Scheme of Studies (Contents) BS Physics Semester 6

6th Semester

 PHY-502 Methods of Mathematical Physics-II 3 (3 – 0) 

Fourier Analysis, Fourier cosine and sine series, change of interval, Fourier integral, complex form of Fourier series, Fourier transform, Fourier transform of derivatives, Laplace transform, Inverse Laplace Transform, Convolution theorem, Initial boundary value problem, Laplace transform of derivatives. Physical significance along with examples of Fourier and Laplace transforms. Special functions, Hermite, Laguerre, Legendre and associate Legendre polynomial. Bessel function, Neumann function, and spherical Bessel function, Gamma function. Nonhomogeneous equations- Green’s function, Green’s function in terms of Eigen-function, the Sturm-Liouville problem, Green’s function for Dirac Delta functions,
Recommended Books: 
1. Arfken G.B and H.J Weber, F.E Harris, 2012, 7th Edition, Mathematical Methods for Physicists, A. Press, New York.
2. Dass H.K, R. Verma, 2011, 6th Edition, Mathematical Physics, S. Chand& Company Ltd. New Delhi.
3. Kreyszig E. 2011, 10th Edition, Advanced Engineering Mathematics. Wiley, New York.
4. Collins R.E, 2011, 2nd Edition, Mathematical Methods for Physicists and Engineers, Dover Publications.
5. Tang K.T, 2010, 2nd Edition, Mathematical Methods for Engineers and Scientists 2, Springer.
6. Spiegel M.R 2009, 1st EditionAdvanced Mathematics for Engineers and Scientists, Schaum’s outlines series, McGraw Hill.
7. Riley K F, M P Hobson and S J Bence. 2006, 3 rd Edition, Mathematical Methods for Physics and Engineering, Cambridge University Press, Cambridge.

 PHY-504 Quantum Mechanics-I 3 (3 – 0) 

Review of concepts of classical mechanics, The state of a system, Dynamical variables and operators, Linear vector space, orthogonal systems, linear transformations, matrices, change of basis, Hilbert space, Commuting and noncommuting operators, Heisenberg uncertainty relations, Functions and expectation values, Dirac notation, Hermitian operators, Symmetry principles and conservation laws, Orbital angular momentum, Spin, The eigenvalues and eigen functions of L2 and Lx, Matrix representation of angular momentum operators, Addition of angular momenta. Properties of one dimensional potential functions, Solutions of Schrödinger equation for free particles, the potential barrier problems, The linear harmonic oscillator, Particle in a box. Schrödinger Equation in Three Dimensions, Separation of Schrodinger equation in Cartesian coordinates, Central potentials, The free particle, Three dimensional square well potential, The hydrogen atom, Three dimensional isotopic oscillator.
Recommended Books:
1. Zettli N. 2009, Quantum Mechanics Concepts and applications. J Willy.
2. Bransden B H and Joachain C J. 1990, Introductory Quantum mechanics. Longman Scientific & Technical London.
3. Greiner W.1980, An Introduction Quantum Mechanics. Addison Wesley Publishing Company, Reading Massachusetts.
4. Liboff, R.L. 1980. “Introductory quantum Mechanics”, by Addison Wesley Publishing Company

 PHY-506 Nuclear Physics-I 3 (3 – 0) 

Nuclear mass, size, nuclear spin, Nuclear Binding energy, magnetic dipole moments, electric quadruple moments, parity and statistics. Observed phenomenon of radio activity, explanation of α-decay: Absorption, Range, Ionization and Stopping power of alpha particles, theory of alpha decay, Fermi theory of β-decay, theory of γ-decay, energetic of γ-decay, Nuclear isomerism, Internal conversion, Mossbauer Effect, Yukawa meson theory of nuclear forces, properties of nuclear forces, n-p and p-p scattering at low energies. Passage of charged particles through matter, Ionization chamber, proportional counter, GM counter, scintillation counter, semi-conductor detector, bubble chamber. Linear accelerator, van de Graff generator, Synchrocyclotron, proton synchrotron, betatron, photographic emulsion.
Recommended Books: 
1. Zhang, Z..M, B.K. Tsai and G. Machin. 2010. Experimental Methods in Physical Science Vol. 2, Academic Press, USA.
2. Alejandro Garcia and Ernest M. Henley, (2007). Subatomic Physics, by publisher: World Scientific Publishing.
3. B R Martin, 2006. Nuclear and Particle Physics, publisher: New York: Wiley
4. David, W.I.F., K. Shankland, L.B McK usker and C. Baerloche. 2006. Structure Determination from Powder Diffraction Data. Oxford University Press, New York.
5. Hanlon, J. F. 2003. A User Guide to Vacuum Technology. John Wiley and sons, USA.
6. Kaplan Irving Nuclear Physics, latest edition.
7. lilley John 2001 Nuclear physics: Basic concepts and applications,
8. Povh B, Rith K, Scholz C and Zetsche F, 2006, Particles and Nuclei: an Introduction to the Physical Concepts, 5th Edition, publisher: Berlin Springer,.
9. S. Krane Kenneth. 1995. “Introducing Nuclear Physics,

 PHY-508 Electrodynamics-II 3 (3 – 0) 

Maxwell’s equations, Differential form of Faraday law of electromagnetic induction, Maxwell correction of Amper’s law and displacement current, Electromagnetic energy vector (Poynting vector), Wave equations for scalar and vector potential, Gauge transformations, Lorentz gauge and Coulombs gauge, Retarded scalar and vector potentials, Wave equations for E and H, Time dependent wave equation, Plane electromagnetic waves in a conducting and non-conducting media, Linear and circular polarization. Electromagnetic wave in matter: Propagation in linear media, Reflection and Transmission at the boundary of non-conducting media (Normal and Oblique incidence), Reflection at conducting surface, Frequency dependence of permittivity, Radiation: Electric and Magnetic dipole, Power radiated by a point charge, Radiation reaction, Electrodynamics and Relativity: Einstein’s Postulates, Geometry of Relativity, Lorentz Transformations, Proper time and velocity, Relativistic energy, momentum, kinematics, and electrodynamics, Magnetism as a relativistic phenomenon.
Recommended Books: 
1. Griffiths D.J. 1999, Introduction to Electrodynamics, 3rd Edition
2. John R. Reitz, 1992, Foundations of Electromagnetic Theory, 4th Edition

 PHY-510 Electronics-II 3 (3 – 0) 

An overview of operational amplifiers (op-amp), the differential amplifier, the inverting and non-inverting amplifiers, op-amp frequency response, negative feedback, comparators, integrators and differentiators, Instrumentation amplifier, Log and Antilog amplifiers, Constant current source, Current to Voltage and Voltage to Current converters, phase shift oscillators, the Wienbridge oscillator, the Colpitts & Hartley oscillators, the crystal oscillator, Schmitt triggers, the 555 timer, monostable, bistable, and astable multi vibrators, switching circuits, introduction to thyristors, silicon-controlled rectifiers, diacs and triacs, Number systems, digital circuits, Logic gates and Boolean algebra, arithmetic circuits, flip flops and latches, binary counters, Analog to Digital and Digital to analog conversion circuits.
Recommended Books:
1. Floyd T L. 2010, Electronic Devices 9TH Ed. Prentice-Hall Intern. Inc., Englewood Cliffs (USA). 2. Floyd, T. L. 2010, Digital Fundamentals 10TH Ed. Prentice-Hall Intern. Inc., Englewood Cliffs (USA).
3. Tocci R J. 2010, Digital Systems: Principles and Applications 11TH Ed. Prentice-Hall Intern. Inc., Englewood Cliffs (USA).
4. Malvino, A P. 2008, Electronic Principles. 7TH Ed. Glencoe-McGraw-Hill Book Co.
5. Nashelsky, L and L B Robert. 2009, Electronic Devices and Circuit Theory 10TH Ed. Prentice-Hall Intern. Inc., Englewood Cliffs (USA).

 PHY-512 Lab Course-IV (Atomic & Nuclear Physics) 3 (0 – 3) 

The candidate must perform at least Eight experiments from the list given below. 50% weightage must be given to viva-voce about apparatus, theory of experiments and estimation of errors. 1. To Expose the students to advance level experimentation in Physics 2. To make them familiar to such experiments where outcome can be used in developing future research capabilities and teaching skills 3. To make the students confident in their studies by showing and measuring parameters mostly used in their theoretical work. 1. To study the characteristics curves of GM counter. 2. To determine the absorption coefficient of lead for Gamma Rays using GM counter assembly. 3. To determine the maximum energy of Beta Particles using GM counter assembly. 4. To determine the range of an Alpha Particle and guess its energy using empirical relations using GM counter assembly. 5. To measure the half life of a radioactive nuclide. 6. To study of Random processes and fluctuations in Random processes (Gaussian distribution curve) using GM counter assembly. 7. To study radioactive equilibrium using Cs137/Ba137 mini generator using GM counter assembly. 8. Demonstration of Interaction of Radiations with matter using absorber kit using GM counter assembly. 9. Verification of inverse square law using GM counter assembly. 10. To study the wave characteristics of an electron. (electron diffraction experiment.) 11. Determination of Planck’s constant using He-Neon laser, and compare its results with Photo cell method. 12. Determination of velocity of light using He-Neon laser and compare it with other standard methods.
Recommended Books: 
1. Gray T S. Applied Electronics (John-willey and Sons)
2. Higgings R J. Experimental Electronics (Mc Graw Hill)
3. Mark H and N.T Olson. Experiments in Modern Physics (Mc Graw Hill)
4. Melissienson A C. Experiments in Modern Physics (Academic)
5. Squares G L. Practical Physics 3rd Ed. Cambridge University Press.

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Scheme of Studies (Contents) BS Physics Semester 5

5th Semester 

PHY-501 Methods of Mathematical Physics-I 3 (3 – 0) 

Vector operations, Physical significance of DEL operator, Gauss’s divergence theorem, Green’s theorem, Stokes’s theorem, Orthogonal curvilinear coordinates system, Gradient, Divergence, Curl and Laplacian in orthogonal curvilinear coordinates, Spherical polar and Cylindrical coordinates systems. Complex numbers, Euler’s formula, De Moivre’s theorem, elementary functions, analytic functions of complex variables, CauchyRiemann equation, harmonic functions, complex integration, Cauchy’s theorem, Cauchy’s integral formula, Taylor and Laurent series, Contour integrals, singularities and residues, residue theorem, branch points and integrals of multivalued functions. Tensors Analysis and applications.
Recommended Books: 
1. Arfken G.B and H.J Weber, F.E Harris, 2012, 7th Edition, Mathematical Methods for Physicists, A. Press, New York.
2. Dass H.K, R. Verma, 2011, 6th Edition, Mathematical Physics, S. Chand& Company Ltd. New Delhi.
3. Kreyszig E. 2011, 10th Edition, Advanced Engineering Mathematics. Wiley, New York.
4. Collins R.E, 2011, 2nd Edition, Mathematical Methods for Physicists and Engineers, Dover Publications.
5. Tang K.T, 2010, 2nd Edition, Mathematical Methods for Engineers and Scientists 2, Springer.
6. Spiegel M.R 2009, 1st EditionAdvanced Mathematics for Engineers and Scientists, Schaum’s outlines series, McGraw Hill.
7. Riley K F, M P Hobson and S J Bence. 2006, 3 rd Edition, Mathematical Methods for Physics and Engineering, Cambridge University Press, Cambridge.

 PHY-503 Classical Mechanics 3 (3 – 0) 

Historical development of classical mechanics, Newtonian mechanics of single particle & system of particles, constraints, generalized coordinates, D’Alembert’s Principle , Derivation of Lagrange’s equations, simple applications of the lagrangian formulation, Hamilton’s Principle, Techniques of the calculus of variation, Derivation of Lagrange’s equation from Hamilton’s principle, Applications of Hamilton’s principle, shortest distance between two points in a plane and space, minimum surface of revolution, the Brachistochrone problem, conservation theorem , Two body central force problem & its reduction to the equivalent one body problem, Kepler’s law as an inverse square law problem, Differential equation for the orbits and the different shapes of the orbit, planetary orbits & their equations, Legendre transformations and its applications, Derivation of Hamilton’s equation of motion, Hamiltonian, cyclic coordinates, Routh’s Procedure, The equations & examples of canonical transformations, Poisson’s brackets & their properties, Poisson’s brackets & other canonical invariants, Poisson’s theorem, invariance of Poisson’s bracket under canonical transformation. Recommended Books: 
1. Goldstein H, P Charle and J L Safko. 2001, Classical Mechanics. Addison-Wesley.
2. Hand L N and J.D Finch. 1998, Analytical Mechanics. Cambridge University Press, Cambridge.
3. Barger V D and M G Olsson. 1995, Classical Mechanics. McGraw-Hill, New York.
4. Landau L D and E M Lifshitz. Mechanics. 1960, Pergamon, Oxford.
5. Classical Mechanics by J.W. Leech Methuen and Co. Ltd., London, 1958.

 PHY-505 Electrodynamics-I 3 (3 – 0) 

Electric dipole, Electric field and electric potential at a point due to dipole, mutual interaction energy of two dipoles, Force and Couple on the dipole placed in an external electric field, Dielectrics: Polarization and polarization density vector, surface and volume charge densities due to polarization, electric field inside the dielectric, electric susceptibility and dielectric constant, Poisson and Laplace equations both for dielectric and space, Solution to Laplace equation in Cartesian, spherical and cylindrical coordinates, Uncharged conducting and dielectric sphere in uniform electric field, Electrostatic Images, Point charge near an infinite grounded conducting plane, Electric potential, electric field intensity and surface charge density in case of point charge and conducting sphere.Electric current: nature of electric current, current density, equation of continuity, Ohm’s law, steady current in media without source of e. m. f., Approach to electrostatic equilibrium, Magnetic properties of steady current: Current carrying element, Force on current carrying conductor, Biot-savart law and their applications, Ampere’s circuital law and their applications, Magnetic vector and scalar potential, Magnetic field of a distant circuit, Magnetic properties of matter: Magnetization vectors M, Magnetic current densities due to surface and volume currents and vector potential, Magnetic field due to the magnetized material, Magnetic scalar potential and pole density, Magnetic intensity vector H, Relation between H and M, Field equation, Magnetic susceptibility and permeability, Boundary conditions on the field vectors.
Recommended Books: 
1. Bo Thide, 2011, The Electromagnetic filed theory 2nd Ed.
2. Martin Dressed, 2002, Electrodynamics of solids (optional properties of electron in matter), 1st Ed. Cambridge University, Press.
3. Griffiths D.J. 1999, Introduction to Electrodynamics, 3rd Edition
4. John R. Reitz, 1992, Foundations of Electromagnetic Theory, 4th Edition

 PHY-507 Electronics-I 3 (3 – 0) 

Liner network analysis; superposition, Thevenin, Norton and Mill man’s theorems, Electronics: the p-n junction, Bias the p-n junction diode, diode, characteristics of diode, different models and types of diodes, halfwave and full-wave rectifier, full-wave bridge rectifier, capacitor, inductive, and πR filters, Clipping and clamping circuits, Zener voltage regulators, regulated power supply, varactor diodes, Optical diodes, Light emitting Diodes. Bipolar junction transistor (BJT), transistor characteristics, biasing circuits such as base bias, emitter bias, voltage-divider bias, feedback bias circuits, amplifier classifications, common emitter amplifier, the emitter followers, the common base amplifier. RC-coupled amplifiers, Power amplifiers, (class A, class B amplifiers, class C amplifier), introduction to Junction field-effect transistors (JFET), JFET biasing circuits, the common source follower, introduction to MOSFET.
Recommended Books: 
1. Floyd, T. L. 2010. Electronic Devices 9TH Ed. Prentice-Hall Intern. Inc., Englewood Cliffs (USA). 2. Nashelsky, L. & Robert, L. B. 2009. Electronic Devices and Circuit Theory 10TH Ed. Prentice-Hall Intern. Inc., Englewood Cliffs (USA).
3. Malvino, A. P. 2008. Electronic Principles. 7TH Ed. Glencoe-McGraw-Hill Book Co.
4. Grob, B. 2003. Basic Electronics 9TH Ed. McGraw-Hill

 PHY-509 Relativity and Cosmology 3 (3 – 0) 

Special Relativity, Galilean relativity, Einstein’s postulates of special relativity. Consequences of special relativity. Michelson-Morley experiment, Lorentz transformations, consequences of Lorentz transformations (the relativity of length, the relativity of time, concept of simultaneity) Relativistic Mechanics, Transformation of relativistic velocities, addition of relativistic velocities, Relativity of mass, Force equation in relativity, rest mass ,KE and total energy, conservation of energy and momentum, the conversion of mass to kinetic energy in Uranium Fission, pair production and annihilation, The Cerenkov Effect and Cerenkov radiation, Einstein’s mass-energy relationship and its practical examples, particle of Zero rest mass, Relativistic Doppler Effect, Aberration of Light, Tachyons, structure of space time, Geometry of space time, Minkowski space time tensors, the light cone, and four vectors (position four vector, four velocity, four momentum, four force). General relativity, Gravity as a Geometry, The equivalence principle, clocks in a gravitation field, space time is curved, geodesics, the geodesic equation, equation of geodesic deviation, Einstein field equation Manifolds and coordinates, curves and surfaces, tensor fields, metric tensor. Cosmology cosmological redshift, Hubble’s law, microwave background, the Big Bang, Theory, Historical background of universe, stars , neutron stars, pulsars , black holes, quasars, singularity, measuring the distance to stars, concept of open, closed and flat universe, dark matter(MACHOs and WIMPs-)
Recommended Books: 
1. James B. 2005, An Introdu ing to Einstein’s General Relativity. Hartle Pearson Education. 2. Beiser A. 2002. 6th E. Perspectives of Modern Physics. McGraw-Hill.
3. Resnick, Halliday and Krane. 2002, Physics Vol. I, 5th Ed. John Wiley and Sons Inc, New York.
4. McComb W D. 1999, Dynamics and Relativity. Oxford University Press.
5. Inverno R.D. Introducing Einstein’s Relativity.1992, Oxford University Press.
6. Narlikar J V. 1989, Introduction to Cosmology. Cambridge University Press.

 PHY-511 Lab Course-III (Electromagnetism) 3 (0 – 3) 

1. To determine the resistance of various DC conductors by recording their current/voltage characteristics.
2. To study the internal resistance and matching in various voltage sources and draw their power diagrams.
3. Establishment of relationship between electrostatic force and charge, electrostatic force and distance between charges and to determine the electric constant using Coulomb’s Law / image charge.
4. To study the ferromagnetic hysterisis of a two ring-shaped iron cores by continuous adjustable direct current and to determine the remanence and coersive field strength.
5. Investigation of induced current and voltage in secondary coil of a transformer as a function of number of turns and current flowing in the primary coil.
6. To determine the inductance and phase displacement of coil (single, parallel and series formations) in AC circuit as a function of frequency of voltage source.
7. To determine the capacitance and phase displacement of capacitor (single, parallel and series formations) in AC circuit as a function of frequency of voltage source.
8. To determine the dielectric constants of different materials.
9. To study the ripple of the output voltage of various rectifier circuits as a function of the load current strength and the charging capacitance.
10. To study the frequency response of simple RC filters by point-by-point measurements and the sweep displayed on the oscilloscope.
11. To investigate the filter characteristics as a function of frequency of a coil, a capacitor, an Ohmic resistance and combinations of these components and to determine the phase displacement of the filters as a function of frequency.
12. To study the behavior of RLC series and parallel circuit and determination of its resonance frequency.(Optional: To determine the dielectric constant using RLC series circuit.)
Recommended Books:- 
1. Kraftmakers, Y. 2007. Experiments and demonstrations in Physics, World Scientific Publishing Co. Ltd.
2. David J. Griffiths, Introduction to Electrodynamics, 3rd Edition
3. Isenberg, C. 1996. Physics Experiments and Projects for students (Physics experiments & Projects). Taylor and Francis, USA

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Scheme of Studies (Contents) BS Physics Semester 4

4 th Semester 

PHY-402 | Electricity & Magnetism-II | 3 (3 – 0) 

Faraday’s Law of Electromagnetic induction, review of emf, Lenz’s Law, Induced electric fields, Inductance, Inductance of a Solenoid and Toroid. Transients, LR Circuits, Growth and Decay of current, Energy stored in a magnetic field, Energy density, Electromagnetic Oscillation, Qualitative and Quantitative analysis, Forced electromagnetic oscillations and resonance, Alternating current, AC current in resistive, inductive and capacitive elements, single loop RLC circuit, acceptor and rejecter circuits, Power in A.C circuits, Summarizing the electro-magnetic equations, Induced magnetic fields & displacement current, Maxwell's equations, Maxwell equations in a medium, dielectrics and magnetic materials, e.m spectrum, generating an electro-magnetic wave, Traveling waves and Maxwell's equations, energy transport and the Poynting Vector, Propagation of electromagnetic waves in conducting media and in ionized gases, reflection and transmission at normal and oblique incidence, absorption and dispersion of electromagnetic waves in a conductor.
Recommended Books: 
1. Serway, Raymond A. and Jerry S. Faughn, 2003, College physics, 6th ed, Brooks/Cole Publishin
2. Resnick, Hlliday and Krane. 2002, Physics, Vol II, 5th Ed. John Wiley and Sons Inc, New York
3. Feynman R.P, R.B Leighton and M.Sands. The Fyenman Lectures of Physics; Electromagnetism and matter. Addison Wesley.
4. Griffiths D. 1989, Introduction to Electrodynamics. Prentice Hall.
5. Lorrain P and D.Corson. Electromagnetic Fields and Waves, 2nd Ed. Freeman publications.

 PHY-404 Modern Physics-II 3 (3 – 0)

 Review of Bohr’s theory, Summerfeld model, Frank Hertz Experiment, Stern Gerlach Experiment, quantum numbers, radiactive transition, selection rules, Zeeman Effect (normal and anomalous Zeeman Effect, The Stark Effect, Pauli exclusion principle, Spin orbit coupling LS coupling, JJ coupling, X-ray spectra. Molecular spectra, Ionic and covalent bonding, diatomic molecular-rotational, vibrational and electronic spectra, polyatomic molecules, black body radiation, Einstein co-efficient (A and B coefficients) and stimulated emission, pumping schemes, characteristics of laser, different types of lasers, laser applications. The fine structure of hydrogen, Helium, the ground state of helium, excited states of helium, transitions in helium. 

Recommended Books: 

1. Halliday Resnick, and Walker, 2011. Fundamental of Physics, 9th Ed , John Wiley and Sons Inc, New York,. 

2. Demtroder. W, 2005. Atoms, Molecules and Photons, publisher: Springer 

3. Foot C J. 2005, Atomic Physics 1st Ed, Oxford University Press. 

4. Haken H and H.C. 2004, The Physics of Atoms and Quanta, 7th Ed, Wolf, publisher: Springer 

5. Beiser, A 2002, Concepts of Modern Physics. 6th Ed. McGraw-Hill, USA. 

6. Bransden B H, and Joachain 2003. Atoms and Molecules 2 nd Ed. publisher: Pearson Education. 

7. Halliday Resnick, and Krane, 2002. Physics Vol. II, 5th Ed, John Wiley and Sons Inc, New York 

 PHY-406 Differential Equations-II 3 (3 – 0) 

Modeling with higher order equations, Linear equations, initial-value problems, Spring/Mass systems (Free undamped motion, Free damped motion and driven motion), Resonance and Beats Series Circuit (RC series circuit, LC series circuit, RL series circuit and RLC series circuit), linear equations: boundary value problems, non-linear equations, Series Solutions, Series solutions about ordinary points, Review of Power series, Power series solution, solution about singular points, Method of Frobenius Series solutions, Legendre’s equation, Bessel’s equations, Bessel function of the first kind, Bessel’s function of second kinds, Parametric Bessel’s equation, Differential recurrence relations, spherical Bessel’s function, Legendre Polynomials, Recurrence relations, Laplace transform, Definition of the Laplace transform, Inverse transforms, Transforms of derivatives, Translation Theorems (translation on the s-axis and t-axis), Additional operational properties, Transforms of an integrals and a periodic functions, Dirac Delta function, Laplace transform of a Dirac Delta function, Applications to differential equations and systems of linear differential equations, Systems of linear first order differential equations, Preliminary theory, Homogeneous systems with constant coefficients, Distinct Real eigenvalues, repeated eigenvalues, Complex eigenvalues, undetermined coefficients, Variation of parameters, Matrix exponential 

Recommended Books: 

1. E.Kreyszig, Wiley,1999.“Advanced Engineering Mathematics” New York, 

2. K.F. Riley, M.P. Hobson and S.J Bence,1997 “Mathematical Methods for Physics and Engineering”,Cambridge University press. 

3. G.B Arfken and H.J 1995, “Mathematical Methods for Physicists”, Weber A Press, New York, .

 PHY-408 Lab Course-II (Optics & Modern Physics) 3 (0 – 3)

 1. Characteristic x-rays of Molybdenum 2. Specific rotation of cane – sugar solution with Laurent’s half shade polarimeter. 3. Ionization potential of mercury / Neon. 4. e/m Experiment (determination of charge to mass ratio of electron) 5. X-ray investigation of crystals 6. Characteristic curves of a solar cell. 7. Plank’s constant using photocell method. 8. Wave length of sodium light using a diffraction grating. 

Recommended Books. 

1. Leimbach G, 2005. Physics Laboratory experiment, Germany. 

2. Demtroder.W. 2005. Atoms, Molecules and Photon, Springer. 

 MTH-422 Linear Algebra 3 (3 – 0) 

Vector space, linear dependence, dimensionality, inner product, Hilbert space, linear operators, Gram-Schmidt method, matrices, addition, multiplication, division, derivatives and integrals of matrices, partition of matrices, elementary row operations, systems of linear equations, transpose, unitary and hermitian matrices, eigenvalues and eigen vectors, diagonalization, singular matrix, trace of a matrix, determinants, Cramer’s rule, inverse matrix, linear transformation. Groups, subgroups, homomorphism and isomorphism, group representation, reducible and irreducible representations, Schurs lemma. 

Recommended Books 

1. E.Kreyszig, Wiley,1999.“Advanced Engineering Mathematics” New York, 

2. K.F. Riley, M.P. Hobson and S.J Bence,1997 “Mathematical Methods for Physics and Engineering”,Cambridge University press. 

3. G.B Arfken and H.J 1995, “Mathematical Methods for Physicists”, Weber A Press, New York

 CHM-402 Chemistry (Special Topics) 4 (3 – 1)

 To be provided by the concerned Department

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Map: Govt Postgraguate College Jaranwala

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Scheme of Studies (Contents) BS Physics Semester 3

3rd Semester 

PHY-401 Electricity & Magnetism-I 3 (3 – 0) 

Electric charge, coulombs law, Electric field, continuous charge distributions, image charges, electric dipole, Gauss’s Law and its applications, electric potential, electric properties of materials, capacitor, dielectric, capacitors in circuits, energy stored in capacitors, electric polarization, Gauss’s Law for dielectrics, electric current, current density and Ohm’s law, equation of continuity, DC circuits, analysis of circuits, electric fields in circuits, resistance in circuits, energy transfers in a circuit, RC circuits, magnetism, magnetic force on a charged particle, magnetic torque due to currents, magnetic dipole, Biot-Savart Law and its applications, Ampere’s law and its applications, Gauss’ law for magnetism, origin of atomic and nuclear magnetism, magnetization, magnetic materials: diamagnetic, paramagnetic, ferroamagnetic. Induced magnetic fields and displacement current.
 Recommended Books: 1. Halliday, Resnick and Walker, 2011. Fundamental of Physics, 9th Ed , John Wiley and Sons Inc, New York,. 2. Griffiths D, 2003, Introduction to Electrodynamics, Prentice Hall. 3. Resnick, Hlliday and Krane, 2002, Physics Vol II, Ed. 5th, John Wiley and Sons Inc, New York. 4. Sears, Zemansky and Young, 2000, University Physics Ed. 11th, Addison-Wesley, reading (MA), USA.

 PHY-403 Modern Physics-I 3 (3 – 0) 

1. Halliday, Resnick and Walker, 2011. Fundamental of Physics, 9th Ed , John Wiley and Sons Inc, New York,. 2. Raymond A. Serway and John W. Jewett, January 11, 2010, 8th Edition, Physics for Scientists and Engineers with Modern Physics. 3. Demtroder. W, 2005. Atoms, Molecules and Photons, publisher: Springer 4. Foot C.J., 2005. Atomic Physics 1st Ed, Oxford University Press 5. H. Haken and H.C. 2004, The Physics of Atoms and Quanta, 7th Ed, Wolf, publisher: Springer 6. Bransden B.H, and Joachain 2003. Atoms and Molecules 2 nd Ed. publisher: Pearson Education. 7. Beiser, A 2002, Concepts of Modern Physics. 6th Ed. McGraw-Hill, USA. 8. Halliday Resnick, and Krane, 2002. Physics Vol. II, 5th Ed, John Wiley and Sons Inc, New York

 PHY-405 Differential Equations-I 3 (3 – 0) 

Introduction to differential equations, Definitions and terminology, Initial-value problems, Linear and nonlinear equations, general solution, Particular solution, explicit solution, implicit solution, Differential equations as mathematical models. First order differential equation, Solution curves without the solution, Separable variables, linear differential equations, exact equations, Solution by substitution. Modeling with first order differential equations, linear differential equations, and Non-linear equations, Systems of linear and non-linear equations. Higher-order differential equations, Preliminary theory, linear equations, initial-value and Boundaryvalue problems, homogeneous equations, non-homogeneous equations, Reduction of order, homogeneous linear equations with constant coefficients, Undetermined coefficients (Superposition approach, Annihilator approach), Variation of parameters, Cauchy-Euler equations, Solving systems of linear equations by elimination, nonlinear equations Bernoulli’s equation, first order non-linear ordinary differential equation, Clairaut’s equation, Riccati equation, higher order exact linear equations
Recommended Books: 
 1. E.Kreyszig, Wiley, , 1999. “Advanced Engineering Mathematics”, New York 2. K.F. Riley, M.P. Hobson and S.J. Bence, 1997. “Mathematical Methods for Physics and Engineering”, Cambridge University Press, 3. G.B Arfken and H.J Weber,1995, “Mathematical Methods for Physicists”, A press, New York,. 4. S.J Farlow, McGraw-Hill, 1994. “An Introduction to Differential Equations and their Applications”

 MTH-421 Applied Mathematics 3 (3 – 0) 

Basic concepts of statistics, concept of probability, axioms of probability, discrete probability, & continuous probability, frequencies and probabilities, binomial, Poisson, and normal distributions, mode, mean, median, regression and correlation, sampling theory, analysis of variance. Numerical Analysis, solutions of algebraic and transcendental equations, roots of cubic and biquadratic equations, numerical methods, bisection methods, Newton-Raphson, formula, the secant method, method of false position, numerical solution of simultaneous linear algebraic equations, Gauss elimination method, Cramer’s rule, Choleski’s factorization method, Jacobi iterative method, numerical integration, rectangular rule, Trapezoidal rule, Simpson’s rule, Error analysis. Recommended Books: 
1. F. Riley, M. P. Hobson and S. J. Bence, 1997. “Mathematical Methods for Physics and Engineering” Cambridge University Press,
 2. G. Arfken and H. J. Weber, 1995. “Mathematical Methods for Physicists” Academic Press, 3. E. Butkov, Addison-Wesley1968, “Mathematical Physics” Publishing Company,. 4. “Experimental Measurements” by Precision, Error and Truth by N. C. Barford, Addison-Wesley Publishing Company, Inc. 5. “Modern Statistics” by Richard Goodman, ARC Books, NY.

 ENG-421 Communication Skills 3 (3 – 0) 

To be provided by the concerned Department

 PHY-407 Lab Course-I (Mechanics, Heat and Vibrations) 3 (0 – 3) 

1. Measurement of Oscillation period of the pendulum as a function of the angle of oscillation Φ of the oscillation plane for two different pendulum lengths. 2. Projectile motion: (a) To determine the range as a function of the angle of inclination. (b) To determine the maximum height of projectile as a function of angle of inclination. (c) To determine the range / height as a function of initial velocity of projectile. 3. To determine the value of ‘g’ be compound pendulum (Kater’s Pendulum). 4. To determine Horizontal/Vertical distance by Sextant. 5. To determine the frequency of A.C supply by Melde’s experiment. 6. To determine the modulus of rigidity of a flat spiral spring. 7. To determine the modulus of rigidity of a wire by solid cylindrical rod. 8. Surface tension of water by capillary flow method.
Recommended Books:-
 1. Kraftmakers, Y. 2007. Experiments and demonstrations in Physics, World Scientific Publishing Co. Ltd. 2. Isenberg, C. 1996. Physics Experiments and Projects for students (Physics experiments & Projects). Taylor and Francis, USA.

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BS Physics: Semester 1 (2017-18) Time Table

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Scheme of Studies (Contents) BS Physics Semester 2

2nd Semester 

PHY-302 | Mechanics-II | 3 (3 – 0)

 Rotational dynamics, Relation between Linear & angular variables, K.E of Rotation & Rotational Inertia of Solid bodies, Torque acting on a particle, Parallel & Perpendicular axes theorem, combined Rotational & translational motion, rolling without slipping, Angular momentum of a Particle & system of Particles, Relation between torque & angular momentum. Conservation of angular momentum, spinning top, stability of spinning objects, Newton’s law of universal gravitation, gravitational effects of spherical distribution of matter, gravitational P.E, Gravitational field & Potential, Motion of planets & satellites, Kepler’s laws, Energy consideration in planetary & satellite motion, Bulk Properties of matter, Hook’s Law , Types of elasticity, variation of pressure in earth’s atmosphere, surface tension, general concepts of fluid flow, Bernoulli’s equations, viscosity, Poiseuille’s law.  
Recommended Books:
1. Halliday, Resnick and Walker, 2011. Fundamental of Physics 9th Ed. John Wiley and Sons Inc, New York.
2. Resnick, Halliday and Krane, 2002. Physics Vol. I & II, 5th Ed. John Wiley and Sons Inc, New York.
3. Sears, Zemansky and Young, 2000. University Physics 8th Ed. Addison-Wesley, Reading (MA), USA.
4. Alonso and Finn, 1999. Physics. Addison-Wesley, Reading (M.A), USA.

 PHY-304 | Heat & Thermodynamics | 3 (3 – 0) 

Macroscopic properties of a gas and the ideal gas law, The ideal gas model, Kinetic calculations of pressure, Kinetic interpretation of the temperature, Work done on an ideal gas, The internal energy of an ideal gas, intermolecular forces, Statistical distributions and the mean values, Mean free path, The distribution of molecular speeds, The distribution of energies, The internal energy of an ideal gas, Brownian motion, Heat, The mechanical equivalent of heat, Heat capacity and specific heat, Heat of transformation, Heat capacities of solids, Heat capacities of an ideal gas, The first law of thermodynamics, Applications of the first law, The transfer of heat, Reversible and irreversible process, Heat engines and the second law, Refrigerators and the second law, The Carnot cycle, Carnot’s theorem and the second law, The thermodynamic temperature scale, Entropy: Reversible process, Entropy : Irreversible Process, Entropy and the second law, Zeroth law, , Maxwell’s thermodynamics relations, TDS equations, Clapeyron’s equation, entropy and second law of thermodynamics, temperature scale, entropy, low temperature physics. Thermoelectricity, Seabeck effect, Peltier effect, thermocouple.
Recommended Books:
1. Halliday, Resnick and Walker, 2011. Fundamental of Physics 9th Ed. John Wiley and Sons Inc, New York.
2. Resnick, Halliday and Krane, 2002. Physics Vol. I & II, 5th Ed. John Wiley and Sons Inc, New York.
3. Sears, Zemansky and Young, 2000. University Physics 8th Ed. Addison-Wesley, Reading (MA), USA.
4. Alonso and Finn, 1999. Physics. Addison-Wesley, Reading (M.A), USA.

PHY-306 | Introduction to Programming for Physicists | 3 (3 – 0) 

Introduction to programming, Significance of computers in the present physical sciences scenario, Software and hardware domains, Scientific computing, high and low level languages, flow charts, scientific programming languages, C/C++ and other scientific Programming language: memory management in C++, structure of C++ program, Generic form, Header files, Constants, Local variables, Input/output statements, Simple program, Variables, Data types, variables, Operators, Loops, Break, Continue, If and if-else statements, Conditional operator, Switch statement, Flags and conditional testing, One-dimensional arrays, Multi-dimensional arrays, String manipulation functions, Arrays as lists, Sorting, Searching, functions, built-in and user defined functions, file system, pointer, inheritance, polymorphism, C++ for scientific programming. Lab work. Recommended Books:
1. Deitel H M and P J Deitel, 2012, C++ How to Program, 8/e, Early Objects Version, Prentice Hall 2. Robert Lafore , 2002, Object-oriented Programming in C++, Ed. 4th, SAMS publishers.
3. Robert L, TURBO C++, 1991, Waite Group. 4. Harrison S P and G Steele Jr. 1987, C: A Reference Manual, Prentice-Hall. 5. Peter Norton, Introduction to computers, 6th Ed., McGraw Hill International Edition

MTH-322 | Calculus-II | 3 (3 – 0) 

Riemann integrals and their applications, fundamental theorems of calculus, area under the curve, integration of rational, irrational, trigonometric, exponential and logarithmic functions, improper integrals, beta and gamma integrals. Real functions of several variables, directional derivatives, partial derivatives, local maxima and minima, gradient, chain rule, stationery points, mean value theorems, total differentials, implicit functions, curve tracing, tangents, one parameter family of curves, envelops of a family of curves. Volumes of solids of revolution, area of a surface of revolution, moments and center of gravity, multiple integrals and applications, infinite series, test for its convergence, root and ratio tests, Gauss and integral tests.
Recommended Books: 
1. J.Stewart, 1999“Calculus”, Books/Cole Publishing Co. USA,.
2. G.B. Thomas and R.L. Finney, 1996“Calculus and Analytic Geometry”,.Addison-Wesley Publishing Company,
3. E.W. Swokowski, M.Olinick, 1994. “Calculus” D.Pence, J.A. Cole, PWS Publishing Co. USA,

PST-322 | Pakistan Studies | 2 (2 – 0) 

Historical Perspective, Ideological rationale with special reference to Sir Syed Ahmed Khan, Allama Muhammad Iqbal and Quaid-i-Azam Muhammad Ali Jinnah, Factors leading to Muslim separatism, People and Land, Indus Civilization, Muslim advent, Location and geo-physical features, Government and Politics in Pakistan, Political and constitutional phases, 1947-58, 1958-71, 1971-77, 1977-88, 1988-99, 1999 onward, Contemporary Pakistan, Economic institutions and issues, Society and social structure, Ethnicity, Foreign policy of Pakistan and challenges, Futuristic outlook of Pakistan.
Recommended Books
1. Akbar, S. Zaidi. 2000. Issue in Pakistan’s Economy. Karachi: Oxford University Press 2. Afzal, M. Rafique. 1998.Political Parties in Pakistan, Vol. I, II & III. Islamabad: National Institute of Historical and cultural Research 3. Mehmood, Safdar. 1994. Pakistan Political Roots & Development. Lahore, 4. S.M. Burke and Lawrence Ziring.1993 Pakistan’s Foreign policy: An Historical analysis. Karachi: Oxford University Press,. 5. Haq, Noor ul. Making of Pakistan: 1993. The Military Perspective. Islamabad: National Commission on Historical and Cultural Research, 6. Muhammad Waseem, 1987 Pakistan Under Martial Law, Lahore: Vanguard 7. Burki, Shahid Javed. 1980 State & Society in Pakistan, The Macmillan Press Ltd. 8. Ziring, Lawrence. 1980 Enigma of Political Development. Kent England: WmDawson & sons Ltd,. 9. Zahid, Ansar. 1980. History & Culture of Sindh. Karachi: Royal Book Company 10. Aziz, K.K. Party, 1976. Politics in Pakistan, Islamabad: National Commission on Historical and Cultural Research, 11. Wilcox, Wayne.The Emergence of Banglades., Washington: American Enterprise, Institute of Public Policy Research, 1972. 12. Mehmood, Safdar. Pakistan Kayyun Toota, Lahore: Idara-e-Saqafat-e-Islamia, Club Road, nd. 13. Amin, Tahir. Ethno - National Movement in Pakistan, Islamabad: Institute of Policy Studies, Islamabad. 14. Sayeed, Khalid Bin. 1967. The Political System of Pakistan. Boston: Houghton Mifflin,

 ENG-323 Reading, writing, speaking and listening skills 3 (3 – 0) 

To be provided by the concerned Department

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