing the concept of arbitrage, and ending with a risk-neutral valuation formula and its analysis. The unit aims to provide a concise mathematical formulation of the main characteristics of financial instruments, with an emphasis on quantitative aspects of stock price, options, and other financial derivatives.

Course Credit: 4

The objective of this course is to develop an understanding of low-speed aerodynamics and an introduction to compressible flows. The course covers concepts in incompressible airfoil theory, including symmetric and cambered airfoils using the analytical approach. The course also covers incompressible lifting theory, including down wash, Kutta condition, application of fundamentals to the design of a wing to meet given performance criteria. The course also covers topics in compressible flow and shock wave including expansion waves, linear theory and linearized supersonic flow. Finally, the course covers several methods/models, Euler codes, CFD tools, credibility of CFD simulations, ground-based test programs, flight-test programs, integration of experimental and computational tools and the aerodynamics design philosophy. The objective of this course is to introduce students to the fundamentals, physical mechanisms, solution techniques, importance of incompressible and compressible flows and the design and operation of flow systems induced by flight vehicles or flying objects or submerged objects in the atmosphere.

Course Credit: 4

The Computational Fluid Dynamics (CFD) is an inherently interdisciplinary branch of science which has an extremely broad spectrum of applications. CFD become an essential tool in analysis and design of thermal and fluid flow systems in wide range of industries. Fluid dynamics uses numerical methods and algorithms to solve and analyze problems that involve fluid flows. Few prominent areas of applications of CFD include meteorology, transport systems (aerospace, automobile, high-speed trains), energy systems, environment, electronics, bio-medical (design of life-support and drug delivery systems), etc. There has been considerable growth in the development and application of CFD in all aspects of fluid dynamics. CFD has become a standard modeling tool widely utilized within industry. The correct use of CFD as a design analysis or diagnostic tool requires a thorough understanding of underlying physics, mathematical modeling and numerical techniques. This course aims to provide precisely these insights of CFD. Finite difference and finite volume methods will be discussed as different means of discretization of the fluid dynamics equations. A necessary theoretical background concerning accuracy, convergence, consistency, and stability of the numerical schemes will be provided.

Course Credit: 4

The objective of the program for the graduate is to become familiar with key atmospheric variables and structures, the types of weather data available, the manner by which these data are collected, and some of the ways (e.g. WRF-ARW and other numerical models) that these data are displayed, analyzed, and used in the forecasting system. Students can demonstrate the ability to produce forecasts of basic weather variables including high and low pressure, temperatures and precipitation that are related to tropical cyclones, tornadoes and thunderstorm and extreme temperature.

Course Credit: 4

Dynamical systems theory is the mathematical theory of time-varying systems and it is used in the modelling of a wide range of physical, biological, engineering, economic and other phenomena. This course presents a broad introduction to the area, with emphasis on those aspects important in the modelling and simulation of systems. General dynamical systems are described, along with the most basic sorts of behaviour that they can show. The dynamical systems most commonly encountered in applications are formed from sets of differential equations. The most regular kinds of behaviour-equilibrium and periodic---are the most easy to analyze theoretically; linearization about such trajectories are discussed, for periodic behaviour this is done using the Poincare’ Map. Much more complex behaviours, including chaos, may be found; these are described by means of their attractors. In applications it is often important to know how the observed behaviour changes with changes in the system parameters; such changes can often be sudden, but frequently conform to one of a relatively small number of scenarios: the study of these forms the subject of bifurcation theory. The simplest bifurcations are discussed. Many physical systems can become unstable in the sense that small disturbances superimposed on their basic state can amplify and significantly alter their initial state. In this course we introduce the basic theoretical and physical methodology required to understand and predict instability in a variety of situations with focus on hydrodynamic instabilities.

Course Credit: 4

Due to its inherent complexity and increasing industrial applications, Biofluid dynamics has evolved as an important research and teaching area and shows how to apply the principles towards solutions of transfer problems in the human body and medical devices. The objective of this course is to equip students with the fluid dynamics tools in order to design and perform research in physiological and biofluid mechanics. Review and understand emerging biomimetic approaches, emphasizing the quantitative understanding and fundamental engineering concepts.

Course Credit: 4

The flight and maneuvers of an aeroplane provide glorious examples of the principles of mechanics. However this course is about flying and is an attempt to explain the flight of an aeroplane in a simple and interesting way. The governing equations for aircraft flight stability and control are presented, and used to analyze the flight performance of aircraft in different situations. Analysis of a range of fundamental aerodynamic problems relevant to aircraft is covered using analytical and numerical techniques.

Course Credit: 4

The course is designed to understand and explore recent advancements of Fluid Mechanics in the urban environment. More than half of the world population live in cities and the built environment dominates day-to-day life of city dwellers. Thus it is important to understand how airflow can be estimated and by far be controlled for a better urban environment. 

Course Credit: 4