Detailed Syllabus of Bachelor of Science (MATH/BIO) (Effective … · 2020. 12. 9. · medium and...

SINGHANIA UNIVERSITY Detailed Syllabus of Bachelor of Science (MATH/BIO)

(Effective from session 2016-17 onward) ---------------------------------------------------------------------------------------------------------------------------------------------

B.Sc (MATH/BIO) 1st , 2nd & 3rd Year Page 1

SYLLABUS & SCHEME (Group A: Physics, Chemistry, Maths ; Group B: Chemistry, Botany, Zoology)

Subject Code Subject Name Sem. Scheme

IA ESE Total Marks L T P

GEN~101 General English Year 1 4 30 70 100

HIN~101 General Hindi Year 1 4 30 70 100

EVS~101 Environmental Studies Theory Year 1 3 1 30 70 100

ECA~101 Elementary Computer Applications Year 1 2 1 1 30 70 100

BSCPH~101 Mechanics Year 1 4 15 35 50

BSCPH~102 Electromagnetism Year 1 4 15 35 50

BSCPH~103 Optics Year 1 4 15 35 50

BSCPH~104 Physics Practical Year 1 4 0 50 50

BSCMT~101 Discrete Mathematics Year 1 4 15 35 50

BSCMT~102 Calculus Year 1 4 15 35 50

BSCMT~103 Three Dimensional Geometry and Optimization Theory Year 1 4 15 35 50

BSCMT~104 Maths Practical Year 1 4 0 50 50

BSCCH~101 Inorganic Chemistry Year 1 4 15 35 50

BSCCH~102 Organic Chemistry Year 1 4 15 35 50

BSCCH~103 Physical Chemistry Year 1 4 15 35 50

BSCCH~104 Chemistry Practical Year 1 4 0 50 50

BSCZO~101 Diversity of Animals and Evolution Year 1 4 15 35 50

BSCZO~102 Cell Biology and Genetics Year 1 3 1 15 35 50

BSCZO~103 Gamete and Developmental Biology Year 1 4 15 35 50

BSCZO~104 Zoology Practical Year 1 4 0 50 50

BSCBO~101 Cell Biology and Plant Breeding Year 1 4 15 35 50

BSCBO~102 Microbiology, Mycology and Plant Pathology Year 1 4 15 35 50

BSCBO~103 Algae, Lichens and Bryophyta Year 1 4 15 35 50

BSCBO~104 Botany Practical Year 1 4 0 50 50

BSCPH~201 Statiscal and Thermodynamical Physics Year 2 4 15 35 50

BSCPH~202 Mathematical Physics and Special Theory of Relativity Year 2 4 15 35 50

BSCPH~203 Electronics and Solid State Devices Year 2 4 15 35 50


BSCMT~201 Real Analysis and Metric Space Year 2 4 15 35 50

BSCMT~202 Differential Equations Year 2 4 15 35 50

BSCMT~203 Numerical Analysis and Vector Calculus Year 2 4 15 35 50






BSCZO~201 Structure and Functions of Invertebrate Types Year 2 4 15 35 50

BSCZO~202 Animal Physiology and Biochemistry Year 2 3 1 15 35 50

BSCZO~203 Immunology, Microbiology & Biotechnology Year 2 4 15 35 50


BSCBO~201 Plant Morphology and Anatomy Year 2 4 15 35 50

BSCBO~202 Cell Biology Genetics and Plant Breeding Year 2 4 15 35 50

BSCBO~203 Plant Physiology and Biochemistry Year 2 4 15 35 50





SYLLABUS & SCHEME

Subject Code Subject Name Sem. Scheme

IA ESE Total Marks L T P

BSCPH~301 Quantum Mechanics and Spectroscopy Year 3 4 15 35 50

BSCPH~302 Nuclear and Particle Physics Year 3 4 15 35 50

BSCPH~303 Solid State Physics Year 3 4 15 35 50


BSCMT~301 Algebra Year 3 4 15 35 50

BSCMT~302 Complex Analysis Year 3 4 15 35 50

BSCMT~303 Dynamics and Computer Programming in "C" Year 3 4 15 35 50






BSCZO~301 Structure of Function of Chordate Types Year 3 4 15 35 50

BSCZO~302 Ecology and Environmental Biology Year 3 3 1 15 35 50

BSCZO~303 Applied Zoology, Ethology and Biostatics Year 3 4 15 35 50


BSCBO~301 Taxonomy and Embryology of Angiosperm Year 3 4 15 35 50

BSCBO~302 Molecular Biology and Biotechnology Year 3 4 15 35 50

BSCBO~303 Plant Ecology & Economic Botany Year 3 4 15 35 50


EXAMINATION SCHEME & PATTERN Max. Marks Internal – 15 ; Term End Exam – 35 (Total – 50)

Min. Pass Marks 36% in Internal, External & Practical individually and 40% Aggregate.

Internal & Continuous Assessment

Assignment 1 – 4 Marks Assignment 2 – 4 Marks Presentation & Viva – 4 Marks Behaviour, Discipline & Attendance – 3 Marks (Total : 15 Marks)

Term End Exam Duration 3 Hrs.

Final Exam Paper pattern Final Exam Paper divides in two parts. Part-A: (10x1 = 10 Marks) SHORT QUESTIONS (Answer in 50 words) Ten questions of two mark each. Two questions from each unit. No choice will be given Part-B: (5x5 = 25 Marks) DESCRPTIVE TYPE QUESTIONS Five questions of ten mark each. Two questions from each unit. 100% Internal Choice will be given from each unit.




PHYSICS




B.Sc. 1st Year (Physics) BSCPH~101 – Mechanics

Unit - I: (a) Inertial and non-inertial frames, Transformation of displacement, velocity, acceleration between different frames of reference involving translation. Galilean transformation and invariance of Newton's laws. (b) Special theory of Relativity: Postulates of Special theory of relativity, Lorentz transformation, transformation of velocity and acceleration, Length contraction and time dilation with experimental verification. Unit - II: Coriolis Force: Transformation of displacement, velocity and acceleration between rotating frame, Pseudo forces, Coriolis force, Motion relative to earth, Focult's pendulum. Introduction about Centre of Mass, Centre of Mass Frame: Collision of two particles in one and two dimensions (elastic and inelastic), Slowing down of neutrons in a moderator, Motion of a system with varying mass, Angular momentum concept, conservation and charge particle scattering by a nucleus. Unit - III: Rigid body: Equation of a motion of a rotating body, Inertial coefficient, Case of J not parallel to o, Kinetic energy of rotation and idea of principal axes, Processional motion of a spinning top. Introduction about Central Forces, Motion under central forces, Gravitational interaction, Inertia and gravitational mass, General solution under gravitational interaction, Keplers Laws, Discussion of trajectories, Cases of elliptical and circular orbits, Rutherford scattering. Unit - IV: Conservative Forces Introduction about conservative and non-conservative forces, rectilinear motion under conservative forces, Discussion of potential energy curve and motion of a particle. Damped Harmonic Oscillations: Introduction about oscillations in a potential well, Damped force and motion under damping, Damped Simple Harmonic Oscillator, Power dissipation, Anharmonic oscillator and simple pendulum as an example. Unit - V: Driven harmonic oscillator with damping, Frequency response, Phase relation, Quality factor, Resonance, Series and parallel of LCR circuit, Electromechanical system-Ballistic Galvanometer. Coupled Oscillations Equation of motion of two coupled Simple Harmonic Oscillators, Normal modes, motion in mixed modes, Transient behavior, Dynamics of a number of oscillators with neighbor interactions. Books Recommended: 1. Mechanics: H S Hans S P Puri, Tata McGraw-Hill 2. Analytical Mechanics L.N. Hand, J.D. Finch. (Cambridge University Press) 3. Mechanics: Berkeley Physics Course Vol- 1, Charles Kittel 4. The Physics of Waves & Oscillations: N.K. Bajaj, Tata McGraw-Hill




BSCPH~102 – Electromagnetism Unit I: Concept of Field, Scalar and Vector Fields, Gradient of scalar field, Physical significance and formalism of Gradient, Divergence and Curl of a vector field in Cartesian co-ordinates system, Problems based on Gradient, Divergence and curl operators. Concept of Solid angle, Gauss divergence and Stoke's theorem. Gauss law from inverse square law. Differential form of Gauss law. Unit II: Potential energy of system of (i) Discrete N-charges (ii) Continuous charge distribution. Energy required to built A uniformly charged sphere, classical radius of electron, Electric field due to a short electric dipole, Interaction of electric dipole with external uniform and non uniform electric field, potential due to a uniformly charged spherical shell. Unit III: Poisson's and Laplace equations in Cartesian co-ordinates and their applications to solve the problems of electrostatics. Invariance of charge, Gaussian and SI units and their inter conversions, Electric field measured in moving frames, Electric field of a point charge moving with constant velocity. Multipole expansion, definition of moments of charge distribution, Dielectrics, Induced dipole moments, polar non polar molecules, Free and bound charges, Polarization, Atomic polarizabilty, electric . displacement vector, electric susceptibility, dielectric constant, relation between' them. Unit IV: Electric potential and electric field due to a uniformly polarized sphere (i) outside the sphere (ii) at the surface of the sphere (iii) inside the sphere, Electric field due to a dielectric sphere placed in a uniform electric field (a) outside the sphere (b) inside the sphere, Electric field due to a charge placed in dielectric medium and Gauss law, Clausius-Mossotti relation in dielectrics, Unit V: Lorentz force, properties of magnetic field, Ampere's law, field due to a current carrying solid conducting cylinder (a) outside (b) at the surface and (ii) inside the cylinder. Ampere's law in differential form, Introduction of Magnetic Vector potential, Poisson's equation for vector potential, Deduction of Bio-Savart law using Magnetic Vector potentials, Differential form of Ampere's law. Atomic magnet, Gyromagnetic ratio, Bohr-Magneton, Larmor frequency, induced magnetic moment and dia-magnetism, spin magnetic moment, para and ferro magnetism, Intensity of Magnetization, Magnetic permeability and Susceptibility, free and bound current densities, Magnetic field due to a uniformly magnetized material and Non-uniformly magnetized material. Books Recommended: 1. Berkley Physics Course, Vol. II 2. Fundamental University Physics Vol II: Fields and Waves, M. Alonso and E.J. Finn; Addison-Wesley Publishing Company, 3. Introduction to Electrodynamics, David J. Griffith, Prentice Hall 4. Electricity & Magnetism; A.S. Mahajan & Abbas A. Rangwala, Tata McGraw-Hill




BSCPH~103 – Optics Unit - I Concept of Spatial and Temporal Coherence, coherence' length, coherence time, Definition and propagation of a wave front. Huygen's principle of secondary wavelets. Young's double slit experiment. Types of interference, interference by division of wave fronts: Fresnel's Biprism, Measurement of wavelength h and thickness of a thin transparent sheet, Interference by division of amplitude: Interference in thin films of constant thickness in transmitted and reflected waves. Interference produced by a wedge shaped film, Newton's rings, Determination of wavelength h and refractive index p by Newton's Rings: fringes of equal inclination (Haidinger fringes) and equal thickness (Fizeau fringes), Michelson's Interferometer, shape of fringes, Measurement of wavelength, difference between two spectral lines and thickness of a thin transparent sheet. Unit - II Fresnel's diffraction, Half period zones, Fresnel's diffraction at a circular aperture, straight eqge and' a 'rectangular slit, Zone plate, Multiple foci of zone plate, comparison between zone plate and convex lens, Fraunhofer diffraction by single slit and a circular aperture, Fraunhofer diffraction by N parallel slits with two slits as a special case, Missing order, Plane diffraction grating and its use in determining wavelength, Dispersion by a grating, Rayleigh's criterion of resolution, Resolving power of a Telescope and a Grating. Unit – III: Polarization : Polarization, Plane, Circular and Elliptically Polarized light, Polarization by reflection, Double refraction and Huygen's explanation of double refraction, Production and detection of Plane, Circular and Elliptically Polarized light, Quarter wave and half wave plates, optical activity, Specific rotation, Biquartz and half shade Polarimeters and their comparison. . Unit – IV Laser: Spontaneous and Stimulated emission Einstein's A&B coefficients, Energy density of radiation as a result f stimulated emission and absorption, population inversion, Methods of Optical pumping, Energy level schemes, He- Ne, Ruby, C02 lasers. Holography: Basic concepts of holography, Principle, Theory, Construction and reconstruction of image, Application of holography Unit – V Wave motion: 1D and 3D wave equation, Transverse waves in a stretched string, elastic waves in solids, Pressure waves in a gas column, spherical waves, Fourier’s Theorem and its application to square and saw tooth waves, Phase and group velocities, Dispersion of waves, Electromagnetic waves, Energy density of Electromagnetic waves, Electromagnetic waves in an Isotropic and Dispersive medium, Spectrum of Electromagnetic waves. Books Recommended: 1. Optics by D. P. Khandelwal. 2. An introduction to Modem Optics by G. R. Fowels. 3. Essentials of Lasers by Allen. 4. Optics by Brij Lal & Subramanium, S. Chand. 5. Principles of optics by B. K. Mathur.




BSCPH~104 - Physics Practical

Section A 1. To determine the specific resistance of a material and determine difference between two small resistance using Carey Fosters Bridge. 2. To convert a galvanometer into a ammeter of a given range 3. To convert a galvanometer into a voltmeter of a given range. 4. To study the variation of charge and current in a RC circuit with a different time constant (using a DC source). 5. To study the variation of power transfer by two different loads by a DC source aid to verify maximum power transfer theorem. 6. To study the behavior of a RC circuit with varying resistance and capacitance using AC mains as a power source and also to determine the impedance and phase relations. 7. To study the rise and decay of current in an LR circuit with a source of constant emf. 8. To study the characteristics of a semiconductor junction diode and determine forward and reverse resistances.

Section B 1. To study the frequency of energy transfer as a function of coupling strength using coupled oscillators. 2. To find J by Callender and Barne's Method. 3. To determine Youngs modulas by bending of beam. 4. To determine Y, o and 7 by Searle's method. 5. To ensure Curie temperature of Monel alloy. 6. To study the random decay and determine the decay constant using the statistical board. 7. To determine modulus of rigidity of a wire using Maxwell's needle. 8. To study variation of surface tension with temperature using Jaegger's method. 9. To study the specific-rotationo f sugar solution by polarimeter. 10. To study the viscous fluid damping of a compound pendulum and determining damping coefficient and Q of the oscillator. 11. Using compound pendulum study the variation of time period with amplitude in large angle oscillations. 12. To study the damping using compound pendulum. 13. To study the excitation of normal modes and measure frequency splitting using two coupled oscillators.




B.Sc. 2nd Year (Physics) BSCPH~201 - Statistical and Thermo dynamical Physics

Unit – I Thermo chemistry: Introduction, Standard state, standard enthalpy of formation-Hess’s Law of heat summation and its applications,Heat of reaction at constant pressure and at constant volume, Enthalpy of neutralization,Bond dissociation energy and its calculation from thermo-chemical data, temperature dependence of enthalpy, Kirchhoff’s equation. Entropy: Introduction, concepts of entropy and temperature, entropy maximum and energy minimum principles. Multiplicity and disorder,Thermodynamic potentials. Thermal equilibrium: Introduction, conditions of equilibrium, concepts of stability, Maxwell’s equations, metastable and unstable equilibrium; components and phases, Gibbs- Duhem relations; first order phase transitions and Clausius-Clapeyron equation; critical phenomena, some chosen applications from magnetic, dielectric and superconducting; black body radiation.

Unit – II Thermodynamics of Irreversible Processes: Introduction, entropy production; Elementary kinetic theory of gases; transport phenomena. First and Second Laws of Thermodynamics: Introduction, Internal Energy and Enthalpy, Heat capacity, Joule’s Law, Need for the Second Law, Different Statements of the Second Law. Interacting Systems in Equilibrium: Introduction, Van der Waals Equation Cluster expansions and related techniques.

Unit – III Critical Phenomena and Phase Transitions: Introduction, First Order Transitions and Phase Equilibria, Critical Points, Magnetic Transitions, Weiss Mean Field Theory, Phase Transitions of the Second Kind, Landau Theory. Theories of Classical Gases and Liquids: Introduction, The Free Energy of an Interacting System, Second Virial Coefficient, High Temperature Expansion, Density Expansion, Computer Simulation of Liquids. Statistical Mechanics: Introduction to statistical mechanics and distribution functions. Occupation M-B, B-E, F-D statistics, distribution functions, criteria for applicability of classical statistics.

Unit – IV The Methodology of Statistical Mechanics: Introduction, the Fundamental Principles, Thermodynamic Averages, Thermodynamic Variables, Classical Statistical Mechanics. Magnetic Systems: Introduction, No interacting Magnetic Moments, Thermodynamics of Magnetism, The Ising Model, The Ising Chain, Mean-Field Theory. Many Particle Systems: Introduction, Classical Statistical Mechanics, Occupation Numbers and Bose and Fermi Statistics, Distribution Functions of Ideal Bose and Fermi Gases, Single Particle Density of States, The Equation of State of an Ideal Classical Gas Application of the Grand Canonical Ensemble, Blackbody Radiation.

Unit – V Critical Phenomena and the Renormalization Group: Introduction, The One-Dimensional Model, Recursion Relations, Critical Phenomena, Phase Transitions, Critical Behaviour. Specific Heat: Introduction, Specific Heat of Classical Gas, Fermi Gas, Electronic Contribution to Specific Heat of Metals, Energy Bands in Conductors, Modifications at Metal-Metal Contact. Thermodynamic Quantities in Equilibrium: Introduction, The Concept of an Ensemble, The Micro Canonical Ensemble, Canonical Ensemble, Macro Canonical (Grand Canonical) Ensemble, Other Ensembles. Books Recommended:

1. Berkeley series Vol. V, Statistical Physics 2. Lokanathan and Khandelwal-Thermodynamics and Statistical -Physics 3. Sears- Thermodynamics, Kinetic theory of gases and statistical Physics 4. Kittte - Thermal Physics




BSCPH~202 - Mathematical Physics and Special Theory of Relativity

UNIT-I Orthogonal curvilinear coordinate system, scale factors, expression for gradient, divergence, curl and their application to Cartesian circular cylindrical and spherical polar coordinate. Coordinate transformation and Jacobian, transformation of covariant, contra-variant and mixed tensor: Addition, multiplication and contraction of tensors; Metric tensor and its use in transformation of tensors. Dirac delta function and its properties.

UNIT-II Lorentz transformation and rotation in space-time like and space like vector, world line, macro causality. Four vector formulation, energy momentum four vector relativistic equation of motion. Invariance of rest mass, orthogonally of four force and four velocity. Lorentz force is an example of force, transformation of four frequency vector. Longitudinal and transverse Doppler effect.

UNIT-3 Transformation between laboratory and canter of mass system, four momentum conservation, kinernatics of decay, products of unstable particles and reaction thresholds. Pair production, inelastic collision of two particles. Compton effect. (a) Transformation of electric and magnetic fields between two inertial frames.

UNIT-4 (b) The second order linear differential equation with variable coefficient and singular points, series solution, method and its application to the Hermite’s Legendre’s and Laguerre’s differential equations. Basic properties like orthogonally, recurrence relations, graphical representation and generating function of Hermite Legendre. Leaguers and Associated Legendre function (simple applications). Techniques of separation of variables and its application to following boundary value problems (i) Laplace equation in three dimensional Cartesian coordinate system line charge between two earthed parallel plates

UNIT-5 Techniques of separation of variables and its application to following boundary value problems (a) Helmholtz equation in circular cylindrical coordinates cylindrical resonantcivity. (b) Wave equation in spherical polar coordinates the vibrations of a circular membrane. (c) Diffusion equation in two dimensional Cartesian coordinate system heat conduction in a thin rectangular plate, (d) Laplace equation in spherical coordinate system electrical potential around a spherical surface.




BSCPH~203 - Electronics and Solid State Devices Unit – I

Circuit analysis: Networks- some important definitions, loop and nodal equation based on D.C. and A.C. circuits (Kirchhoffs Laws). Four terminal netivork: Ampere volt conventions, open, close and hybrid parameters of any four terminal netivorh. Input, output and mutual impendence for an active four terminal network. Various circuit theorems: Superposition, Thevenin, Norton. reciprocity. compensation, maximum power transfer and hliller theorems. PN junction: Charge densities in N and P materialb: Cond~lction by drift and diffusion of charge carriers. PN diode equation; capacitance effects. P-N Junction: Built in potential, width and capacitance of depletion region; Current flow in biased p-n

junction, Varactor diode; Zener breakdown mechanism, Zener diode and its characteristics, Photo diode

and Solar cell.

Unit – II

Basic Semiconductor Physics: Basic features of energy band theory of solids; energy band pictures of

semiconductors, electron-hole densities.

Electrical conductivity of intrinsic and extrinsic semiconductors: minority and majority charge carriers drift

and diffusion currents, concept of continuity equation for minority charge carrier.

Rectifiers: Half-wave, full wave and bridge rectifier calculation of ripple facto, efficiency and regulation, Filters: series inductor. Shunt capacitor. L section and n-section filters. Voltage regulation: Voltage regulation and voltage stabilization by Zener diode, voltage multiplier.

Unit – III

Transistors: n-p-n and p-n-p transistors, current flow in transistors, potential divider biasing of transistors,

characteristics in all three configurations; á, â and hybrid parameters and their relationship, FET and

MOSFET, Principle of operation, characteristics and parameters.

Amplifiers: Small signal hybrid equivalent circuit of BJT, RC coupled CE amplifiers, frequency and phase

response. Amplifier circuit using FET.

Unit – IV

Oscillators: Oscillator as positive feedback amplifier, Barkhausen criteria of sustained oscillation, LC tuned

collector oscillator, Hartley and Colpitts transistor oscillator.

Modulation and Demodulation: Definition of three kinds of modulations, expression for AM, FM and PM

waves, Vander-Brijl modulator, linear diode detector.

Radio Transmitter and Receiver: AM transmitter (block diagram and function of different blocks); Principle

of simple and super heterodyne radio receiver, Qualities of radio receiver (selectivity, sensitivity, and

fidelity), Standard broadcast radio receiver, Image frequency, AVC and tuning indicator.

Unit – V

Number system: Introduction, binary numbers, Decimal Number System, Bi-stable Devices, Octal number

System, Hexadecimal Number System, conversion.

Boolean algebra: Introduction, De Morgan’s theorem. Logic Gates: Introduction,OR,AND, NOT, NAND, NOR and XOR gates. Universality of NOR and NAND gates. Books Recommended:

1. John D. Ryder, Engineering Electronics, McGraw Hill Book Company, New Delhi. 2. Jacob Millman and Christose Hailkias, Integrated Electronics Analog and Digital Circuits and systems: MCG&-HiII Ltd. 3. G.K. Mithal, Hala Book of Electronics. 4. Kumar & Gupta, Hand book of Electronics.




BSCPH~204 - Physics Practical

Section – A 1. Study of dependence of velocity of wave propagation on line parameter using tosional Wave

apparatus. 2. Using platinum resistance thermometer finds the melting point of a given substance. 3. Using Newton's rings method find out the wave length of a .monochromatic source-and find .the

refractive index of liquid. 4. To determine dispersive power of prism. 5. To determine wave length of sodium light using grating. 6. To determine wave length of sodium light using Biprism. 7. To determine thermal conductivity of a bad conductor by Leo’s method.' 8. Determination of ballistic constant of a ballistic galvanometer. 9. Study of variation of total thermal radiation with temperature.

Section – B 1. Study of half wave rectifier using single diode and application of L and π section filters. 2. Determination of band gap using a junction diode. 3. Study of single stage transistor audio amplifier ( Variation of gain with frequency) 4. To determine e/m by Thomson’s method. 5. Determination of velocity of sound in air by standing wave method using speaker, microphone, and

CRO. 6. Measurement of inductance of a coil by Anderson’s bridge. 7. Study of power supply using two diodes/bridge rectifiers with various filter circuits.

Plot thermo emf V/S temperature graph and find the neutral temperature




B.Sc. 3rd Year (Physics) BSCPH~301 - Quantum Mechanics and Spectroscopy

Unit – I Origin of Quantum Theory : Failure of classical Physics to explain the phenomenon such as black body spectrum, Planck’s radiation law, photoelectric effect and Einstein explanation, Compton effect de Broglie hypothesis, evidence for diffraction and interference of particles. Uncertainty principle and its consequences gamma ray microscope, diffraction at a single slit, Application of uncertainty principle, (i) Non existence of electron in nucleus. (ii) Ground state energy of H-atom Ground state energy of harmonic oscillator, Energy-time uncertainty. Classical Theory of Radiation: Maxwell’s equation and electromagnetic waves. Poynting vector. Classical dipole radiation. Simple harmonic oscillator. Absorption cross-section. Thomson and Rayleigh scattering formula. Bremstrahlung, Gyromagnetic, Synchrotron and Cerenkov radiations. Quantum Mechanics and Spectroscopy: Bohr-Sommerfeld theory of atomic spectra. Electron spin. LS and JJ coupling. Spectroscopic terminology. de Broglie waves. Schrodinger equation for stationary states. Simple harmonic oscillator in one and three dimensions. Hydrogen atom. Quantum mechanical operators. Angular momentum. Elementary perturbation theory. Semi-classical treatment of Zeeman and Stark effects. Pauli’s exclusion principle. Periodic Table. Unit – II Molecular Spectra: Pure rotational spectrum of a diatomic molecule. Vibration-rotation spectrum. Electronic bands and sequences. Frank-Condon principle. Strengths of bands, lines and continuum. Multiple structure of electronic states. Isotope effect in band spectra. Schrodinger Equation : time dependent and time independent form, Physical significance of the wave function and its interpretation, probability current density, operators in quantum mechanics, linear and Hermitian operators, Expectation values of dynamical variables, the position, momentum, energy. Fundamental Postulates of Quantum Mechanics: eigen function and eigen value, degeneracy, orthogonality of eigen functions, commutation relations . Ehrenfest theorem, concept of group and phase velocities, wave packet Unit – III Simple Solutions of Schrodinger Equation : Time independent Schrodinger equation and stationary state solution, Boundary and continuity conditions on the wave function, particle in one dimensional box, eigen function and eigen values, discrete energy levels, extension of results for three dimensional case and degeneracy of levels. Potential step and rectangular potential barrier, calculation of reflection and transmission coefficient, Qualitative discussion of the application to alpha decay (tunnel effect), square well potential problem, calculation of transmission coefficient Bound State Problems: Particle in one dimensional infinite potential well and finite depth potential well, energy value and Eigen functions. Simple harmonic oscillator (one dimensional) eigen function, energy eigen values, zero point energy. Schrodinger equation for a spherically symmetric potential, Separation of variables, Orbital angular momentum and its quantisation, spherical harmonics, energy levels of H-atom, shape of n=1, n=2 wave functions, comparison with Bohr model and Correspondence principle. Elementary Spectroscopy: Quantum features of one electron atoms, Frank-Hertz experiment and discrete energy states, Stern and Gerlach experiment, Spin and Magnetic moment, Spin Orbit coupling and qualitative explanation of fine structure. Atoms in a magnetic field, Zeeman Effect, Zeeman splitting.




Unit – IV Qualitative Features of Molecular Spectroscopy: Rigid rotator, discussion of energy eigenvalues and eigenfunctions, Rotational energy levels of diatomic molecules, Rotational spectra, Vibrational energy levels of diatomic molecules, Vibrational spectra, Vibrational Rotational spectra, Raman Mechanics. Applications of Quantum : The particle in a box energy quantization, wave functions, Momentum Quantization, The particle in a three dimensional box. Schrodinger equation for the hydrogen atom, separation of variables, Quantum numbers –Total quantum number, Orbital quantum number, Magnetic quantum number. Atomic Physics : The vector atom model, Quantum numbers associated with the vector atom model, L-S and J-J coupling, The Pauli’s exclusion Principle, Selection rules, Intensity rules, Interval rule, Normal Zeeman effect, Anomalous Zeeman effect, Stark effect. Unit –V Molecular Spectra: Theory of pure rotational spectra, Theory of rotation-vibration spectra, Raman Effect, Experimental study, Raman Effect in solids, liquids and gases. Matter Waves: Introduction, Compton Effect, de Broglie wave length, Wave function, Relation between Wave and Group velocity, Davisson and Germer experiment, G.P.Thomson’s Experiment, Heisenberg’s uncertainty principle and its applications. Spectroscopic Techniques : Electromagnetic Radiation, Visible and Ultraviolet Spectroscopy, Beer-Lambert Law, Recording and Interpreting UV-vis Spectra, Vibrational Spectroscopy, Fundamental Vibrational Modes, Infrared Spectroscopy, Infrared Spectra, Raman Spectroscopy, Origin of Raman Scattering, Raman Scattering, Raman vs. IR, Surface Enhanced Raman Spectroscopy (SERS), Single Molecule SERS, Coherent Anti-Stokes Raman Spectroscopy (CARS), Nuclear Magnetic Resonance Spectroscopy (NMR), Theory of NMR, Theory of NMR, NMR Spectra, Solid State NMR, Electron Spin Resonance (ESR) Spectroscopy, Theory of ESR, ESR Spectrum, NMR vs. ESR, X-ray Spectroscopy, X-ray Emission, Absorption Techniques, X-ray Absorption Near Edge Structure (XANES), Extended X-ray Absorption Fine Structure (EXAFS), Electron Spectroscopics, ESCA and Auger Process, X-ray Photoelectron Spectroscopy (XPS), Mössbauer Spectroscopy, Mass Spectrometry, Instrumentation of Mass Spectrometer, Ionization Methods, MS Spectrum, Thermal Analysis, Applications of Thermal Analysis, Applications of Thermal Analysis. Books Recommended:

1. R. Shankar, Principles of Quantum Mechanics, 2nd edition. 2. AK Ghatak and S Lokanathan, Quantum Mechanics: Theory and application. 3. HS Mani, GK Mehta, Introduction to modem Physics. 4. H.E. White, introduction to atomic physics, 5. David J. Griffiths, Introduction to Quantum Mechanics, 2nd edition.




BSCPH~302 - Nuclear and Particle Physics Unit – I Nuclear Detector: Introduction, Ionization Chamber, Differentiating and Integrating Circuited. Particle Accelerators: Introduction, Ion Sources, High Voltage Acceleration Devices, The Cyclotron, Betatrons, The Principle of Phase Stability. General Properties of Atomic Nuclei: Introduction, Nuclear Size, Nuclear Mass and Mass Spectroscopy, Double Focussing Spectrometer, Mass Synchrometer.

Unit – II Two Body Problem and Nuclear Forces: Introduction, The Deuteron, The Meson Theory of Nuclear Forces, High Energy Nucleon-Nucleon Scattering. (E > 10 MeV), Interpretation of High Energy Nucleon-Nucleon Scattering-Exchange Forces. Nuclear Models: Introduction, The Degenerate Gas Model, The Liquid Drop Model, Simple Shell Model, Collective Model. Radio Activity: Introduction, Law of Radioactive Decay, Average or mean Life or an Atom, Units of Radioactivity, Radioactive Processes.

Unit –III Alpha Ray Emission: Introduction, Properties or Alpha-Particles, Scattering of Alpha-Particle, Energetic of á Decay, Nuclear Energy Levels. Beta Decay: Introduction, Transverse Type-Spectrometers, General Features of -Ray Spectrum, Fermi’s Theory of -Decay, Forms of Interaction and Selection Rules. Gamma-Rays: Introduction, The Absorption of -rays By Matter, Photo-electric Absorption, Compton Scattering, The Measurement of -Rays Energies, Multipole Radiations.

Unit – IV Neutron and Reactor Physics: Introduction, Neutron Sources, Nuclear Reactors as Neutron Sources, Detection of Fast Neutrons, Neutron Spectrometers and Mono-Chromators. Nuclear Reactions: Introduction, Conservation Laws for Nuclear Reactions, Reaction Energetic -The Q•Value Equation, Charged Particle Induced Nuclear Reactions, Charged Particle Reaction Spectroscopy. Theories of Nuclear Reactions: Introduction, The Compound Nucleus, Resonance Scattering and Reaction Cross-Sections, Continum Theory of Nuclear Reactions.

Unit – V Nuclear Energy: Introduction, Mass and Energy Distribution of Fission Fragments, Theory of Nuclear Fission and the Liquid Drop Model, Heterogeneous Reactors, Nuclear Fusion-Thermo-Nuclear Energy. Elementary Particles: Introduction, Classification of Elementary Particles, Fundamental Interactions, Response of Particles to Strong, Electromagnetic and Weak Interactions, Conservation Laws and there Validity. Properties of Elementary Particles: Introduction, The Massless Bosons, The Leptons, The Mesons, Resonance States of Elementary Particles. Books Recommended:

1. H.S. Mani, G.K. Mehta, Introduction to Modern Physics, East West Press Pvt. Ltd., Now Delhi. (1988) 2. Richtmeyer, Kennard and Cooper, Mc Graw-Hill, 1959, sixth edition. 3. A. Beiser, Perspectives of Modem Physics 4. S.S. Rawat and S.Singh, Elementary Quantum Mechanics and Spectroscopy (in Hindi) 5. Parasmal Agrawal, Q.uantum Theory 6. Concepts of Modern Physics, A. Beiser, McGraw-Hill Book Company. 7. Nuclear and Particle Physics, Brian R Martin, John Wiley & Sons.




BSCPH~303 - Solid State Physics Unit – I

Atomic Structure: Introduction, The Rutherford Model of the Atom, Bohr Model of Atom 1.3 Bohr’s Interpretation of Hydrogen Spectrum. Sommerfeld’s Relativistic Atom Model: Introduction, Elliptical Orbits for Hydrogen, Sommerfeld’s Relativistic Correction, Fine Structure of H Line, The Characteristic Quantum Numbers, The Pauli’s Exclusion Principle. Inter-Atomic Force and Bonding in Solid: Introduction, Cohesion of Atoms, Cohesive Energy, Properties of Ionic Compoun, 3.4 ionic bonding.

Unit – II Covalent Bond in Solids: Introduction, Saturation in Covalent Bonds, Hybridization, Metallic Bonding, Solid State Structure, Primary Metallic Crystalline Structures (BCC, FCC, HCP). Crystal Physics: Introduction,, Lattice Points and Space Lattice, Crystal System. Metallic Crystals Structure: Introduction, Other Cubic Structures, Direction, plane and Miller Indices6.3 Summary, Allotropy and Polymorphism.

Unit – III Wave Nature of Matter and X –Ray Diffraction: Introduction, The de Broglie hypothesis, Experimental Study of Matter Waves, The Davisson –Germer Experiment, X- Ray Diffraction. Electrical Properties of Metals : Introduction, Classical Free Electron Theory of Metals, Drift Velocity, Mobility, Mean Collision Time, Relaxation Time and Mean Free Path, Quantum Free-Electron Theory, Heat Capacity, Classical Wave Equations. Thermal Conductivity in Metals : Introduction, Thermal Expansion, Mechanical Effects on Electrical Resistance, Thermal Emission, Magnetism in Metal, Classical Wave Equations.

Unit – IV Thermal Properties of Solids : Introduction, Lattice Specific Heat, Classical Theory (Dulong and Petit Law), Einsteins Theory of Specific Heat, Debye’s Theory. Superconductive : Introduction, A survey of superconductors, Mechanisms of superconductors, Thermal Properties.

Unit – V Thermodynamics of Superconductors: Introduction, BCS Theory, Quantum Theory, New Superconductors Magnetic Properties of Materials: Introduction, Magnetic Permeability, Magnetization, Demagnetization, Paramagnetism. Ferromagnetism : Introduction, Spontaneous Magnetization in Ferromagnetic Materials, Weiss Molecular Field, Domain theory of Ferromagnetism, Domains, Antiferromagnetism, Magnetic Materials Semiconductor: Introduction, Preparation of Semiconductor Materials, Intrinsic Semiconductors, Electron and hole Densities, Hall Effect. Books Recommended:

1. Introduction to Nuclear Physics, Wong 2. Nuclear Physics, R C Bhandari & D Somayajulu 3. Solid state Physics by G.1 Epifanov (Mir R Publisher,) 4. Introduction to Nuclear Physics, W.E. Burcharn 5. Modern Physics, HS Mani & G K Mehta




BSCPH~304 - Physics Practical Section – A

1. Study of polarization by reflection from a glass plate with the help of Nichol's prism and photo cell and verification of Brewster law and law of Malus. 2. Study of the temperature dependence of resistance of a semiconductor (four probe method). 3. Determination of Planck's constant by photo cell (retarding potential method using optical filters, preferably five wave length). 4. Study of B-absorption in Al foil using GM Counter. 5. To find the magnetic susceptibility of a paramagnetic solution using Quinck’s method. Also find the ionic molecular susceptibility of the ion and magnetic moment of the ion in terms of Bohr magneton. 6. Determination of coefficient of rigidity as a function of temperature using torsional oscillator (resonance method). 7. Measurernent of electric charge by Millikan's oil drop method.. 8. Determination of Planck's constant using solar cell. 9. Determination of Stefan's constant (Black body method) 10. Study of Iodine spectrum -with the help of grating and spectrorneter and ordinary bulb light. 11. Study of characteristics of a GM counter and verification of inverse square law for the same strength of a radioactive source.

Section – B 1. Study of a KC transmission line at 50 Hz 2. Study of the characteristics of junction diode & Zener diode. 3. To design Zener regulated power supply and study the regulation with various loads. 4. To study the frequency response .of a transistor amplifier and obtain the input and output

impendence of the amplifier. 5. To study a voltage multiplier circuit to generate high voltage D.C. from A.C. 6. Using discrete components, study OR, AND, NOT logic gates, compare with TTL integrated- circuits

(I.C.'s). 7. Study of

(i) Recovery time of junction diode and point contact diode. (ii) Recovery time as a function of frequency of operation and switching current.

8. To design and study of an R-C phase shift oscillator and measure output impedance (frequency response with change of component of R and C)

9. Application of operational amplifier (OP-AMP) as : Minimum two of the following exercises-fa) Buffer (for accurate voltage measurement) (b) Inverting amplifier (c) Non inverting amplifier (d) Summing amplifier.




MATHEMATICS




B.Sc. 1st Year (Mathematics) BSCMT~101 - Discrete Mathematics

Unit – I

Sets and Propositions - Cardinality, Principal of inclusion and exclusion, Mathematical induction. Relations and Functions- Binary relations, Equivalence relations and Partitions, Partial ordered relations and Lattices, Chains and Antichains, Pigeon Hale principle.

Unit – II

Algebraic structures - Groups, Rings, Integral domains, Fields (Definitions, simple examples and elementary properties only).

Boolean Algebras- Lattices and Algebraic structure, Duality, Distributive and Complemented Lattices. Boolean Lattices, Boolean functions and expressions.

Unit – III

Logic and Propositional Calculus, Propositions, Simple and compound, Basic Logical operations, Truth tables, Tautologies and contradictions, Propositional Functions, quantifiers.

Discrete numeric functions and Generating functions. Recurrence relations and Recursive Algorithms - Linear Recurrence relations with constant coefficients. Homogeneous solutions. Particular solution. Total solution. Solution by the method of generating functions.

Unit – IV

Graphs - Basic 'terminology, Multigraphs, Weighted graphs, Paths and circuits, Shortest paths, Eulerian paths and Circuits. Travelling Salesman problem. Union, Join, Product and composition of graphs. Planar graphs and Geometric dual graphs.

Unit – V

Trees - Properties, Spanning tree, Binary and Rooted tree.

Digraphs - Simple digraph, Asymmetric digraphs, Symmetric digraphs and complete digraphs. Digraph and Binary relations. Matrix representation of graphs and digraphs.




BSCMT~102 - Calculus Unit I:

Series - Infinite series and Convergent series. Tests for convergence of a series- Comparison test, D'Alembert’s ratio test, Cauchy's n-th root test, Raabe's test, De-Morgan-Bertrand's test, Cauchy's condensation test, Gauss's test, (Derivation of tests is not required). Alternating series. Absolute convergence. Taylor's theorem. Maclaurin's theorem. Power series expansion of a function. Power series expansion of sinx, cosx,

Unit – II Exact Differential Equations: Introduction, Exact Differential Equations, Non Exact Differential Equation.

Differential Equations of First Order and Higher Degree: Introduction, Differential Equation of First Order and Higher Degree, Clairaut’s Equations, Singular Solutions.

Geometrical Meaning of a Differential Equation: Introduction, Geometrical meaning of a Differential Equation, Orthogonal Trajectories, Linear Differential Equations with Constant Coefficients, Ordinary Homogeneous Linear Differential Equations.

Unit – III

Envelopes, Maxima and Minima: of functions of two variables. Lagrange's method of undetermined multipliers. Asymptotes. Multiple points. Curve tracing of standard curves (Cartesian and Polar curves).

Unit – IV

Double integrals in Cartesian and Polar Coordinates, Change of order of integration. Triple integrals. Application of double and triple integrals in finding areas and volumes. Dirichlet's integral.

Unit – V Rectification: Introduction, Rectification (Length of a Curve), Different Forms of Rectification.




BSCMT~103 - Three Dimensional Geometry and Optimization Theory

Unit – I

Polar equation of conics, polar equation of tangent, normal and asymptotes, chord of contact, auxiliary circle, dircector circle of conics.

Unit – II

Sphere, Cone.

Unit – III

Cylinder, Central Conicoids - Ellipsoid, Hyperboloid of one and two sheets, tangent lines and tangent planes, Direct sphere, Normal’s.

Unit – IV

Generating lines of hyperboloid of one sheet system of generating lines and its properties. Reduction of a general equation of second degree in three-dimensions to standard forms.

Unit – V

The linear programming problem. Basic solution. Some basic properties and theorems on convex sets. Fundamental theorem of L.P.P. Theory of simplex method only Duality. Fundamental theorem of duality, properties and elementary theorems on duality only.




BSCMT~104 - Maths Practical Group A: Modelling of industrial and engineering problems in to mathematical LPP and its dual and their solution by Simplex Method. Group B: Modelling of industrial and engineering problems into (i)Assignment Problems and (ii) Balanced and unbalanced Transportation Problems. And their solution. Note: 1. Problems will be solved by using Scientific Calculators (non-Programmable). 2. Candidates must know about all functions and operations of Scientific Calculator.




B.Sc. 2nd Year (Mathematics) BSCMT~201 - Real Analysis and Metric Space

Unit – I Properties of the Real Numbers: Introduction, The Real Number System, Order Structure, Bounds, Sups and Infs, the Rational Numbers Are Dense, Inductive Property of IN, The Metric Structure of R. Elementary Topology: Introduction, Compactness Arguments, Bolzano-Weierstrass Property, Cantors Intersection Property, Cousins Property, Heine-Borel Property, Compact Sets. Infinite Sum: Finite Sums, Infinite Unordered Sums, Ordered Sums: Series.

Unit – II Sets of Real Numbers: Introduction, Points, Sets, Elementary Topology. Contraction Maps: Introduction, Applications of Contraction Maps (I), Applications of Contraction Maps (II), Compactness, Continuous Functions on Compact Sets, Total Boundedness, Compact Sets in C [a, b]. The Integral: Introduction, Cauchy’s First Method, Scope of Cauchy’s First Method, Properties of the Integral, Cauchy’s Second Method, Cauchy’s Second Method (Continued), The Riemann Integral, The Improper Riemann Integral.

Unit – III Differentiation: Introduction, Defined the Derivative, Mean Value Theorem, Monotonicity, Dini Derivates, Convexity. Sequences: Introduction, Sequences, Divergence, Convergence, Sub sequences. Sequences and Series of Functions: Introduction, Point-wise Limits, Uniform Limits, Uniform Convergence and Continuity.

Unit – IV Continuous Functions: Introduction, Limits (å-ä Definition), Limits (Sequential Definition), Limits (Mapping Definition), One-Sided Limits, Infinite Limits, Properties of Limits. More on Continuous Functions and Sets: Introduction, the Baire Category Theorem, Cantor Sets, An Arithmetic Construction of K, The Cantor Function, Borel Sets. Metric Spaces: Introduction, Metric Spaces, Additional Examples, Function Spaces, Convergence, Functions.

Unit – V The LP Spaces: Introduction, The Basic Inequalities, The lp and Lp Spaces (1 d” p < “), The Spaces l” and L”, Separability, The Spaces l2 and L2, Continuous Linear Functional, The Lp Spaces (0 < p < 1). The Euclidean Spaces: Introduction, The Algebraic Structure of Rn, The Metric Structure of Rn, Elementary Topology of Rn, Sequences in Rn, Coordinate-Wise Convergence, Functions and Mappings, Limits of Functions from Rn ’! Rm, Coordinate-Wise Convergence. Differentiation on Euclidean Spaces: Introduction, Partial and Directional Derivatives, Integrals Depending on a Parameter, Differentiable Functions.




BSCMT~202 - Differential Equations

Unit – I Equations of First Order and First Degree: Introduction, Homogeneous Equations, Non- homogeneous Equations of First Degree in x and y, Exact Differential Equations, Integrating Factors (I.F). Equations of First Order but not of First Degree: Introduction, Equations which can be factorised into Factors of First Degree, Equations which cannot be factorised into Factors of First Degree, Equations Solvable for y, Equations Solvable for x, Equations in which either x or y is absent, Equations Homogeneous in x and y, Equations of First Degree in x and y. Linear Equations with Constant Coefficients: Introduction, Symbolic Operator, Method of finding C. F, Methods of finding Particular Integral, To Find Particular Integral when X= eax where ‘a’ is

1 m

constant, To Find Particular Integral when X=cos ax or sin ax, To Find the value of f D x where m is a positive integer.

Unit – II Homogeneous Linear Equations with Variable Coefficients: Introduction, Method of Solution, To Find Complementary Function, Symbolic Notation in 5ØÉÞ, To find Particular Integral, Particular

1 m f x case to find, Equations Reducible to Homogeneous Linear Equations. Exact Differential Equations and Equations of Particular Forms: Introduction, Condition for the Exactness of the Linear Differential Equation, Solution of Non-linear Equations which are Exact, Equations of the form y(n) =f(x), Equations of the form y(2) =f(y), Equations that do not contain y directly, Equations that do not Contain x Directly, Equations in which y Appears in only Two Derivatives whose Orders Differ by Two, Homogeneous Equations. Linear Equations of Second Order: Introduction, Method of solving Equation when an integral included in the C.F. is known, Method of Solving Equation by Changing the Dependent Variable, Method of Solving Equation by Changing the Independent Variable, Solution by Factorization of the Operator, Method of Variation of Parameters, Method of Undetermined Coefficients.

Unit – III

Simultaneous Differential Equations: Introduction, Simultaneous Equations with Constant Coefficients, Simultaneous Equations with Variable Coefficients, Method of Solution of Equations in Symmetrical Form, Method of Introduction of a New Variable. Total Differential Equations: Introduction, Condition of Integrability, Method of Obtaining the Primitive, Solution by Inspection, Non-Integrable Single Differential Equations, Equations Containing More Than Three Variables, Equations Containing More Than Three Variables of Method of Solution. Partial Differential Equations of First Order: Introduction, Classification of Integrals, Singular Integral, Geometrical Interpretation of three Types of Integrals, Singular Integral from the Partial Differential




Equation Directly, Derivation of Partial Differential Equations by the Elimination of Arbitrary Functions, Solution of Partial Differential Equations.

Unit – IV

Linear Partial Differential Equations With Constant Co-efficient: Introduction, to find Complementary Function, Particular Integral. Partial Diff Equations of Order Two with Variable Co-efficient: Introduction, Laplace’s Transformation, Non-Linear Partial Differential Equations of order two, Monge’s Method of integrating Rr+Ss+Tt=V. Legendre’s Equation and Simple Properties of Pn (x): Introduction, Solution of Legendre’s Equation, Legendre Polynomial, Rodrigue’s Formula, Recurrence Formulae, Laplace’s First Integral for Pn(x), Laplace’s Second Integral for Pn(x).

Unit – V Bessel’s Equation and Bessel Function: Introduction, Solution of Bessel’s Equation, Recurrence Formula for Jn(x). Laplace Transform and its Application to Differential Equations: Introduction, Laplace Transform of some Elementary Functions, Properties of Laplace Transforms, Laplace Transform of Derivatives, Laplace Transform of Integrals, Properties of Inverse Laplace Transforms, Applications to Differential Equations. Fourier Transform and Its Application to Partial Differential Equations: Introduction, Derivative of Fourier Transform, Fourier Sine and Cosine-Transforms, Finite Fourier Transform, Application to Partial Differential Equations.




BSCMT~203 - Numerical Analysis and Vector Calculus Unit – I

Approximations and Errors in Computation: Introduction, Accuracy of Numbers, Error in the Approximation of a Function, Error in a Series Approximation, Order of Approximation, Propagation of Error. Finite Differences: Introduction, Finite Differences, Differences of a Polynomial, Factorial Notation, Effect of an Error on a Difference Table, Relations between the Operators, Application to Summation of Series. Interpolation: Introduction, Newton’s Forward Interpolation Formula, Newton’s Backward Interpolation Formula.

Unit – II Central Differences Interpolation Formula: Introduction, Central Difference Interpolation Formulae, Gauss’s Forward Interpolation Formula, Gauss’s Backward Interpolation Formula, Stirling’s Formula, Bessel’s Formula, Laplace-Everett’s Formula, Choice of an Interpolation Formula. Interpolation for Unequal Intervals: Introduction, Lagrange’s Interpolation Formula, Divided Differences, Newton’s Divided Difference Formula, Hermite’s Interpolation Formula, Spline Interpolation, Lagrange’s Method, Iterative Method. Inverse Interpolation: Introduction, Lagrange’s Method, Summation of a Series, Cubic-Spline Interpolation Formulas, Bivariate Interpolation, Least Square Approximation.

Unit – III Solution of Algebraic And Transcendental Equations: Introduction, Basic Properties of Equations, Transformation of Equations, Bisection (Or Bolzano) Method, Method of False Position or Regula-Falsi-Method, Newton-Raphson Method. Solutions of Simultaneous Linear Equations: Introduction, Direct Methods of Solution, Comparison of Various Methods. Numerical Solution of Differential Equations: Introduction, Formulae for Derivatives, Numerical Integration, Newton-Cotes Quadrature Formula, Euler-Maclaurin Formula.

Unit – IV Numerical Solution of Linear Differential Equations: Introduction, Picard’s Method, Taylor’s Series Method, Euler’s Method, Runge’s Method, Runge-Kutta Method. Numerical Solution of Ordinary Differential Equations: Introduction, Classification of Second Order Equations, Finite Difference Approximations to Partial Derivatives, Elliptic Equations, Solution of Laplace Equation, Solution of Poisson’s Equation, Solution of Elliptic Equations by Relaxation Method, Parabolic Equations. Vector: Introduction, Addition of Vectors, Rectangular Resolution of a Vector, Unit Vector, Position Vector of a Point, Ratio Formula, Vector Product or Cross Product, Moment of a Force, Angular Velocity.

Unit – V Vector Calculus: Introduction, Vector Differentiation, Gradient, Divergence and Curl, More Identities Involving, Vector Integration. Vector Theorem: Introduction, Theorems of Gauss, Green’s Theorems, Stokes’s Theorems, Verification of Stocks and Gauss Theorem. Ordinary Differential Equations: Introduction, Concept and Formation of a Differential Equation, Order and Degree of a Differential Equation.




BSCMT~204 - Maths Practical

Group A: Numerical Integration using Trapezoidal and Simpson's rules. Numerical solution of Algebraic and Transcendental equation using (i) Iteration method (ii) Newton-Raphson method and (iii) Regula-Falsi method.

Group B: Numerical solutions of the system of linear equations by Jacoli and Gauss-Seidel method solution of linear differential equation of first order and first degree with initial and boundary condition using Picards and modified Euler’s method.




B.Sc. 3rd Year (Mathematics) BSCMT~301 – Algebra

Unit – I

Theory of Equations : Polynomials in one variable and the division algorithm. Relations between the roots and the coefficients. Transformation of equations. Descartes rule of signs. Solution of cubic and biquadratic (quartic) equations.

Matrix Addition and Multiplication : Diagonal, permutation, triangular, and symmetric matrices. Rectangular matrices and column vectors. Non-singular transformations. Inverse of a Matrix. Rank-nullity theorem. Equivalence of row and column ranks. Elementary matrices and elementary operations. Equivalence and canonical form. Determinants. Eigenvalues, eigenvectors, and the characteristic equation of a matrix. Cayley-Hamilton theorem and its use in finding the inverse of a matrix.

Matrix Theory and Linear Algebra : Matrix Theory and Linear Algebra in R”. Systems of linear equations, Gauss elimination, and consistency. Subspaces of R”, linear dependence, and dimension. Matrices, elementary row operations, row-equivalence, and row space.

Unit – II

Linear Equations as Matrix Equations : Systems of linear equations as matrix equations, and the invariance of its solution set under row-equivalence. Row-reduced matrices, row-reduced echelon matrices, row-rank, and using these as tests for linear dependence. The dimension of the solution space of a system of independent homogeneous linear equations.Linear transformations and matrix representation.

Modern Algebra : Commutative rings, integral domains, and their elementary properties. Ordered integral domain: The integers and the well-ordering property of positive elements. Finite induction. Divisibility, the division algorithm, primes, GCDs, and the Euclidean algorithm.

Unit – III

The Fundamental Theorem of Arithmetic : Congruence modulo n and residue classes. The rings Z„ and

their properties. Units in Zn, and Zp for prime p. Subrings and ideals. Characteristic of a ring. Fields.Sets, relations, and mappings. Bijective, injective, and surjective maps. Composition and restriction of maps. Direct and inverse images and their properties. Finite, infinite, countable, uncountable sets, and cardinality.

Equivalence Relations and Partitions : Ordering relations. Definition of a group, with examples and simple properties. Groups of transformations. Subgroups. Generation of groups and cyclic groups.

Various subgroups of GL2(R). Coset decomposition. Lagrange’s theorem and its consequences. Fermat’s and Euler’s theorems. Permutation groups. Even and odd permutations. The alternating groups An.

Isomorphism and Homomorphism : Normal subgroups. Quotient groups.First homomorphism theorem.

Cayley’s theorem.Trigonometry. De-Moivre’s theorem and applications. Direct and inverse, circular and hyperbolic, functions. Logarithm of a complex quantity. Expansion of trigonometric functions.




Unit – IV

Linear Algebra : Vector spaces over a field, subspaces. Sum and direct sum of subspaces. Linear span. Linear dependence and independence. Basis. Finite dimensional spaces. Existence theorem for bases in the finite dimensional case. Invariance of the number of vectors in a basis, dimension. Existence of complementary subspace of any subspace of a finite-dimensional vector space. Dimensions of sums of subspaces. Quotient space and its dimension.

Algebra of Linear Transformations : Matrices and linear transformations, change of basis and similarity. Algebra of linear transformations. The rank-nullity theorem. Change of basis. Dual space. Bidual space and natural isomorphism. Adjoints of linear transformations. Eigenvalues and eigenvectors. Determinants, characteristic and minimal polynomials,

Unit – V

Cayley-Hamilton Theorem : Cayley-Hamilton Theorem. Annihilators. Diagonalization and triangularization of operators. Invariant subspaces and decomposition of operators. Canonical forms. Inner product spaces. Cauchy-Schwartz inequality. Orthogonal vectors and orthogonal complements. Orthonormal sets and bases. Bessel’s inequality. GramSchmidt orthogonalization method. Hermitian, Self-Adjoint, Unitary, and Orthogonal transformation for complex and real spaces. Bilinear and Quadratic forms. The Spectral Theorem. The structure of orthogonal transformations in real Euclidean spaces. Applications to linear differential equations with constant coefficients.

Advanced Group Theory : Advanced Group Theory. Group automorphisms, inner automorphisms. Automorphism groups and their computations. Conjugacy relation. Normalizer. Counting principle and the class equation of a finite group. Center of a group. Free abelian groups. Structure theorem of finitely generated abelian groups.

Ring Theory : Rings and ring homomorphisms. Ideals and quotient rings. Prime and maximal ideals. The quotient field of an integral domain. Euclidean rings. Polynomial rings. Polynomials over Q and Eisenstein’s criterion. Polynomial rings over arbitrary commutative rings. UFDs. If A is a UFD, then so is A[x\, x2,..., xn]




BSCMT~302 - Complex Analysis

Unit – I Complex Functions: The complex number system, Polar form of complex numbers, Square roots, Stereographic projection. Möbius transforms, Polynomials, rational functions and power series Analytic Functions: Conformal mappings and analyticity, Analyticity of power series; elementary functions, Conformal mappings by elementary functions Integration: Complex integration, Goursat’s theorem, Local properties of analytic functions, A general form of Cauchy’s integral theorem, Analyticity on the Riemann sphere Unit – II Singularities: Singular points, Laurent expansions and the residue theorem, Residue calculus, The argument principle Harmonic functions: Fundamental properties Dirichlet’s problem Entire functions: Sequences of analytic functions, Inûnite products, Canonical products, Partial fractions. Hadamard’s theorem Unit – III The Riemann mapping theorem The Gamma function: Complex Numbers and the Complex Plane, Complex Numbers and Their Properties, Complex Plane, Polar Form of Complex Numbers, Powers and Roots, Sets of Points in the Complex Plane, Applications Complex Functions and Mappings : Complex Functions, Complex Functions as Mappings, Linear Mappings, Special Power Functions, The Power Function zn, The Power Function z1/n, Reciprocal Function, Limits and Continuity, Limits, Continuity, Applications Unit - IV Analytic Functions : Diûerentiability and Analyticity, Cauchy-Riemann Equations, HarmonicFunctions, Applications, Elementary Functions : Exponential and Logarithmic Functions, Complex Exponential Function, Complex Logarithmic Function, Complex Powers, Trigonometric and Hyperbolic Functions, Complex Trigonometric Functions, Complex Hyperbolic Functions, Inverse Trigonometric and Hyperbolic Functions, Applications Integration in the Complex Plane : Real Integrals, Complex Integrals, Cauchy-Goursat Theorem, Independence of Path, Cauchy’s Integral Formulas and Their Consequences, Cauchy’s. Two Integral Formulas, Some Consequences of the Integral Formulas, Applications Unit – V Laurent Series : Zeros and Poles, Residues and Residue Theorem, Some Consequences of the Residue Theorem, Evaluation of Real Trigonometric Integrals, Evaluation of Real Improper Integrals, Integration along a Branch Cut, The Argument Principle and Rouch´e’s Theorem, Summing Inûnite Series, Applications Conformal Mappings: Conformal Mapping, Linear Fractional Transformations, Schwarz-Christoûel Transformations, Poisson Integral Formulas, Applications, Boundary-Value Problems, Fluid Flow Conformal Mappings: Conformal Mapping, Linear Fractional Transformations, Schwarz-Christoûel Transformations, Poisson Integral Formulas, Applications, Boundary-Value Problems, Fluid Flow




BSCMT~303 - Dynamics and Computer Programming in "C" Unit – I

Velocity and acceleration-along radial and transverse directions, along tangential and normal directions. S.H.M., Hooke's law, motion along horizontal and vertical elastic strings.

Unit – II

Motion in resisting medium-Resistance varies as velocity and square of velocity. Work and Energy. Motion on a smooth curve in a vertical plane. Motion on the. inside and outside of a smooth vertical circle.

Unit – III

Central orbits-pr equations, Apses, Time in an orbit, Kepler's laws of planetary motion. Moment of inertia-MJ. of rods, Circular rings, Circular disks, Solid and Hollow spheres, Rectangular lamina, Ellipse and Triangle.

Unit – IV

Theorem of parallel axis. Product of inertia.

Programming languages and problem solving on computers, Algorithm, Flow chart.

Unit – V

Programming in C-Constants, Variables, Arithmetic and logical expressions, Input-Output, Conditional statements, implementing loops in Programs, Defining and manipulation arrays and functions.




BSCMT~304 - Maths Practical

The paper will contain Two practical. The candidates are required to attempt both practical. Programming in C and execution for the result of 1. Solution of linear algebraic equations by Gauss elimination method 2. Solution of algebraic and transcendental equations by Bisection, False position and Newton-Raphson Method. 3. Solution of ordinary differential equations by Euler's and Runga- Kutta 4th order method 4. Numerical integration by Trapezoidal and Simpson's one third rule.




CHEMISTRY




B.Sc. 1st Year (Chemistry) BSCCH~101 - Inorganic Chemistry

Unit-I

Ionic Solids: Ionic structures, radius ratio effect and coordination number, limitation of radius ratio rule, lattice defects, semiconductors.

Lattice Energy: Lattice energy and Born-Haber cycle, solvation energy and solubility of ionic solids, polarizing power and polarisability of ions, Fajan's rule.

Unit-II

Covalent Bond: Valence bond theory and its limitations, directional and shapes of simple inorganic molecules and ions. Valence shell electron pair repulsion (VSEPR) theory to

Molecular Orbital Theory: Homonuclear and heteronuclear (CO and NO) diatomic molecules. Multicenter bonding in electron deficient molecules, bond strength anti bond energy, percentage ionic character from dipole moment and electronegativity difference.

Unit-III

s-Block Elements: Comparative study, diagonal relationships, salient features of hydrides, solvation and complexation tendencies including their function in biosystems, an introduction to alkyls and aryls.

Unit-IV

Periodicity of p block elements: Periodicity in properties of p-block elements with special reference to atomic and ionic radii, ionization energy, electron-affinity, electronegativity, diagonal relationship, catenation.

Some Important Compound of p-block Elements: Hydrides of boron, diborane and higher boranes, borazine, borohydrides, fullerenes, carbides, fluorocarbons, silicates (structural principle), tetrasulphurtetranitride, basic propel-ties of halogens, interhalogens and pol alides.

Unit- V

Chemistry of Noble Gases: Introduction, Chemical properties of the noble gases, chemistry of xenon,

structure and bonding in xenon compounds.




BSCCH~102 - Organic Chemistry Unit – I Structure and Bonding: Introduction, Hybridization, bond lengths and bond angles, bond energy, localized and delocalized chemical bond, van der Waals interactions, inclusion compounds, clatherates, charge transfer complexes, resonance, hyperconjugation, aromaticity, inductive and field effects, hydrogen bonding.Mechanism of Organic Reactions: Introduction, Curved arrow notation, drawing electron movements with arrows, halfheaded and double headed arrows, homolytic and heterolytic bond breaking. Unit – II Stereochemistry of Organic Compounds I: Introduction, Isomerism: Concept of isomerism. Types of isomerism. Optical isomerism-elements of symmetry, molecular chirality, enatiomers, stereogenic centre, optical activity, chiral and achiral molecules with two stereogenic centres, diastereomers, threo and erythro diastereomers, meso compounds, resolution of ennantiomers, inversion, retention and racemization. Relative and absolute configuration, sequence rules, D & L and R & S systems of nomenclature.Stereochemistry of Organic Compounds II: Introduction, Determination of Configuration of Geometric Isomers, E and Z system of nomenclature, Geometric Isomerism in Oximes and Alicyclic Compounds, Conformational Isomerism, Fischer, Newman Projection and Sawhorse Formulae, Difference between Configuration and Conformation.Geometric Isomerism: Determination of configuration of geometric isomers – cis / trans and E / Z systems of nomenclatrue Geometric isomerism in oximes and alicyclic compounds.Conformational Isomerism: Newman projection and Sawhorse formulae, Conformational analysis of ethanen, n-butane and cyclohexane.

Unit – III Alkanes and Cycloalkanes I: Introduction, IUPAC nomenclature of branched and unbranched alkanes, the alkyl group, classification of carbon atoms in alkanes. Isomerism in alkanes, sources, methods of formation (with special reference to Wurtz reaction, Kolbe reaction, Corey-House reaction and decarboxylation of carboxylic acids), physical properties and chemical reactions of alkanes.Alkanes and Cycloalkanes II: Introduction, Mechanism of free radical halogenation of alkanes: orientation, reactivity and selectivity Cycloalkanes- nomenclature, methods of formation, chemical reactions, Baeyer’s strain theory and its limitations. Ring strain in small rings (cyclopropane and cyclobutane), theory of strainless rings. The case of cyclopropane ring: banana bonds.Alkenes: Introduction, Nomenclature of alkenes, methods of formation, mechanism of dehydration of alcohols and dehydrohalogenation of alkyl halides, regioselectivity in alcohol dehydration. The Saytzeff rule, Hofmann elimination, physical properties and relative stabilities of alkenes. Chemical reactions of alkenes: Introduction, mechanisms involved in hydrogenation, electrophilic and free radical additions. Markownikoff ’s rule, hydroboration-oxidation, oxymercuration-reduction. Epoxidation, ozonolysis, hydration hydroxylation and oxidation with KMnO4. Polymerization of alkenes. Substitution at the allylic and vinylic positions of alkenes. Industrial applications of ethylene and propene.Cycloalkenes, Dienes and Alkynes: Introduction, Formation of Cycloalkene, Structure and Preparation Methods of Diensex and Alkynes, Acidity of Alkynes, Conformation of Cycloalkenes, Allenes and Butadiene, Electrophilic and Nucleophilic Addition Reactions of Alkynes

Unit – IV Arenes and Aromaticity: Introduction, Nomenclature of benzene derivatives. The aryl group. Aromatic nucleus and side chain. Structure of benzene: molecular formula and Kekule structure. Stability and carbon- carbon bond lengths of benzene, resonance structure, MO picture. Aromaticity: the Huckle rule, aromatic ions.Aromatic electrophilic substitution: Introduction, General Pattern of the Mechanism, Role of σ and π Complexes, Mechanism of Nitration, Halogenation, Sulphonation, Mercuration, and Friedel-Crafts Reaction, Energy Profile Diagrams, Activating and Deactivating Substituent’s, Orientation and Ortho/ Para Ratio, Side Chain Reactions of Benzene Berivatives and Birch Reduction, Methods of Formation and Chemical Reactions of Alkyl benzenes, Alkynylbenzenes, and biphenyl.

Unit – V Alkyl and Aryl Halides-I: Introduction, Nomenclature and classes of alkyl halides, Methods of formation, chemical reaction. Mechanisms of nucleophilic substitution reactions of alkyl halides, SN2 and SN1 reactions with energy profile diagrams. Polyhalogen compounds: chloroform, carbon tetrachloride.Alkyl and Aryl Halides-II: Introduction, Methods of formation of aryl halides, nuclear and side chain reactions. The addition elimination and the elimination-addition mechanisms of nucleophilic aromatic substitution reactions. Relative reactivities of alkyl halides vs allyl, vinyl and aryl halides. Synthesis and uses of DDT and BHC.Functional Group Chemistry: Introduction, Functional Group, Orientation Effect in Aromatic Substitution, Groups




BSCCH~103 - Physical Chemistry Unit – I

Mathematical Concepts and Computers I: Introduction, Logarithmic Relations, Curve Sketching, Linear Graphs and

Calculation of Slopes, Differentiation of Functions, Maxima and Minima, Partial Differentiation and Reciprocity

Relations, Integration of Some Useful/ Relevant Functions, Permutations and Combinations, Factorials, Probability

Mathematical Concepts and Computers II: Introduction, Computers - General Introduction to Computers, Different

Components of a Computer, Hardware and Software, Input-Output Devices; Binary Numbers and Arithmetic.

Introduction to Computer Language: Programming, operating systems.

Unit – II Gaseous States: Introduction, Postulates of kinetic theory of gases, deviation from ideal behavior, Vander Waals

equation of state.

Critical Phenomena: Introduction, PV isotherms of real gases, continuity of states, the isotherms of Vander Waals

equation, relationship between critical constant and Vander Waals constants, the law of corresponding states,

reduced equation of state.

Molecular Velocities: Introduction, Root Mean Square, Average and Most Probable Velocities, Qualitative Discussion

of The Maxwell’s Distribution of Molecular Velocities, Collision Number, Mean Free Path and Collision Diameter,

Liquefaction of Gases (Based On Joule-Thomson Effect).

Unit – III Solid State: Introduction, Definition of space lattice, unit cell. Laws of crystallography-(i) Law of constancy of

interfacial angles (ii) Law of rationality of indices (iii) Law of symmetry, Symmetry elements in crystals,

X-ray diffraction by crystals.

Derivation of Bragg Equation: Introduction, Determination of crystal structure of NaCl, KCl and CsCl (Laue’s method and powder method).

Unit –IV Colloidal State: Introduction, Definition of Colloids, Classification of Colloids, Solids in Liquids (Sols): Properties-Kinetic, Optical and Electrical, Stability of Colloids, Protective Action and Gold Number Emulsions: Introduction, types of emulsions, preparation. emulsifier. Liquids in solids (gels): classification, preparation and properties, inhibition, general applications of colloids.

Unit – V Chemical Kinetics: Chemical kinetics and its scope, rate of a reaction, factors influencing the rate of a reaction: concentration, temperature, pressure, solvent, light, catalyst. Concentration dependence of rates, mathematical characteristics of simple chemical reactions - zero order, first order, second order and pseudo order; half-life and mean-life. Determination of the order of reaction - differential method, method of integration, method of half-life period and isolation method. Radioactive decay as a first order phenomenon. Experimental methods of chemical kinetics: Conductometric, Potentiometric, optical methods, (polarimetry) and spectrophotonletric method. Theories of chemical kinetics. Effect of temperature on rate of reaction, Arrhenius equation, concept of activation energy. Simple collision theory based on hard sphere model transition state theory (equilibrium hypothesis). Expression for the rate constant bases on equilibrium constant and thermodynamic aspects. Books Recommended :

1. Physical Chemistry: Ira N. Levine. 2. A Text Book of Physical Chemistry: A. S. Negi and S. C. Anand. 3. Physical Chemistry, Pt. I & IT: C. M. Gupta, J. K. Saxena and M. C. Purnhit. 4. Principles of Physical Chemistry: B. R. Puri and L. R. Shanna.




BSCCH~104 - Chemistry Practical Inorganic Chemistry

Separation and identification of six radicals (3 cations and 3 anions) in the given inorganic mixture including special combinations.

Organic Chemistry Laboratory Techniques (a) Determination of melting point (naphthalene, benzoic acid, urea, etc.); boiling point (methanol, ethanol, cyclohexane, etc.); mixed melting point (urea-cinnamic acid, etc.). (b) Crystallization of phthalic acid and benzoic acid &om hot water, acetanilide from boiling water, naphthalene from ethanol etc.; Sublimation of naphthalene, camphor, etc. Qualitative Analysis Element Detectio

Detailed Syllabus of Bachelor of Science (MATH/BIO) (Effective … · 2020. 12. 9. · medium and...

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