Curvature and torsion for spherical indicatrices. Involute and Evolute of a given curve, Bertrand curves. Surface: Curvilinear coordinates, parametric curves, Metric first fundamental form , geometrical interpretation of metric, relation between coefficients E, F, G.
Derivatives of surface normal M Weingarten equations , Third fundamental form, Principal sections, Principal sections, direction and curvature, first curvature, mean curvature, Gaussian curvature, normal curvature, lines of curvature, centre of curvature, Rodrigues's formula, condition for parametric curves to be line of curvature, Euler's Theorem, Elliptic, hyperbolic and parabolic points, Dupin Indicatrix. MAT Complex Analysis 3 credits Introduction to complex numbers and their properties, complex functions, limits and continuity of complex functions, Analytic functions, Cauchy Riemann equations, harmonic functions, Rational functions, Exponential functions, Trigonometric functions, Logarithmic functions, Hyperbolic functions.
Contour integration: Cauchy's Theorem, Simply and Multiply connected domain, Cauchy integral formula, Morera's theorem, Liouville's theorem. Convergent series of analytic functions, Laurent and Taylor series, Zeroes , Singularities and Poles, residues, Cauchy's Residue theorem and its applications, Conformal Mapping. Prerequisite: MAT MAT History of Mathematics 3 credits A Survey of the development of mathematics beginning with the history of numeration and continuing through the development of the calculus.
The study of selected topics from each field is extended to the 20th century. Biographical and historical aspects will be reinforced with studies of procedures and techniques of earlier mathematical cultures. MAT Operations Research I 3 credits Convex sets and related theorems, Introduction to linear programming, Formulation of linear programming problems, Graphical solutions, Simplex method, Duality of linear programming and related theorems, Sensitivity.
Unconstrained optimization: Newton's method, Trust region algorithms, Least Squares and zero finding. Linear programming: Simplex method, primal dual interior point methods. Connected set: Compact sets, locally compact sets and related theorems, connected sets, locally connected sets, continuity and compactness. Sequence in metric space: Convergent and Cauchy sequence, Completeness, Banach Fixed Point theorem with applications, sequence and series of functions, pointwise and uniform convergence, differentiation and integration of series.
Continuous function on metric space: Boundedness, Intermediate Value Theorem, uniform continuity. Dependence of solutions on initial conditions and equation parameters. Existence and uniqueness theorems for systems of equations and higher order equations. Eigen value problems and Strum-Liouville boundary value problems: Regular Strum-Liouville boundary value problems. Solution by eigenfunction expansion. Green's functions.
Singular Strum-Liouville boundary value problems. Oscillation and comparison theory. Nonlinear differential equations: Phase plane, paths and critical points. Critical points and paths of linear systems. PDE: First order equations: complete integral, General solution. Cauchy problems. Method of characteristics for linear and quasilinear equations.
Charpit's method for finding complete integrals. Methods for finding general solutions. Second order equations: Classifications, Reduction to canonical forms. Boundary value problems related to linear equations. Applications of Fourier methods Coordinates systems and separability. Homogeneous equations. Boundary value problems involving special functions. Transformation methods for boundary value problems, Applications of the Laplace transform.
Application of Fourier sine and cosine transforms. Statics of Particles: Review of vectors, vector addition of forces, resultant of several concurrent forces, resolution of forces into components, equilibrium of particles in a plane and in space. Rigid bodies: momentum of a force and a couple, Varignon's theorem, equivalent system of forces and vectors, reduction of system of forces. Equilibrium of rigid bodies: reactions at supports and connections of rigid bodies in two dimensions.
Centroid and center of gravity: CG of two and three dimensional bodies, centroids of areas, lines and volumes. Moment of inertia, moments and products of inertia, radius of gyration, parallel axis theorem, principal axis and principal moments of inertia.
Dynamics: Kinematics of particles: rectilinear and curvilinear motion of particles. Kinematics of particles: Newton's second law of motion, linear and angular momentum of a particle, conservation of energy and momentum, principle of work and energy and their applications, motion under a central force and conservative central force, impulsive motion. System of particles: Newton's law, effective forces, linear and angular momentum, conservation of momentum and energy, work energy principle.
Kinematics of rigid bodies: translation, rotation, and plane motion relative to rotating frame, Coriolis force. Plane motion of a rigid body: motion in two dimensions, Euler's equation of motion about a fixed point. MAT Graph Theory 3 credits Number System: Numbers with different bases, their conversion and arithmetic operations, normalized scientific notations.
Logic: Introduction to logic, logical operations, application of logic to sets. Mathematical Reasoning: Methods of proof, Mathematical induction, recurrence relations, generating functions. Boolean Algebra: Ordered sets, lattices, Boolean algebra and operations, Boolean expressions, logic gates, minimization of Boolean expressions, Karnaugh maps, Karnaugh map algorithm.
Graphs: introduction and definitions, representing graphs, graph isomorphism, connected graph, planar graph, path and circuit, shortest path algorithm, Eulerian path, Euler's theorem, Seven Bridges of Problem, graph coloring. Application of graph: tree, tree reversal, trees and sorting, spanning trees, minimum spanning trees: related algorithms.
Search trees: binary search tree, leaves on a rooted tree, spanning trees and the MST problems, network and flows, the max flow and the min-cut theorem. Binary trees. MAT Mathematical Methods 3 credits Series solution: singularity of a rational function, series solution of linear differential equations at nonsingular and regular singular points.
Fourier series: Introduction to orthogonal functions and Integral transform, Fourier integral, Fourier transform and their applications. Laplace transformation method: Definition, existence and properties of Laplace transform, Inverse Laplace transform, Transforms of discontinuous and periodic functions. Impulses and Dirac delta function. Solving initial value problems. Solving linear systems, Harmonic functions: Laplace equation in different coordinates and its applications.
Special functions: Legendre functions of first and second kinds, Hermite polynomials, generating function, Hypergeometric functions, Laguerre functions, Bessel function and their properties. Equation of motion: Equation of continuity; Euler's equation of motion, conservative forces, Bernoulli's equation; circulation and Kelvin's circulation theorem; vorticity, irrotational and rotational motion, velocity potential; energy equation, Kelvin's minimum energy theorem.
Two dimensional motion: vorticity, stream function and velocity potential function, streaming motion, complex potential and complex velocity, stagnation points, motion past a circular cylinder, circle theorem, motion past a cylinder, Joukowaski transformation, Blasius theorem; two dimensional source, sink and doublets, source and sink in a stream, the method of image.
Vortex motion: vortex line, tube and filament, rectilinear and circular vortices, kinetic energy of system of vortices, vortex sheet, Karman's vortex street. Open sets. Closed sets. Baire's theorem. Continuous mappings. Spaces of continuous functions. Euclidean and unitary spaces. Topological Spaces: Definition and some examples. Elementary concepts. Open bases and open subbases. Weak topologies. Function algebras. Compactness: Compact spaces. Product spaces.
Tychonoff's Theorem. Locally compact spaces. Compactness for metric spaces. Separation: T1-spaces and Hausdorff spaces. Completely regular spaces and normal spaces. Urysohn's lemma. Connectedness: Connected spaces.
Locally connected spaces. Pathwise connectedness. Banach Spaces: Definition and some examples. Continuous linear transformations. Hahn-Banach theorem. Natural embedding. Open mapping theorem. Conjugate of an operator. Hilbert Spaces: Definition and some simple properties. Orthogonal complements.
Orthogonal sets. Conjugate spaces. Adjoint and self-adjoint operators. Fixed point theory: Banach contraction principle. Schauder Principle. Galerkin's weighted residual method for one-dimensional BVP, the modified Galerkin's technique. Shape functions for one-dimensional elements. Division of a region into elements, linear and quadratic elements, numerical integration over elements.
Finite element solution of one dimensional BVPs. Finite Element approximations of line and double integrals: line integral using quadratic elements, double integrals using triangular and quadrilateral elements, double integrals using curved elements. Three-nodded triangular elements. Variational formulation of BVP: construction of variational functions, the Ritz method and finite elements, matrix formulation of the Ritz procedure, solution of two-dimensional problems.
Pre-processing and solution assembly: mesh generation in one and two dimensions, techniques of assembly and solutions. MAT Tensor Calculus 3 credits Tensor: Coordinates, Vectors and tensors: Curvilinear coordinates, Kronecker delta, summation convention, space of N dimensions, Euclidean and Riemannian space, coordinate transformation, Contravariant and covariant vectors, the tensor concept, symmetric and skewsymmetric tensor.
Riemannian metric and metric tensors: Basis and reciprocal basis vectors, Euclidean metric in three dimensions, reciprocal or conjugate tensors, Conjugate metric tensor, associated vectors and tensor's length and angle between two vector's, The Christoffel symbols. Covariant Differentiation of Tensors and applications: Covariant derivatives and its higher rank tensor and covariant curvature tensor. Stress and rate of strain, General stress state of deformable bodies, General state of deformation of flowing fluid, Relation between stress and rate of deformation in general orthogonal coordinates.
Equations of motion: Thermodynamic equation of state, Equation of continuity, Navier-Stokes equations, Energy equation, Equations of motion in different coordinate system. Exact solution of Navier-Stokes equations, Steady plane flow, Couette-Poiseuille flow, Plane stagnation-point flow, flow past parabolic body and circular cylinder, Steady axisymmetric flow, Circular pipe flow Hagen-Poiseuille flow , Flow between two concentric rotating cylinders, Flow at a rotating disc, Unsteady plane flow, First Stokes problem, Second Stokes problem, Startup of Couette flow, Unsteady plane stagnation-point flow.
Similarity analysis: Reynolds law of similarity, Dimensional analysis and theorem, Important non-dimensional quantities. Very slow motion: Equations of slow motion, Motion of a sphere in a viscous fluid, Theory of lubrication. Laminar boundary layer: Introduction to boundary layer, boundary layer equations in two dimensions, Dimensional representation of boundary layer equations, Displacement thickness, Friction drag, Flat plate boundary layer, Momentum thickness, Energy thickness, Similar solutions of boundary layer equations: Derivation of ODE, Wedge flow, Flow in a convergent channel, Integral relations of the boundary layer: Momentum-Integral equation, Energy-Integral equation.
Euclidean algorithm. Continued fractions. Chinese Remainder Theorem. Linear Diophantine equations. Arithmetical functions. Dirichlet convolution. Multiplicative function. Representation by sum of two and four squares. Arithmetic of quadratic fields. Euclidean quadratic Fields. Discrete population models for single species: Simple models, Cobwebbing, Discrete logistic models, Stability, Periodic fluctuations and Bifurcations, Discrete Delay models, Continuous models for interacting populations: Predator-prey models, Lotka-Volterra systems, Complexity and stability, Periodic behaviour, Competition Models, Mutualism.
Discrete growth models for interacting populations: Predator-prey models. Epidemic models and dynamics of infectious diseases: Simple epidemic models and practical applications. Modelling in Economics Theory of the household: Preference and indifference relations, Utility function, Order conditions of optimization, Stutsky equation, Demand functions, Revealed Preference hypothesis, Von Neumann-Morgenstern utility.
Theory of the firm: Production function, Laws of production and scale, Optimizing behaviour, Cost curves and cost functions, Constrained output maximization. Theory of factor demand: Optimal input mix, Factor demand and supply curves, Elasticity of derived demand. Market structures and equilibrium: Market Economy and equilibrium, Stability of equilibrium, Dynamic stability.
Prerequisite: MAT Network models: shortest route problems, minimal spanning, maximal-flow problem. Sequencing problem: Minimax-maximin strategies, mixed strategies, expected pay-off, solution of and games, games by linear programming and Brown's algorithm. Dynamic programming: Investment problem, Production Scheduling problem, Stagecoach problem, Equipment replacement problem.
Non-linear programming: Introduction, unconstrained problem, Lagrange method for equality constraint problem, Kuhn-Tucker method for inequality constraint problem. Quadratic programming. Approximation theory: discrete least square applications, Chebyshev polynomial applications, rational function approximation, trigonometric polynomial approximation, Fast Fourier Transform.
Approximating Eigenvalues: Honseholder's method, QR algorithm. BVP involving ODE: shooting method for linear and nonlinear problems, finite difference method for linear and nonlinear problems. PDE: Finite difference methods for elliptic, parabolic and hyperbolic problems. The topics covered in any particular semester depend on the interest of the students and instructor. Emphasis is on basic ideas and on applications in physics, economics, engineering.
Notes attached to the course in a particular semester will describe the actual contents. PHY Introduction to Physics 3 Credits Vectors and scalars, Newton's Laws of motion, inertia, force, momentum, conservation of linear momentum, work, energy, conservation of energy, power, gravitation, escape velocity, projectile motion, simple harmonic motion, uniform circular motion.
Structural properties of matter, elasticity, Hooke's Law, viscosity, surface tension. Heat and temperature, different scales of temperature, thermal expansion, specific heat, gas laws, heat transfer. Reflection and refraction of light, mirrors and lenses, total internal reflection, interference, diffraction.
Coulomb's Law, ohm's law; resistance, potential difference, capacitance. Magnetic force on a moving charge, electromagnetic spectrum, velocity of light. PHY Fundamentals of Physics 2 Credits Vectors and scalars, Newton's Laws of motion, principles of conservation of linear momentum and energy, gravitation, projectile motion, simple harmonic motion, rotation of rigid bodies. Elasticity, Hooke's Law, viscosity, Stokes' Law , surface tension.
Huygens' principle, electromagnetic waves, reflection, refraction, interference, diffraction. Properties of Matter: Hooke's Law, elastic modulii, adhesive and cohesive forces, molecular theory of surface tension, capillarity, variation of surface tension with temperature. PHY Principles of Physics I 3 Credits Vectors and scalars, unit vector, scalar and vector products, static equilibrium, Newton's Laws of motion, principles of conservation of linear momentum and energy, friction, elastic and inelastic collisions, projectile motion, uniform circular motion, centripetal force, simple harmonic motion, rotation of rigid bodies, angular momentum, torque, moment of inertia and examples, Newton's Law of gravitation, gravitational field, potential and potential energy.
Structure of matter, stresses and strains, Modulii of elasticity Poisson's ratio, relations between elastic constants, work done in deforming a body, bending of beams, fluid motion and viscosity, Bernoulli's Theorem, Stokes' Law, surface tension and surface energy, pressure across a liquid surface, capillarity.
Temperature and Zeroth Law of thermodynamics, temperature scales, isotherms, heat capacity and specific heat, Newton's Law of cooling, thermal expansion, First Law of thermodynamics, change of state, Second Law of thermodynamics, Carnot cycle, efficiency, kinetic theory of gases, heat transfer. Huygens' principle, electromagnetic waves, velocity of light, reflection, refraction, lenses, interference, diffraction, polarization. Magnetic field, Biot-Savart Law, Ampere's Law, electromagnetic induction, Faraday's Law, Lenz's Law, self inductance and mutual inductance, alternating current, magnetic properties of matter, diamagnetism, paramagnetism and ferromagnetism.
Maxwell's equations of electromagnetic waves, transmission along wave- guides. Special theory of relativity, length contraction and time dilation, mass-energy relation. Quantum theory, Photoelectric effect, x-rays, Compton effect, dual nature of matter and radiation, Heisenberg uncertainty principle. Atomic model, Bohr's postulates, electron orbits and electron energy, Rutherford nuclear model, isotopes, isobars and isotones, radioactive decay, half-life, alpha, beta and gamma rays, nuclear binding energy, fission and fusion.
Fundamentals of solid state physics, lasers, holography. Gauss's Law, electric dipole, dielectrics, capacitance, energy of charged systems, electrical images, magnetic dipole, energy in a magnetic field. Special Theory of Relativity: Galilean relativity, Michelson-Morley experiment, postulates of special theory of relativity, Lorentz transformation, length contraction, time dilation, twin paradox, variation of mass, relativistic kinematics, mass energy relation.
PHY Classical Electrodynamics 3 Credits Solution of Laplace's equation and Poisson's equation and applications to electrostatic problems, dielectrics, electrostatic energy, Maxwell's equations, electromagnetic waves, propagation of electromagnetic waves in conducting and non-conducting media, reflection and refraction, polarization, dispersion, scattering, waves in the presence of metallic boundaries, waveguides and resonators, solution of the inhomogeneous wave equations, simple radiating system, antennas, accelerated charge, Cerenkov radiation, elements of plasma physics.
PHY Fluid Mechanics 3 Credits Fluid properties, fluid statics, manometry, force on submerged planes and curved surface, buoyancy and floatation, one dimensional flow of fluid, equation of continuity, Euler's equation, flow of fluid in pipes, Bernoulli's equation, flow through orifice, mouthpiece, venturimeter, fundamental relations of compressible flow, frictional losses in pipes and fittings, types of fluid machinery, impulse and reaction turbines, centrifugal and axial flow pumps, deep well turbine pumps, specific speed, unit power, unit speed, unit discharge, performance and characteristics of turbines and pumps, design of pumps, reciprocating pumps.
Prerequisite PHY PHY Quantum Mechanics I 3 Credits Breakdown of classical physics, quantum nature of radiation, Planck's Law, photoelectric effect, Einstein's photon concept and explanation of photoelectric effect, de Broglie wave, wave particle duality, electron diffraction, Davisson-Germer experiment, emergence of quantum mechanics, Schrodinger equation, basic postulates of quantum mechanics, physical interpretation of wave function, wave packets, Heisenberg's uncertainty principle, linear operators, Hermitian operators, eigenvalue equation, one-dimensional potential problem, harmonic oscillator, orbital angular momentum, rotation operator, spherical harmonics, spin angular momentum, addition of angular momenta, solution of the Schrodinger equation for hydrogen atom, matrix formulation of quantum mechanics.
PHY Quantum Mechanics II 3 Credits Rutherford scattering experiment, Discovery of the nucleus, Bohr quantization rules, hydrogen atom spectra, Franck-Hertz experiment, Sommerfeld-Wilson quantization rules, electron spin, Stern — Gerlach experiment, Pauli exclusion principle, electronic configuration of atoms, vector atom model, coupling schemes, Hund's rule, multiplet structure, fine structure in hydrogen spectral lines, Zeeman effect, Paschen-Beck effect, production of X-rays, measurement of X-ray wavelength, X-ray scattering, Compton Effect, Mosely's Law, molecular spectra, rotational and vibrational levels, Raman Effect and its applications, lasers.
PHY Quantum Mechanics III 3 Credits Basic properties of nuclei, constituents of nuclei, nuclear mass, charge, size and density, nuclear force, spin, angular momentum, electric and magnetic moments, binding energy, separation energy, semi-empirical mass formula, radioactive decay law, transformation laws of successive changes, measurement of decay constant, artificial radioactivity, radioisotopes, theory of alpha decay, gamma radiation, energy measurement, pair spectrometer, classical treatment of gamma emission, internal conversion, Mossbauer Effect, beta decay, energy measurement, conservation of energy and momentum in beta decay, neutrino hypothesis, orbital electron capture, positron emission, interaction of radiation in matter, ionisation, multiple scattering, range determination, bremsstrahlung, pair production, annihilation.
Discovery of neutrons, production and properties of neutrons, nuclear reactions, elastic and inelastic scattering, Q-value of a reaction and its measurements, nuclear cross-section, compound nucleus theory, direct reaction and kinematics. Rotary pump, diffusion pump, ion pump and turbo pump, pirani, penning and ionisation gauges, measurement of current and voltages, potentiometer, VTVM, oscilloscope, D.
Prerequisite PHY PHY X-Rays 3 Credits Continuous and Characteristic X-rays, Bremsstrahlung, Properties of X-rays, X-ray technique, Weissenberg and precession methods, identification of crystal structure from powder photograph and diffraction traces, Laue photograph for single crystal, geometrical and physical factors affecting X-ray intensities, analysis of amorphous solids and fibre textured crystal. Prerequisite PHY PHY Nuclear Physics II 3 Credits Determination of nuclear size by scattering methods and electromagnetic methods, mirror nuclei, electron scattering, nuclear shapes, electric and magnetic multiple moments, isotopic spin formalism, two-nucleon problem, nuclear forces, exchange force, meson theory of nuclear forces.
Prerequisite PHY PHY Physics for Development 3 Credits Twenty first century development issues, physics and break through technologies, ICT, fibre optics, quantum information theory, physics in genetics engineering and molecular biology, physics and health issues, bio and medical physics, materials science and physics, high temperature superconducting materials, space physics, microgravity experiments, econo-physics, physics principles applied in sociology.
PHY Particle and Reactor Physics 3 Credits Interactions of neutrons with matter, cross — sections for neutron reactions, thermal neutron cross-sections, nuclear fission, energy release in fission, neutron multiplication, nuclear chain reaction, steady state reactor theory, criticality condition, homogeneous and heterogeneous reactor systems, neutron moderation, neutron diffusion, control of nuclear reactions, coolant, types of nuclear reactors: power reactor, research reactor, fast reactor, breeder reactor, reactor shielding, waste disposal.
Prerequisite PHY PHY Atmospheric Physics 3 Credits Structure of the atmosphere, elementary ideas about the sun and the laws of radiation, definitions and units of solar radiation, depletion of solar radiation in the atmosphere, terrestrial radiation, radiation transfer, heat balance in the atmosphere, heat budget, vertical temperature profile, radiation charts and their uses, composition of the atmosphere, mean molecular weight, humidity, mixing ratio, density and saturation vapour pressure.
Fundamental equations of atmospheric motion, approximations of the equation, circulation and vorticity and their equations. Introduction to atmospheric thermodynamics. Introduction to astrophysics, formation of stars and galaxies, evolution of stars, the notion of cosmology, Cosmological Principle, various cosmological models of the universe, expansion of universe, Hubble's Law, problem of singularity in time, solutions of Friedmann, de Sitter and others, density of matter in the universe, cosmological term, self screening effect for matter.
Introduction to transistor level design of CMOS digital circuits. Laplace transforms: definition, Laplace transformations of some elementary functions, inverse Laplace transformations, Laplace transformations of derivatives, Dirac delta function, some special theorem on Laplace transformations, solution of differential equations by Laplace transformations, evaluation of improper integrals; finite Fourier series, Fourier transforms, Fourier integrals, Fourier transform and application to solution BVP, beta and gamma functions, Legendre functions, Bessel functions, solution of boundary value problem by method of separation of variables, solution PDE of mathematical physics: Helmholtz equation, wave equation: vibrating string, vibrating membrane, diffusion equation, Laplace equation, Hermite polynomials, Laguerre polynomials, hyper-geometric functions.
PHY Mathematical Modelling in Physics 3 Credits Basic concept of mathematical modelling, formulation and solution, overview of computational methods of classical and quantum physics, numerical procedure for special functions, Random numbers generator, Brownian motion simulation, linear system of equations, sparse linear system, eigen value problems, BVP involving ODE, Sturm-Liouville problems, BVP involving PDE: elliptic, parabolic and hyperbolic problems using finite difference and other methods, Monte Carlo integration and simulation, mathematical modelling of problems of physics using above techniques.
Prerequisite MAT PHY Advanced Quantum Mechanics 3 Credits Heisenberg and Dirac or interaction pictures, time-independent perturbation theory, degenerate perturbation theory, variation method, hydrogen atom and helium atom, WB approximation method, Sommerfeld-Wilson quantisation condition, time-dependent perturbation theory, Fermi's golden rule, applications, identical particles, parity, Pauli principle, applications, non- relativistic scattering theory, partial wave expansion, optical theorem, S matrix, solution of the wave equation by the method of Green's function, Lippmann Schwinger equation, Neumann series, Born approximation, applications, Klein-Gordon and Dirac equations, existence of electron spin, magnetic moment, plane wave solution of the Dirac equation, hole theory; prediction of the positron.
Prerequisite PHY PHY Physics of Radiology 3 Credits The production and properties of X-rays, diagnostic and therapeutic X-ray tubes, X-ray circuit with rectification, electron interaction, characteristic radiation, bremsstrahlung, angular distribution of X-rays, quality of X-rays, beam restricting devices, the grid, radiographic film, radiographic quality, factors affecting the image, image modification, image intensification, contrast media, modulation transfer function, exposure in diagnostic radiology, fluoroscopy, computed tomography, ultrasound, magnetic resonance imaging MRI.
Prerequisite PHY PHY Geophysics 3 Credits Solar system, the planets, meteorites, cosmic ray exposures of meteorites, Poynting-Robertson effect, compositions of the terrestrial planet, pre-radioactivity age problem, radioactive elements and the principle of radiometric dating, growth of constituents and of atmospheric argon, age of the earth and of meteorites, dating the nuclear synthesis, figure of the earth, precession of the equinoxes, the Chandler- wobble, tidal friction and the history of the earth moon system, fluctuation in rotation and excitation of the wobble, seismology of the earth, elastic wave and seismic rays, travel time and velocity depth curves for body waves, shockwave, internal pressure of earth core, internal density and composition, free oscillation, earthquake prediction problem, terrestrial magnetism, earth magnetic field, geophysical prospecting; seismic, gravitational, magnetic, electrical and nuclear methods.
Prerequisite PHY PHY General Theory of Relativity 3 Credits Gravitation, Lagrangian Einstein equations, approximation of weak field and Hilbert's auxiliary conditions, comparison of corresponding relations with those of Newton's theory of gravitation, source of gravitation field, Schwarzschild's solution in isotropic and other coordinate systems, analogy between gravitation and electromagnetism, motion of test mass and geodetic lines, motion in Schwarszchild's field, equations of motion in general relativistic mechanics as a consequence of Einstein's equation of gravitational field, gravitational waves in weak field approximation, problem of energy transfer, exact wave solutions in the case of gravitational field, waves of matrices or wave of curvature, locally plane gravitational waves, Weber's and Braginski's experiments, prospects of future gravitational experiments.
PHY Field Theory 3 Credits Equation of motion, quantization, conservation laws, construction of Hilbert space, Lagrangian, equation of motion, quantization of neutral and charged Klein-Gordon fields, Dirac equation, spinors, quantization of Dirac field, Maxwell fields, Gupta-Bleuler formalism, theory of gauge fields, invariant functions propagators for Klein-Gordon field, Dirac fields and electromagnetic fields, symmetries of interactions, interaction picture; U and S matrices, Feynman diagrams, Wick's theorem, Feynman rules, lowest order, amplitude and cross section for Compton scattering, GSW model of electroweak interactions, elements of QCD, path integral in field theory, introduction to string theory.
PHY Neutron Scattering 3 Credits Neutron sources, continuous and pulsed sources, monochromatization, collimation and moderation of neutrons, neutron detectors, scattering of neutrons and its advantages, elastic scattering of neutrons, magnetic scattering and determination of magnetic structure, inelastic scattering, thermal vibration of crystal lattices, lattice dynamics and phonons, neutron polarization, polarized neutron applications, scattering by liquids and molecules, Van Hove correlation formalism, some experimental results of scattering by liquids and molecules, small angle neutron scattering and its applications in the study of biological molecules and defects, experimental techniques of scattering measurements, time-of-flight method, crystal diffraction techniques, neutron diffractometer and triple-axis spectrometer, constant Q-method.
Prerequisite PHY PHY Radiation Biophysics 3 Credits Nucleus, ionizing radiations, radiation doses, interaction of radiation with matter, cell structure, radiation effects on independent cell systems, oxygen effect, hyperthermia, LET and RBE, lethal, potentially lethal and sub-lethal radiation damage, dose-rate effect, acute effects of radiation, somatic effects, late effects, non-specific life shortening and carcinogenesis, genetic changes, nominal standard dose NSD , time dose fractionation TDF , Standquist curve.
This course provides the students with an understanding of the fundamental concepts of computer networking. Important concepts related to layered architecture, wired and wireless local area networks, wide area networks, packet switching and routing, transport protocol, flow control, and congestion control are covered in this course. This course will introduce the basic concepts in database systems and architectures, including data models, database design, and database implementation.
It emphasis on topics in ER model and relational databases, including relational data model, SQL, functional dependency and normalization, database design process. The course introduces techniques for modelling and optimizing real-world problems using mathematics, statistics, and computers. Topics may include linear programming, integer linear programming, non-linear programming, dynamic programming, game theory and queuing theory.
The primary emphasis will be on Linear programming: the simplex method and its linear algebra foundations, duality, post-optimality, and sensitivity analysis; the transportation problem; the critical path method; non-linear programming methods. The main topics include Modeling of electrical, mechanical, and electromechanical systems as differential equations, transfer functions, and state-space; Block diagram reduction and Signal Flow Graph representation of LTI control systems; Analysis of stability of open-loop and closed-loop systems; Time and Frequency domain Analysis of LTI systems; Design of controllers for enhancing the performance of LTI control systems.
To train the students in working places to master the essential skills in computer engineering through daily work activities. CAD tools for schematic, layout, functionality, timing analysis, synthesis, and performance. The graduation project aka Capstone Design Project challenges students to go beyond the learning that occurs as a result of their prescribed educational program, by developing design projects that demonstrate their intellectual, technical and creative abilities.
The teams demonstrate their ability to analyze, design, implement solutions, and communicate significant knowledge and comprehension. After achieving the graduation project 1 goals, students submit a comprehensive report and make a presentation to the examination committee.
This course describes how to evaluate alternatives to choose the most viable option based on engineering economic criteria. Topics include: decision making, cost types and estimates, time value of money, interest rate calculations, economic equivalence, comparison of alternative investments, evaluating economic life and replacement alternatives, inflation, depreciation, development of business case analyses for new product development projects, concept of time value of money in Islamic economy, Islamic investment tools like, Musharaka, Mudaraba, Sukuk, Murabaha.
The course intends to cover the computer crime viruses, worms, Trojan horses, hacking and the ways to implementing computer ethics computer professionals and social responsibility. Also, the software copyright, piracy, privacy, security, and civil liberties and some selected topics such: Philosophical Foundations of Ethics, Ethics, Ethical Dissent and Whistle-blowing. Monopolies and their Economic, Social and Ethical Implications. This course provides a general overview of the social and ethical issues in computing.
Students will learn about the impacts on and implications of the development, management and use of technology in various aspects. Emphasis is given to the issues which are relevant to the field of Information Systems. This course will introduce the different aspects of software development for reliable systems. Study the software development process models, project management techniques, modeling notations, requirement analysis, architecture design methods, and testing techniques.
During the second semester and after implementing, testing, and evaluating the proposed solution, students submit a final report, a poster, and prepare a PowerPoint presentation for the examination committee. In both projects the students are expected to show their abilities on designing, developing, orally presenting and documenting a project, just like they will need to in their professional lives.
That is to say, the students are expected to display their social and communication skills as well as their technical abilities. This course provides in depth coverage of some basic topics in computer networks related to network layer, link layer, and physical layer.
Topic include, routing protocols, medium access control of existing and emerging wired and wireless networks, and physical technology and standards. This course offers an introduction to the theory of multidimensional signal processing and digital image processing.
Topics include; human visual system, image acquisition and display, image sampling and quantization, color representations, image filtering, image transforms; FFT and DCT, image enhancement, morphological image processing, image restoration, image denoising, image segmentation, and image compression.
This course covers emerging and advanced topics in computer engineering. The contents will vary depending on the topic. Parallel Computing is a study of the hardware and software issues in parallel computing.
Topics include an introduction to the basic concepts, parallel architectures and network topologies, parallel algorithms, parallel metrics, parallel languages, granularity, applications, parallel programming design and debugging. Students will become familiar with various types of parallel architectures and programming environments. This course covers basic concepts of dependable computing. Reliability of non-redundant and redundant systems.
Dealing with circuit-level defects. Logic-level fault testing and tolerance. Error detection and correction. Diagnosis and reconfiguration for system-level malfunctions. Degradation management. Failure modeling and risk assessment. Use of JAVA to develop stand-alone and network applications.
This course introduces fundamental concepts of wireless networks. It covers the following topics: wireless networking challenges, wireless communication overview, signal propagation characteristics of wireless channels, wireless MAC concepts, overview of cellular standards LTE and WiMAX , overview of wireless MAC protocols including Making wireless work in today's Internet: supporting mobility, TCP over wireless, mobility, security, etc. Review of selected advanced topics, e.
This course covers the mobility issues of wireless networks. Cellular networks, ad hoc networks; access protocols; radio and network resource management; quality of service; mobility and location management; routing; mobile-IP; current wireless technologies for personal, local and satellite networks will be covered in the course. Physics of optical components: nature of light, optical material, propagation, diffraction, polarization. Optical fiber transmission medium: fiber modes, signal degradation, attenuation, dispersion.
Optical components: filters, directional couplers, power attenuators, beam splitters, multiplexers, demultiplexers, cross connects, modulators, amplifiers. This course provides students with the most common cryptographic algorithms and protocols and how to use cryptographic algorithms and protocols to secure distributed applications and computer networks Need for computer system security, Security attacks and threats, Security service, Conventional cryptography: concepts and methods, Conventional cryptography algorithms: DES, AES, etc.
This course covers emerging and advanced topics in computer networks. This course provides a broad introduction to machine learning topics. These include: i Data preprocessing acquiring datasets, identifying and handling missing values, encoding data. The course will also draw from many case studies and applications so that students will learn about not only the theoretical foundations of learning, but also gain the practical skills needed to apply these techniques to new problems.
This course focuses on the techniques used for analysis and design of the digital control systems. It identifies different aspects of digital control systems. The course covers: Z-transform and its inverse to represent and analyze discrete-time systems, pulse transfer function, block diagram, signal flow graph, state space, bilinear transformation, stability analysis, transient response and steady state errors, design of digital controllers, and evaluation of systems performance.
The purpose of this course is to introduce the basics of modeling, design, planning, and control of robot systems. In essence, the material treated in this course is a brief survey of relevant results from geometry, kinematics, statics, dynamics, navigation and control. The course will use the LEGO robot kits to cover and illustrate the historical development of robotics as a field, the importance of integrating sensors, effectors and control, basic control, the key approaches to mobile robot control.
In this course, basic concepts will be discussed, including coordinate transformations, sensors, path planning, kinematics, feedback and feedforward control, stressing the importance of integrating sensors, motors and control. We will get hands on experience of NXC programming language to program the Mindstorm robot in order to perform required tasks. This course covers emerging and advanced topics in signal processing.
Introduce the concepts and motivations of distributed systems, types of distributed systems, distributed system architectures, concept of process, communications and synchronization, distributed concurrency control, and distributed algorithms. This course introduces the basic concepts of computer vision, its applications, and techniques.
Topics treated in the course include low level image processing, segmentation, boundary detection, fitting, stereo correspondence, 3-D reconstruction, recognition and detection. Student E-mail. Reset your email password.
Code Course Name Fundamental of Mathematics Credit Hours 3 Prerequisite -- Course Description The course presents fundamental concepts and reasoning, distilled from mathematics science and other computational sciences, for types of proofs, Induction, number theory, Relations, Sums, Approximations, and Asymptotic, counting and functions.
Code Course Name Scientific Computing Credit Hours 2 Prerequisite -- Course Description The course introduces the practical aspects of scientific computing where students will be exposed to fundamental coding elements and concepts to solve a wide range of computing and engineering problems. Code Course Name Discrete Structures Credit Hours 3 Prerequisite -- Course Description Introduce propositional logic, predicates, quantifiers; sets, functions, sequences; proof strategy, induction, recursion; relations, equivalence relations, partial orders; basic counting techniques.
Code Course Name Computer programming 1 Credit Hours 3 Prerequisite -- Introduce the fundamental concepts of programming and problem-solving techniques. Code Course Name Calculus 1 Credit Hours 3 Prerequisite -- Course Description This course teaches the concepts and techniques of limits, differentiation and integration and their application to problems in science and engineering.
Code Course Name Calculus 2 Credit Hours 3 Prerequisite Course Description This course reinforces and extends the concepts and techniques of limits, differentiation and integration of functions taught in Calculus I, and introduces the concept of sequences and series and their application to problems in science and engineering.
Code Course Name Digital Logic Design Credit Hours 4 Prerequisite Course Description This course covers many basic topics such as numbering systems, Boolean algebra, simplification using Boolean algebra and Karnaugh maps, and different logic gates. Code Course Name Data Structures Credit Hours 3 Prerequisite Course Description Introduces students to development, implementation, and analysis of efficient data structures and algorithms.
Code Course Name Calculus 3 Credit Hours 3 Prerequisite Course Description This course covers the calculus of several variables and is the third calculus course in a three-course sequence. Code Course Name Computer Architecture Credit Hours 3 Prerequisite Course Description This course will provide the student with an in-depth study of the organization of the central processing unit, arithmetic logic unit, control unit, instruction set design, and addressing modes of digital computers.
Code Course Name Differential Equations Credit Hours 3 Prerequisite Course Description This course covers linear equations of the first order, linear equations with constant coefficients, the general linear equation, variation of parameters, undetermined coefficients, linear independence, the Wronskian, exact equations, separation of variables, and applications, systems of linear differential equations, solution of Laplace transforms, existence, and uniqueness of solutions.
Code Course Name Linear Algebra Credit Hours 3 Prerequisite -- Course Description This course is an introduction to Linear Algebra during a study of linear systems of equations and its solutions methods, and a study of Matrices, determinants, operations on matrices and Eigenvalues and Eigenvectors. Code Course Name Probability and Statistics Credit Hours 3 Prerequisite Course Description Statistical methods and the application of probability theory are essential to the understanding of data and underlying processes in many fields of sciences and engineering.
Code Course Name Electric Circuits Credit Hours 4 Prerequisite , Course Description Units and dimensions, Electric circuit elements and variables, energy stored, and power dissipated in circuit elements.
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The calculation hinges around the fact that the voltage at both inputs is the same. This arises from the fact that the gain of the amplifier is exceedingly high. If the output of the circuit remains within the supply rails of the amplifier, then the output voltage divided by the gain means that there is virtually no difference between the two inputs. As the input to the op-amp draws no current this means that the current flowing in the resistors R1 and R2 is the same.
The voltage at the inverting input is formed from a potential divider consisting of R1 and R2, and as the voltage at both inputs is the same, the voltage at the inverting input must be the same as that at the non-inverting input. Hence the voltage gain of the circuit Av can be taken as:. As an example, an amplifier requiring a gain of eleven could be built by making R2 47 k ohms and R1 4. For most circuit applications any loading effect of the circuit on previous stages can be completely ignored as it is so high, unless they are exceedingly sensitive.
This is a significant difference to the inverting configuration of an operational amplifier circuit which provided only a relatively low impedance dependent upon the value of the input resistor. In most cases it is possible to DC couple the circuit. Where AC coupling is required it is necessary to ensure that the non-inverting has a DC path to earth for the very small input current that is needed to bias the input devices within the IC.
This can be achieved by inserting a high value resistor, R3 in the diagram, to ground as shown below. If this resistor is not inserted the output of the operational amplifier will be driven into one of the voltage rails. The cut off point occurs at a frequency where the capacitive reactance is equal to the resistance.
Similarly the output capacitor should be chosen so that it is able to pass the lowest frequencies needed for the system. In this case the output impedance of the op amp will be low and therefore the largest impedance is likely to be that of the following stage. Operational amplifier circuits are normally designed to operate from dual supplies, e. This is not always easy to achieve and therefore it is often convenient to use a single ended or single supply version of the electronic circuit design.
So the voltage at the two terminals is equivalent to each other. In this amplifier, the reference voltage can be given to the inverting terminal. In this amplifier, the reference voltage can be given to the non-inverting terminal. What is the function of the inverting amplifier? This amplifier is used to satisfy barkhausen criteria within oscillator circuits to generate sustained oscillations.
What is the function of the non-inverting amplifier? Which feedback is used in the inverting amplifier? What is the voltage gain of an inverting amplifier? What is the voltage gain of the Non-inverting Amplifier? What is the effect of negative feedback on the non-inverting amplifier? Thus, this is all about the difference between the inverting and non-inverting amplifiers. In most cases, an inverting amplifier is most commonly used due to its features like low impedance, less gain, etc.
It provides signal phase shifts for signal analysis within communication circuits. It is in the implementation of filter circuits like Chebyshev, Butterworth, etc. Difference between Inverting and Non-inverting Amplifier.
This set of Electric Circuits Multiple Choice Questions & Answers (MCQs) focuses on “The Inverting and Non-Inverting Amplifier Circuit”. This set of Linear Integrated Circuit Problems focuses on “Summing, Scaling & Averaging Amplifier – 2”. 1. Which type of amplifier has output voltage equal. Just invest little times to admittance this on-line broadcast Non Solve "Microorganisms and Applications in Biotechnology MCQ" PDF book.