B.Sc. (Hons) Maths

Semester I

  • COURSE CODE
    COURSE NAME
    CREDITS
  • JBMH-101

    Calculus-I

    UNIT-I

    Hyperbolic functions, higher order derivatives, Leibnitz rule and its applications to problem of Xn(0), concavity and inflection points, asymptotes, curve tracing in Cartesian coordinates, L’Hospital rule

    UNIT-II

    Reduction formulae, derivations and illustrations of reduction formulae of the type ʃ sinnx, ʃ tannx, ʃ cosnx, ʃ (logx)n, ʃ sinnxcosnx dx.

    UNIT-III

    Parametric equations, parameterizing a curve, arc length, arc length of parametric curves, area of surface of revolution, area of solid of revolution.

    UNIT-IV

    Triple product, introduction to vector functions, operations with vector valued functions, limits and continuity of vector functions, differentiation and integration of vector functions, tangent and normal components of acceleration, modeling ballistic and planetary motion, Kepler’s second law.

    Books:

    • 1. M.J. Strauss, G.L. Bardley and K.J. Smith, Calculus (3rd Edition), Dorling Kindersley (india) Pvt Ltd. (Pearson Education), Delhi, 2007.
    • 2. H. Anton, I. Bivens and S. Davis, Calculus (7th Edition), John Wiley and Sons (Asia) Pvt Ltd. Singapore, 2002.
    • 3. Differential Calculus by Gorakh Prasad, Pothishala, Pvt. Ltd., Allahabad.
    • 4. Calculus by P.K. Mittal, S.Chand Publication.
    04
  • JBPH-101

    Mechanics:

    UNIT-I

    Inertial and Non- Inertial Systems: Reference Frames: Inertial Frames and Galilean Transformations. Galilean Invariance and Conservation Laws. Non-inertial Frames and Fictitious Forces. Uniformly Rotating Frame. Physics Laws in Rotating Coordinate Systems. Centrifugal forces: Coriolis Force and its Applications. Components of Velocity and Acceleration in Cylindrical and Spherical Coordinate Systems.

    UNIT-II

    Special theory of Relativity: Michelson-Morley Experiment and its Outcome. Postulates of Special Theory of Relativity. Lorentz Transformations. Simultaneity and Order of Events. Lorentz Contraction. Time Dilation. Relativistic Transformation of Velocity, Frequency and Wave Number. Relativistic Addition of Velocities. Variation of Mass with Velocity. Rest Mass. Massless Particles. Massenergy Equivalence. Bucherer’s experiment. Relativistic Doppler effect. Relativistic Kinematics. Transformation of Energy and Momentum. Energy-Momentum Four Vector.

    UNIT-III

    Fundamentals of Dynamics: Dynamics of a System of Particles. Centre of Mass. Conservation of Momentum. Idea of Conservation of Momentum from Newton’s Third Law. Impulse. Momentum of Variable Mass System: Motion of Rocket.
    Work and Energy Theorem: Work and Kinetic Energy Theorem. Conservative and Non- Conservative Forces. Potential Energy. Energy Diagram. Stable and Unstable Equilibrium. Gravitational Potential Energy. Elastic Potential Energy. Force as Gradient of Potential Energy. Work and Potential energy. Work done by Non-conservative Forces. Law of Conservation of Energy. Elastic and Inelastic Collisions between particles. Centre of Mass and Laboratory Frames.

    UNIT-IV

    Rotational Dynamics: Angular Momentum of a Particle and System of Particles. Torque. Conservation of Angular Momentum. Rotation about a Fixed Axis. Moment of Inertia. Calculation of Moment of Inertia for Rectangular, Cylindrical, and Spherical Bodies. Kinetic Energy of Rotation. Motion involving both Translation and Rotation.

    UNIT-V

    Gravitation and Central Force Motion: Law of gravitation. Inertial and Gravitational Mass. Potential and Field due to Spherical Shell and Solid Sphere. Motion of a Particle under Central Force Field. Two Body Problem and its Reduction to One Body Problem and its Solution. The Energy Equation and Energy Diagram. Kepler’s Laws (Ideas Only). Orbits of Artificial Satellites.
    Elasticity: Relation between Elastic Constants. Twisting Torque on a Cylinder or Wire.
    Fluid Motion: Kinematics of Moving Fluids: Poiseuille’s Equation for Flow of a Liquid through a Capillary Tube.
    04
  • JBCH-101

    Foundation Chemistry:

    UNIT-I

    Atomic structure: Idea of de Broglie matter waves, Heisenberg uncertainty principle, atomic orbitals, Schrodinger wave equation, significance of Ψ and Ψ2, quantum numbers, radial and angular wave functions and probability distribution curves, shapes of s, p, d orbitals. Aufbau and Pauli exclusion Principle, Hunds multiplicity rule, electronic configuration of elements.

    UNIT-II

    Periodicity of Elements: s, p, d, f block elements, the long form of periodic table. Detailed discussion of the following properties of the elements, with reference to s & p- block.

    • a) Effective nuclear charge, shielding or screening effect, Slater rules, variation of effective nuclear charge in periodic table.
    • b) Atomic radii (van der Waals)
    • c) Ionic and crystal radii.
    • d) Covalent radii (octahedral and tetrahedral )
    • e) Ionization enthalpy, Successive ionization enthalpies and factors affecting ionization energy. Applications of ionization enthalpy.
    • f) Electron gain enthalpy, trends of electron gain enthalpy.
    • g) Electronegativity, Pauling’s/ Mulliken’s/ Allred Rachow’s/ and Mulliken-Jaffe’s electronegativity scales. Variation of electronegativity with bond order, partial charge, hybridization, group electronegativity. Sanderson’s electron density ratio.

    UNIT-III

    Mechanism of Organic reaction reactions: Curved arrow notation, drawing electron movements with arrow, half-headed and double-headed arrows, homolytic and heterolytic bond breaking. Types of reagents-electrophiles and nucleophiles, Types of organic reactions. Energy considerations. Reactive intermediates-carbocations, carbanions, free radicals, carbenes, arynes and nitrenes (with examples). Assigning formal charges in intermediates and other ionic species. IUPAC nomenclature of organic compounds.

    UNIT-IV

    Liquid State: Intermolecular forces, structure of liquids (a qualitative description). Structural differences between solids, liquids and gases. Liquid crystals: Difference between liquid crystal, solid and liquid. Classification, structure of nematic and cholestric phases. Thermography and seven segment cell. Volumetric analysis and concept of normality, molarity, equivalent weight preparation of standard solution equivalence point and end point.

    Books:

    • 1. New Concise Inorganic Chemistry by J.D. Lee, Compton Printing Ltd London.
    • 2. Principles of Inorganic Chemistry by HR Puri, R. Sharma & S.P. Jauhar, Vishal Publications Jalandhar.
    • 3. Basic Inorganic Chemistry F.A. Cotton and G. Willkinson III Edition
    • 4. Lee, J.D. Concise Inorganic Chemistry, ELBS, 1991.
    04
  • JBPH-151

    Mechanics Lab:

    • A. General
      • 1. To determine Radius of Given Rod & Wire by Using Vernier Calipers & screw gauge
      • 2. To use a Multimeter for measuring (a) Resistances, (b) A/C and DC Voltages, (c) ACand DC Currents, (d) Capacitances, and (e) Frequencies.
      • 3. To test a Diode and Transistor using (a) a Multimeter and (b) a CRO.
      • 4. To measure (a) Voltage, (b) Frequency and (c) Phase Difference using a CRO.
      • 5. To study Random Errors.
    • B. Mechanics
      • 1. To determine the Acceleration due to Gravity and Velocity for a freely falling body,using Digital Timing Techniques.
      • 2. To determine the Moment of Inertia of a Flywheel.
      • 3. To determine the Coefficient of Viscosity of water by Capillary Flow Method (Poiseuille’smethod).
      • 4. To determine the Young's Modulus of a Wire by Optical Lever Method.
      • 5. To determine the Spring Constant.
      • 6. To determine the Elastic Constants of a Wire by Searle’s method.
    02
  • JBCH-151

    Inorganic Chemistry-I Lab:

    • A. Titrimetric Analysis
      • i. Calibration and use of apparatus
      • ii. Preparation of solutions of different Molarity/Normality of titrants
    • B. Acid- Base Titrations
      • i. Estimation of carbonate and hydroxide present together in mixture.
      • ii. Estimation of carbonate and bicarbonate present together in a mixture.
      • iii. Estimation of percentage of ammonia in an ammonium salt
    • C. Oxidation- Reduction Titrimetry
      • i. Estimation of Fe (II) (Mohr salt) using standardized KMnO4 solution.
      • ii. Estimation of Fe (II) with K2Cr2O7 using internal (diphenylamine, anthranilic acid) indicator.
    • D. Complexometric Titrations
      • i. To determine the total, permanent and temporary hardness of water by complexometric method using EDTA.
    02
  • Total Credits
     
    16