# Course Details

The contents of the undergraduate courses offered by the **MNS Department** for its BS programme in Physics and also for other departments of BRACU are given in the following:

**BI0 101: Introduction to Biology**

An introduction to the cellular aspects of modern biology including the chemical basis of life, cell theory, energetics, genetics, development, physiology, behaviour, homeostasis and diversity, and evolution and ecology. This course will explain the development of cell structure and function as a consequence of evolutionary process, and stress the dynamic property of living systems.3 credits **CHE 101: Introduction to Chemistry**

The course is designed to give an understanding of basics in chemistry. Topics include nature of atoms and molecules; valence and periodic tables, chemical bonds, aliphatic and aromatic hydrocarbons, optical isomerism, chemical reactions.3 credits **ENV 101: Introduction to Environmental Sciences**

Fundamental concepts and scope of environmental science, Earth's atmosphere, hydrosphere, lithosphere and biosphere, men and nature, technology and population, ecological concepts and ecosystems, environmental quality and management, agriculture, water resources, fisheries, forestry and wildlife, energy and mineral energy sources; renewable and non renewable resources, environmental degradation; pollution and waste management, environmental impact analysis, remote sensing & environmental monitoring. 3 credits **GEO 101: Introduction to Economic Geography**

Introduction: The field and environment of economic Geography; Bases of Economic Geography: Relief, Climate, Vegetation, Soils and Population; Extractive resources and human-environment relations; Primary Activities: types and brief descriptions; Secondary Activities: types and factors of localization, Stages in growth; Tertiary Activities: Trade, Transportation, Utilities, Technical and Professional services; Regional Economy: classification, Growth and Development; Economic Geography of Bangladesh: A brief account.3 credits**MAT 091: Basic Course in Mathematics**

Topics including sets, relations and functions, real and complex numbers system, exponents and radicals, algebraic expressions; quadratic and cubic equations, systems of linear equations, matrices and determinants with simple applications; binomial theorem, sequences, summation of series (arithmetic and geometric), permutations and combinations, elementary trigonometry; trigonometric, exponential and logarithmic functions; co-ordinate geometry; statics-composition and resolution of forces, equilibrium of concurrent forces; dynamics-speed and velocity, acceleration, equations of motion. No credit.**MAT 101: Fundamentals of Mathematics**

The real number system, exponents, polynomial, factoring, rational expression, radicals, complex

number, linear equation, quadratic equation, variation, inequalities, coordinate system, functions, equations of line, equation of circle, exponential and logarithmic function, system of equations, system of inequalities, properties of matrix, matrix solution of linear system, determinant, Cramer's rule, limit, rate of change, derivative. 3 credits**MAT 102: Introduction to Mathematics**

Factorisation, Synthetic Division, Zeros (Roots) of Polynomials, Relation between Roots and Coefficients, Nature of Roots (Descarte's Rule of signs); Complex Number System, Graphical representation of Complex Numbers (Argand Diagram), Polar form of Complex Numbers; Conic Sections, Parabola, Circle, Ellipse, Hyperbola, Transformation of Coordinates and Applications; Exponential Growth & Decay. Applications; Mathematical Induction; Determinants, Fundamental Properties of Determinants, Minors and Cofactors, Application of Determinants to solve System of Linear Equations (Cramers, Rule); Introduction to Matrix Algebra, Matrix Multiplication, Augmented Matrix, Adjoint Matrix, Inverse Matrix, Application of Matrices-solution of System of Linear Equations (homogeneous & non-homogeneous), Consistency of System of Equations.3 credits**MAT 103: Basic Concepts in Mathematics**

The real numbers, Absolute value of real numbers, Exponents, Polynomials, Basic operation and Factoring of polynomials, Rational expressions, Radicals. Linear Equations, Solution, graphs and applications. Variation, Linear inequalities. Exponential and Logarithmic Functions, Exponential growth and decay, Ratios, proportions, percent, application of simple and compound interest. Trigonometric Functions, The Sine and Cosine Functions, Cartesian coordinate systems, Graphing, Relations. Equations of a straight line its slope, Equation of a circle, Systems of Linear Equations, Matrix. Population, Sample, Variable, Raw data, Frequency distribution table, Graphical presentation, Measures of central tendency and measures of dispersion. 3 credits**MAT 104: Mathematics**

Calculus, definition of limit, continuity and differentiability, successive and partial differentiation, maxima and minima. Integration by parts, standard integrals, definite integrals. Solid geometry, system of coordinates. Distance between two points. Coordinate Transformation, Straight lines sphere and ellipsoid. 2 credits **MAT 105: Calculus**

Differential Calculus: Limits, continuity and differentiability, differentiation, Taylor's, Maclaurine's & Euler's theorems, indeterminate forms, tangent and normal, sub tangent and subnormal, maxima and minima, radius of curvature & their applications, introduction to calculus of function of several variables, Taylor's theorem, maxima and minima for function of several variables. Transformation of coordinates & rotation of axes, conic sections.

Integral Calculus: Definition of integration, techniques of integration for definite & indefinite integrals, improper integrals, area, volume and surface integration, arc length and their applications, multiple integrals, Jacobian, line integrals, divergence theorem and Stokes' theorem, beta function and gamma function.3 credits**MAT 110: MATH I Differential Calculus and Co-ordinate Geometry**

Differential Calculus: Limits, Continuity and differentiability. Differentiation. Taylor's Maclaurine's & Euler's theorem. Indeterminate forms. Partial differentiation. Tangent and normal. Subtangent and subnormal. Maximum and minimum, radius of curvature & their applications. Co-ordinate Geometry: Transformation of coordinates & rotation of axis. Pair of straight lines. General equation of second degree. System of circles. Conics section. Tangent and normal, asymptotes & their applications.3 credits **MAT 120: MATH II Integral Calculus and Differential Equations**

Integral Calculus: Definitions of integration. Integration by the method of substitution. Integration by parts. Standard integrals. Integration by method of successive reduction. Definite integrals, its properties and use in summing series. Walli's formula. Improper integrals. Beta function and Gamma function. Area under a plane curve in Cartesian and polar coordinates. Area of the region enclosed by two curves in Cartesian and polar coordinates. Trapezoidal rule. Simpson's rule. Arc lengths of curves in Cartesian and polar coordinates, parametric and pedal equations. Intrinsic equations. Volumes of solids of revolution. Volume of hollow solids of revolutions by shell method. Area of surface of revolution. Ordinary Differential Equations: Degree of order of ordinary differential equations. Formation of differential equations. Solution of first order differential equations by various methods. Solutions of general linear equations of second and higher order with constant coefficients. Solution of homogeneous linear equations. Applications. Solution of differential equations of the higher order when the dependent and independent variables are absent. Solution of differential equations by the method based on the factorisation of the operators. [Students will be expected to attend a 3 hour tutorial class, once each week and submit tutorial worksheets.]3 credits

Prerequisite: MAT 110**MAT 203: Matrices, Linear Algebra and Differential Equations 3 credits**

Matrices: Types of matrices, algebraic operation on matrices, determinants, adjoint & inverse matrix, orthogonality & diagonalization of matrix.

Linear Algebra: System of linear equations, vector space; 2D-space, 3D-space, Euclidean nD-space, sub space, linear dependence, basis and dimension, row space, column space, rank and nullity, linear transformation, eigen value and eigen vector, matrix diagonalization and similarity, application of linear algebra.

Ordinary Differential Equations: Introduction to differential equations, first-order differential equations and applications, higher order differential equations and applications, series solutions of linear equations, systems of linear first-order differential equations. Prerequisite MAT 105**MAT 204: Complex Variables and Fourier Analysis 3 credits**

Complex Variables: Complex number systems, general functions of a complex variable, limits and continuity of a function of complex variables and related theorems, complex differentiation and Cauchy-Riemann equations, mapping by elementary functions, line integral of a complex function. Cauchy's integral theorem, Cauchy's integral formula, Liouville's theorem, Taylor's and Laurent's theorem, singular points, residue, Cauchy's residue theorem, evaluation of residues, contour integration and conformal mapping.

Fourier analysis: Real and complex form, finite Fourier transform, Fourier integrals, Fourier transforms and their use in solving boundary value problems. Prerequisite MAT 105**MAT 205: Introduction to Numerical Methods**

Computer arithmetic: floating point representation of numbers, arithmetic operations with normalized floating point numbers; iterative methods, different iterative methods for finding the roots of an equation f (x) = 0 and their computer implementation; solution of simultaneous algebraic equations by various methods, solution of tri-diagonal system of equations, interpolation for equispaced and non-equispaced nodes, least square approximation of functions, curve fitting, Taylor series representation, Chebyshev series, numerical differentiation and integration and numerical solution of ordinary differential equations & partial differential equations.3 credits

Prerequisite MAT 203 **MAT 215: MATH III Complex Variables and Laplace Transformations**

Complex Variables: Complex number systems. General functions of a complex variable. Limits and continuity of a function of complex variables and related theorems. Complex differentiation and Couchy-Riemann equations. Mapping by elementary functions. Line integral of a complex function. Cauchy's integral theorem. Cauchy's integral formula. Liouville's theorem. Taylor's and Laurent's theorem. Singular points. Residue. Cauchy's residue theorem. Evaluation of residues. Contour integration. And conformal mapping Laplace Transforms: Definition. Laplace transforms of some elementary functions. Sufficient conditions for existence of Laplace transforms. Inverse Laplace transforms. Laplace transforms of derivatives. The unit step function. Periodic function. Some special theorems on Laplace transforms. Solutions of differential equations by Laplace transformations. Evaluation of improper integrals.3 credits

Prerequisite: MAT120**MAT 216: MATH IV Linear Algebra and Fourier Analysis**

Linear Algebra: Basic subject on matrix theory and linear algebra, emphasizing topics useful in other discipline, including systems of equations, vector spaces, determinants, Eigenvalues, similarity, and positive definite matrices, Applications to Gauss elimination with pivoting. Fourier Analysis: Real and complex form. Finite transform. Fourier integral. Fourier transforms and their uses in solving boundary value problems. Multiple integrals; surface and volume integrals, divergence and Stoke's theorem.3 Credits

Prerequisite: MAT 120**MAT 301: Group Theory**

Definition and various examples of groups, subgroups, cosets, normal subgroups, quotient (factor) groups, permutation groups, cyclic groups, generator of a cyclic group, centre of a group, Abelian group, normalizer and centralizer of an element/subset of a group and its application to physics, group homomorphism, isomorphism and automorphism and related theorems, symmetry groups, SU (3), SU (6), application of group theory in solid state physics & elementary particles.3 Credits**MAT 303: Tensor Analysis**

Definition of tensor, tensor density, affine tensor and geometrical object, properties of tensor symmetry, criteria of tensor properties, metric tensor, Kronecker symbol and Levi-Civita's symbol, determinant of metric tensor, connection between metric tensor and Dirac's matrices in the Sommerfeld representation, evolution of square root from four dimensional interval in matrix sense, transformation properties of vector partial derivatives by coordinates, connection coefficients and covariant derivatives, Christoffel's symbols, geodetic lines (geodetics) as a generalization of notion of straight line, variation principle for geodetics, parallel transport, connection between geodetics and covariant differentiation, transport along closed line curvature tensor of the 4th rank, curvature tensor of the 2 D rank, scalar curvature, equations of geodetic deviation, curvature expression in terms of Dirac's matrices, Bianchi's identity, Einstein's conservative tensor, integral operations and corresponding theorems.3 Credits**PHY 101: 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. Waves and oscillations, longitudinal and transverse waves, sound waves, velocity of sound, ultrasonic waves & their applications. 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. Atoms and nuclei, mass number and atomic number, isotopes, isobars & isotones, atomic theory, Planck's Law, Photo-electric effect, wave-particle duality, special theory of relativity, radioactive decay, nuclear fission & nuclear fusion, nuclear energy, fossil fuels & other sources of energy. Structure & vastness of the universe, big bang theory, light year, solar system, Kepler's Laws of planetary motion, cosmological principle, Hubble's Law, red shift, stellar energy, neutron stars, quasars, supernovae, pulsars, black holes. **PHY 102: Fundamentals of Physics**

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. Heat & temperature, specific heat, gas laws, Newton's Law of cooling, First and Second Laws of thermodynamics, kinetic theory of gases, heat transfer. Wave motion, stationary waves, sound waves, Doppler Effect, beats, acoustics, ultrasonic & applications. Huygens' principle, electromagnetic waves, reflection, refraction, interference, diffraction.2 Credits **PHY 110: Mechanics and Properties of Matter 3 credits**

Mechanics: Vectors & scalars, vector addition and subtraction, unit vectors, scalar and vector products, scalar & triple vector product, scalar and vector fields, gradient, divergence and curl, curvilinear co-ordinates, motion in one dimension, motion in a plane, work and energy, conservation laws, conservative force, projectile motion, uniform circular motion, simple harmonic motion, rotational motion, moment of inertia, radius of gyration, angular momentum, Kater's pendulum, Newton's Law of gravitation, gravitational field, potential, escape velocity.

Properties of Matter: Hooke's Law, elastic modulii, adhesive and cohesive forces, molecular theory of surface tension, capillarity, variation of surface tension with temperature. Streamline flow, Poiseulle's formula, streamline flow and turbulent flow, Reynold's Number, Equation of Continuity, Bernoulli's Theorem, Stokes' Law.**PHY 111: Principles of Physics I**

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. Waves & their propagation, differential equation of wave motion, stationary waves, vibration in strings & columns, sound wave & its velocity, Doppler effect, beats, intensity & loudness, ultrasonics and its practical applications. Huygens' principle, electromagnetic waves, velocity of light, reflection, refraction, lenses, interference, diffraction, polarization.3 Credits**PHY 112: Principles of Physics II**

Electric charge, Coulomb's Law, electric field & flux density, Gauss's Law, electric potential, capacitors, steady current, Ohm's law, Kirchhoff's Laws. 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.3 Credits**PHY 113: Waves, Oscillation and Acoustics**

Principle of superposition, interference of waves, phase velocity and group velocity, simple harmonic motion, combination of SHM, Lissajous figures, damped SHM, forced oscillation, resonance, power and intensity of wave motion, waves in elastic media, vibration of strings, beats, Doppler Effect, acoustics, stroboscopy, velocity of sound, ultrasonics, and their applications.3 Credits**PHY 114: Thermal Physics and Radiation**

Heat and temperature, thermal equilibrium, Zeroth Law of thermodynamics, specific heat & calorimetry, Newton's Law of cooling, Kinetic Theory of Gases, idea of pressure due to collisions of molecules, mean free path, Boltzmann Distribution Law, Brownian motion, Law of equipartition of energy; Vander Waals' equation of state, heat transfer, conduction, convection and radiation, conduction of heat in solids, co-efficient of thermal conductivity and its measurement, First Law of thermodynamics, isothermal & adiabatic changes, reversible and irreversible processes, Carnot's cycle, efficiency of heat engines, Second Law of thermodynamics, entropy and disorder, absolute scale of temperature, thermodynamic functions, Maxwell's relations, Clausius-Clapeyron Equation, Gibb's phase rule, Third Law of thermodynamics, Nernst heat theorem, radiation theory, black body radiation, Wien's Law, Stefan-Boltzman Law, Rayleigh Jeans Law, Planck's Law, variation of specific heat with temperature, Einstein's theory, Debye's theory, conduction of heat in solids, measurement of conductivity, Joule-Thomson expansion, refrigeration, heat engines, Rankine cycles, cryogenics, measurement of high temperature. 3 Credits**PHY 115: Electricity and Magnetism**

Charge, quantization of charge, Coulomb's Law, electric field and potential. Gauss's Law, electric dipole, dielectrics, capacitance, energy of charged systems, electrical images, magnetic dipole, energy in a magnetic field. Direct current and electromotive force, Ohm's Law, Kirchhoff's Laws, Wheatstone Bridge, Lorentz force, magnetic field of a current and Ampere's Law, Biot-Savart Law, electromagnetic induction, Faraday's Law, self-induction, mutual induction, alternating current, RMS value, power factor, CR, LR and LCR circuits, resonance.3 Credits**PHY 201: Solid State Physics**

Crystalline state, Bravais lattices, crystal symmetry, point group & space group, unit cells, Miller indices, x-ray diffraction, Bragg's Law, reciprocal lattice, structure factor, interatomic force and classification of solids, ionic, covalent, molecular, hydrogen bonded crystals, lattice energy of ionic crystals, Madelung constant, lattice vibration, phonons, normal modes in monatomic and diatomic linear chains, theory of specific heat, Einstein and Debye models, thermal expansion, defects in crystals, dislocations, consequences of defects on mechanical properties.3 Credits **PHY 202: Optics**

Laws of reflection and refraction, total internal reflection, Huygens' Principle, velocity of light, Young's experiment, Fresnel's bi-prism, Newton's rings, Michelson's interferometer, multiple reflections, Fabry-Perot interferometer, diffraction of light, Fresnel and Fraunhoffer diffraction, single, double and multiple-slit diffraction, diffraction grating, spectrometer, resolving power of a grating, polarization of light, production of polarized light, plane, circular and elliptically polarized light, optical activity, double refraction, optic axis, half-wave and quarter-wave plate, nicol prism, dispersion of light, scattering of light, Thomson scattering.3 Credits **PHY 204: Classical Mechanics and Special Theory of Relativity**

Classical Mechanics: Newtonian equations of motion, conservation laws of a system of particles, variable mass, generalized co-ordinates, generalized force, D' Alembert's Principle, variational method, Euler-Lagrange equations of motion, Hamilton's principles, two-body central force problem, elliptic orbit, scattering in a central field, Rutherford formula, kinematics of rigid body motion, Euler angles, rotating co-ordinates, Coriolis force, wind motion, principal axis transformation, top motion, principle of least action, Hamiltonian equations of motion, small oscillations, normal co-ordinates, normal modes.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.3 Credits**PHY 205: Statistical Mechanics**

Statistical Mechanics: Phase space, concept of state and ensemble, microcanonical, canonical and grand canonical ensembles, Boltzmann probability distribution, Maxwell velocity distribution, derivation of Bose-Einstein and Fermi-Dirac statistics, ideal Fermi gas, degenerate Fermi system, equation of state of ideal gases, ideal Bose gas, application of Statistical mechanics in various fields in physical, biological, social sciences, economics, finance and in engineering & ICT.3 Credits**PHY 210: Quantum Physics of Atoms, Solids and Nuclei**

Special Theory of Relativity: Michelson-Morley Experiment, Special Theory of Relativity, Lorentz Transformations, Time Dilation, Length Contraction, Mass-Energy Relation. Quantum Phenomena: Blackbody Radiation, Planck's Law, Photoelectric Effect, Bohr Atomic Model, Energy Levels & Atomic Spectra, Correspondence Principle, Dual Nature of Matter & Waves. Introductory Quantum Mechanics: Wave Function, Operators, Expectation Values, Schrodinger's Wave Equation, Particle in Box, Schrodinger Equation for Hydrogen Atom, Energy Levels, Magnetic & Orbital Angular Momentum, Concept of Quantum Numbers. Solid State Physics: Crystal Structure, Crystal Diffraction, Bragg Law, Lattice Vibrations & Phonons, Free Electron Model, Energy Levels & Density of States, Fermi-Dirac distribution function, Free Electron gas in Three dimension, Electrical conductivity & Thermal Conductivity, Hall Effect, Band Theory of Solids, Band Diagrams of Insulator, Semiconductor & Metals, Superconductivity, Lasers & Holography. Nuclear Physics: Rutherford Nuclear Model, Radioactivity, Half life & Mean life, Nuclear Binding Energy, Fission & Fusion, Particle Accelerator, Elementary Particles & Nuclear Interactions, Quarks, Lepton & Hadrons, Big Bang & Origin of the Universe.3 Credits**PHY 301: Classical Electrodynamics**

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.3 Credits

Prerequisite PHY 115.**PHY 302: 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.3 Credits

Prerequisite PHY 110**PHY 303: Quantum Mechanics**

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.3 Credits**PHY 304: Atomic and Molecular Physics**

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.3 Credits**PHY 305: Nuclear Physics I**

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.3 Credits

Prerequisite PHY 304**PHY 306: Basic Electronics**

Network theorems, filters, transmission line, basic semiconductor concepts, energy bands, electrons and holes, semiconductor diode, rectification, regulators, Zener diode, diode circuits, unijunction transistor, FET and its characteristics, transistor amplifier, FET amplifier; amplifier circuits, voltage amplifiers, RC coupled amplifiers and tuned amplifiers, frequency response, bandwidth, power amplifier, push-pull amplifier, feedback and amplifier stability, operational amplifier and its characteristics, oscillators, modulation and demodulation, digital electronics, digital logic, logic gates, Boolean algebra, logic circuits, information registers, flip-flop circuit.3 Credits **PHY 308: Methods of Experimental Physics and Instrumentation**

Optical and spectroscopic instruments, defects of images and their remedies, optical blooming, phase contrast and polarizing microscope, spectrophotometers, optical transmittance, reflectance and absorption, application of interferometry, production and measurement of high and ultrahigh vacuum. Rotary pump, diffusion pump, ion pump and turbo pump, pirani, penning and ionisation gauges, measurement of current and voltages, potentiometer, VTVM, oscilloscope, D.C. amplifier, lock-in amplifier, frequency meter and counter, four point probe, flux meter and Hall probed transducers, piezoelectric, thermistor, photo-transducers, voltage regulator, SCR type temperature controllers. 3 Credits

Prerequisites PHY 202 and PHY 306 **PHY 309: Introduction to Materials Science**

Crystalline solids, amorphous, composite, fibrous materials, polymers, plastics, binding forces, elastic properties, dislocations, defects etc, specific heat, thermal expansion, thermal conductivity and electrical conductivity of metals, dielectric properties of solids, modes of dielectric polarisation, ferro electricity, piezo electricity, optical properties of solids ,classical and semi classical theory, free carrier effects, lattice absorption, electronic absorption, magnetic properties of solid, atomic magnetic moments, dia and paramagnatism, ferro & ferrimagnetism, antiferromagnetism, ferrites, magnetic resonance, superconductivity, type-1, type-2 superconductors, liquid crystals.3 Credits

Prerequisite PHY 201**PHY 310: Advanced Solid State Physics**

Free electron theory, transport properties, Sommerfeld theory, Hall Effect, box quantization, density of states, Fermi surface, Fermi energy, electrical conductivity, WiedmannFranz law, band theory of solids, electron in a periodic potential, Schrodinger equation, Bloch function, LCAO and OPW methods, dielectric properties of insulators, Clausius-Mosotti relations, dielectric loss, relaxation time, polarization mechanism, direct & indirect band gap semiconductors, extrinsic semiconductors, charge carrier concentration, recombination process of p-n junction, superconductivity, Meissner Effect, London equation, BCS theory, introduction to high temperature superconductivity, magnetic materials, quantum theory of diamagnetism and paramagentism, theory of ferromagnetic, ferrimagnetic and anti-ferromagnetic orders, magnetic resonance.3 Credits

Prerequisite PHY 201**PHY 311: X-Rays**

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.3 Credits

Prerequisite PHY 201**PHY 312: Nuclear Physics II**

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. Shell model, refinement of extreme single particle model, collective model, nuclear reactions, compound nucleus model, concept of optical potential, energy averaged cross section and the optical model at low energies, phenomenological optical model, direct reactions, parity violation in beta decay, nuclear fission and nuclear reactor, nuclear fusion, nuclear liquid drop model & shell model, magic numbers (qualitative) accelerators, Van de Graaff generator, linear accelerator, cyclotron, synchrotron, detection of charged particles, photons and neutrons, nuclear pulse counting systems, elementary particles.3 Credits

Prerequisite PHY 305**PHY 313: Physics for Development**

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.3 Credits **PHY 400: Thesis/Project**

A student is required to carry out thesis/project work in her/his last two semesters in a chosen field. There will be a supervisor who will either be a BRAC University faculty or any other suitable expert from universities and R/D organizations of the country to guide the thesis/project work. On completion of study and research s/he will have to submit the dissertation paper and to face a viva board for the defence.4.5 Credits**PHY 401: Reactor Physics**

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. 3 Credits

Prerequisite PHY 305**PHY 402: Atmospheric Physics**

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.3 Credits **PHY 403: Plasma and Astrophysics 3 Credits**

General introduction to plasma physics, plasma as a fourth state of matter, definition, screening, and Debye shielding, plasma frequency, ideal plasma, temperature and pressure of plasma, magnetic pressure and plasma drifts, plasma waves, Landau damping, collisions in plasmas, hydrodynamic description of plasma, one fluid model, two fluid model,Chew-Goldberg theory, low waves in magneto-hydrodynamics, description of plasma, dielectric tensor, longitudinal and transverse waves, plasma instabilities, transport in plasmas, plasma kinetic theory, Vlasov equation, linear waves, waves in magnetized plasma, electromagnetic waves, waves in hot plasmas, nonlinear waves, Landau damping, quasi linear theory, plasmas in fusion research, astrophysical plasmas.

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.3 Credits

Prerequisites PHY 301 and PHY 304.**PHY 404: Electronic Devices and Circuits**

Modelling and application of Semiconductor devices and integrated circuits, advanced transistor amplifier analysis, including feedback effects. Design for power amplifiers, operational amplifiers (OPAMP), analog filters, oscillators, A/D and D/A converters and power converters. Introduction to transistor level design of CMOS digital circuits.3 Credits

Prerequisite PHY 306 **PHY 405: Mathematical Physics**

Series solution of 2nd order ordinary differential equations about ordinary and singular points, orthogonal set functions, Sturm-Liouville boundary value problem (SLP), eigen values and eigen functions of different SLP, series of orthogonal set of function. 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.3 Credits

Prerequisite MAT 203**PHY 406: Medical Physics and Instrumentation**

Ultrasound imaging, A-scan, B-scan, M-scan, clinical applications, rectilinear scanner, gamma camera, CAT scanner, MRI, clinical applications, audiology, hearing aids, vascular measurements, blood pressure, blood flow, blood velocity, cardiac measurements; ECG, ECG planes, elementary ideas on heart disorders, defibrillators, pacemakers, neuromuscular measurements; EEG, EMG, stimulation of neural tissue, nerve conduction measurements, bio-electric amplifiers, patient safety, radiopharmaceuticals, radiotherapy, radiation protection, radiation dosimetry.3 Credits**PHY 407: Mathematical Modelling in Physics**

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.3 Credits

Prerequisite MAT 205**PHY 408: Advanced Quantum Mechanics**

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, Smatrix, solution of the wave equation by the method of Green's function, LippmannSchwinger 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.3 Credits

Prerequisite PHY 303**PHY 409: Physics of Radiology**

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).3 Credits **PHY 410: Laser Physics**

Spontaneous and stimulated emission, absorption, pumping schemes, characteristic properties of laser beam, laser speckle, grain size calculation for free-space propagation, semi classical treatment of absorption and stimulated emission, spontaneous emission, results of QED treatment, electric dipole, allowed and forbidden transitions, Einstein's A and B coefficient, radiation trapping, superfluorescence, superradiane and amplified spontaneous emission, nonradiative decay, homogeneous and inhomogeneous broadening, linewidth calculations for naturally, collisionally and Doppler broadened line, two level and four, level saturation, saturation of absorption & inhomogeneously broadened line, passive optical resonators, continuous wave and transient laser behaviour, laser beam transformation, types of lasers, their construction and use, applications of lasers, optical communications, laser in fusion research, holography.3 Credits

Prerequisite PHY 304**PHY 411: Geophysics**

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.3 Credits**PHY 412: Dynamical and Tropical Meteorology**

Geophysical fluid dynamics, Navier-Stokes' equation, rotating and stratified flow, scale analysis, hydrostatic approximation, Coriolis force, geopotential etc., gradient and thermal wind, vorticity and circulation theorems, Proudmen-Taylor theorem, atmospheric wave, atmospheric turbulence, barotroic and baroclinic instabilities, numerical weather forecasting, quasi-geotropic approximation, barotropic vorticity equation, primitive equation, multilayered models, tropical cyclones, norwesters and tornadoes, the monsoons, dynamical climatology, physics of upper atmosphere: geomagnetism, neutral atmosphere, ionosphere and magnetosphere.3 Credits

Prerequisite PHY 402**PHY 413: General Theory of Relativity**

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.3 Credits**PHY 414: Field Theory**

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.3 Credits**PHY 415: Neutron Scattering**

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.3 Credits

Prerequisite: PHY 305**PHY 416: Radiation Biophysics**

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.3 Credits

Prerequisite: PHY 305**STA 101: Introduction To Statistics**

Frequency distribution. Mean, median, mode and other measures of central tendency. Standard deviation and other measures of dispersion. Moments, Skews and kurtosis. Elementary probability theory and discontinuous probability distribution, e.g. binomial, Poisson and negative binomial. Continuous probability distribution, e.g. normal and exponential. Characteristics of distributions. Hypothesis testing and regression analysis. Basic concepts and applications of probability theory and statistics. Chi-square test.3 credits**STA 201: Elements of Statistics and Probability**

Frequency distribution, mean, median, mode and other measures of central tendency, standard deviation and other measures of dispersion, moments, skewness and kurtosis, elementary probability theory and discontinuous probability distribution, binomial, Poisson and negative binomial distribution, continuous probability distributions, normal and exponential, characteristics of distributions, hypothesis testing and regression analysis, basic concepts and applications of probability theory and statistics, chi-squared test.3 credits**LAB COURSES****PHY 116: Physics Lab I 1.5 Credits**

List of Experiments:

EXP 1: Determination of the Young's Modulus of a Short Wire by Searle's Dynamic Method

EXP 2: Determination of the Modulus of Rigidity of a Wire by the Method of Oscillations

EXP 3: Determination of g by means of a Compound Pendulum

EXP 4: Determination of the Moment of Inertia of a Flywheel about its Axis of Rotation

EXP 5: Determination of the Spring Constant and Effective Mass of a given Spiral Spring

EXP 6: Determination of Surface Tension of Water by Capillary Tube Method

EXP 7: Determination of Surface Tension of Mercury and the Angle of Contact by Quincke's Method

EXP 8: Determination of the Viscosity of Glycerine by Applying Stokes' Law.

EXP 9: Determination of the Specific Heat of a Liquid by the Method of Mixture

EXP 10: Determination of the Specific Heat of a Liquid by the Method of Cooling

EXP 11: Determination of the Thermal Conductivity of a Bad Conductor by Lee's Method

EXP 12: Determination of the Pressure Co-efficient of a Gas at Constant Volume by Constant Volume Air Thermometer

EXP 13: Determination of the Stefan's Constant

EXP 14: Study of Variation of the Frequency of a Tuning Fork with the Length of a Sonometer (n-l curve) under given Tension and Hence to Determine the Unknown Frequency

EXP 15: Determination of the Frequency of a Tuning Fork by Melde's Experiment

EXP 16: Determination of Velocity of Sound by Kundt's Tube.**PHY 203: Physics Lab II 1.5 Credits**

List of Experiments:

EXP 1: Determination of the Focal Length and Hence the Power of a Convex Lens by Displacement Method with the Help of an Optical Bench

EXP 2: Determination of the Refractive Index of a Liquid by Plane Mirror and Pin Method using a Convex Lens

EXP 3: Determination of the Radius of Curvature of a Lens by Newton's Rings Method

EXP 4: Determination of the Refractive Index of the Material of a Prism by using a Spectrometer

EXP 5: Determination of the Wavelengths of Various Spectral Lines by Spectrometer by using Plane Diffraction Grating

EXP 6: Determination of the Value of an Unknown Resistance and Verification of the Laws of Series and Parallel Resistances by Means of a Post Office Box

EXP 7: Determination of the Internal Resistance of a Cell by a Potentiometer

EXP 8: Determination of the Specific Resistance of a Wire using a Meter Bridge

EXP 9: Determination of the Resistance of a Galvanometer by the Half-Deflection Method

EXP 10: Determination of the High Resistance of a Suspended Coil Galvanometer by the Method of Deflection

EXP 11: Comparison of the EMF of Two Cells with a Potentiometer

EXP 12: Determination of the Resistance per Unit Length of a Meter Bridge

EXP 13: Determination of the Temperature Co-efficient of Resistance of the Material of a Wire

EXP 14: Determination of the Value of J by Electrical Method

EXP 15: Determination of the Line Frequency by Lissajous Figure using an Oscilloscope and a Function Generator and Verification of the Calibration of Time/Div Knob at a Particular Position for Different Frequencies

EXP 16: Determination of the Self-Inductance of a Coil by Anderson's Method.

EXP 17: Charging and Discharging of Capacitors and Study of Their Various Characteristics.

**PHY 307: Physics Lab III 1.5 Credits**

List of Experiments:

EXP 1: Determination of the Excitation and Ionization Potentials (of mercury) by Frank-Hertz Experiment.

EXP 2: Determination of the e/m of Electron Using Helmholtz Coil.

EXP 3: Determination of the Threshold Frequency for Photoelectric Effect of a Photo-Cathode and the Value of Planck's Constant by Using a Photoelectric Cell.

EXP 4: Determination of the Plateau of a Geiger-Muller Counter and Hence to Find its Operating voltage.

EXP 5: Study of the Variation of Electrical Conductivity of a Semiconductor and Determine of its Energy Gap.

EXP 6: Study of the Characteristics of a PN Junction and Zener Diode.

EXP 7: Study of the Characteristics of PNP and NPN Transistors.

EXP 8: Study of the Frequency Response Characteristics of an RC Low pass, RC High pass, a Band pass and a Parallel T Filter.

EXP 9: Study of the Frequency Response in LRC Series Circuit and the Variation of Q-factor with Resistance.

EXP 10: Determination of the Frequency Response in LRC Parallel Circuit and Determination of Q-factor.

EXP 11: Study of Variation of Reactance due to L and C with Frequency.

EXP 12: Designing and Construction a Summing Amplifier Using 741 Operation Amplifier (OPAMP).

EXP 13: Construction of Full Wave Bridge Rectifier Using Semiconducting Diodes and Study of the Effect of Filters.

EXP 14: Determination of Transistor Characteristics in Common Emitter Configuration and Determination of Hybrid Parameter.

EXP 15: Determination of the Coefficient of Mutual Inductance Between Two Coils and Hence to Show its Variation with the Separation Between the Coils.

EXP 16: Determination of the Absorption Coefficients of Different Materials for the Radiation Emitted by a Radioactive Source by Using a Geiger-Mueller Counter.