B.Sc. (Hons) Maths

Semester II

  • JBMH-201

    Differential Equation-I:


    Differential equations and mathematical models, order and degree of differential equation, solution of first order differential equations, reducible to variable separable form, linear differential equation, reducible to linear differential equation, exact differential equation and integrating factor of first order differential equation.


    Differential equation of second order with constant coefficients, Different form of P.I., homogeneous and non-homogeneous linear differential equation of order ‘n’ with constant coefficients, Cauchy-Euler’s equation of order ‘n’, method of variation of parameters, application of second order differential equation to mechanical vibrations.


    Solution of differential equation by changing it into dependent and independent variable. Solution of Legendre differential equation and its properties, Solution of Bessel’s differential equation and its properties, Wronskian, its properties and applications.


    Periodic functions, Trigonometric series, Laplace transform, Existence theorem, Laplace transform of derivatives and integrals, Inverse Laplace transform, Unit step, Dirac delta function, Laplace transform of Periodic functions, Convolution theorem, Application to solve simple linear and simultaneous differential equations.


    • 1. H. Edwards and D. E. Penny, Differential Equations and Boundary Value Problems: Computing and Modelling, Pearson education, India 2005.
    • 2. Dennis G. Zill, A first course in differential equations,
    • 3. S. L. Ross: Differential equations, John Wiley and Sons, 2004.
    • 4. Zafar Ahsan: Text Book of Differential Equations and their Applications, PHI.
    • 5. Khalil Ahmad: Text Book of Differential Equations, World Education Publishers.
    • 6. Prof. Sanjeev Rajan, Differential Equations and Transformation, S.J. Publication, Meerut.
  • JBPH-201



    Geometrical Optics: Fermat’s Principle: Optical Path. Fermat’s Principle of Least Time or Extremum Path. Examples of Fermat’s Principle:- (1) Reflection and (2) Refraction. Lenses: Transverse Magnification of a Spherically Refracting Surface. Lagrange and Helmholtz Laws of Magnification. Cardinal Points of a Coaxial Optical System. Graphical Construction of Image using Cardinal Points. Deviation produced by a Thin Lens. Equivalent Focal Length of Two Thin Lenses separated by a distance. Cardinal Points of a Coaxial System of Two Thin Lenses. Thick Lenses. Focal Length of a Thick Lens. Variation of Focal Length of a Convex Lens with Thickness. Cardinal Points of a Thick Lens.


    Wave Optics: Nature of Light: Theories of Light. Electromagnetic Nature of Light Definition of a Wave Front. Propagation of a Wave Front. Huygens Principle of Secondary Wavelets.
    Interference: Division of Amplitude and Division of Wavefront. Young’s Double Slit Experiment. Lloyd’s Mirror and Fresnel’s Biprism. Phase Change on Reflection: Stoke’s treatment.. Interference in Thin Films: Parallel and Wedge-shaped Films. Fringes of Equal Inclination (Haidinger Fringes) and Fringes of Equal Thickness (Fizeau Fringes). Newton’s Rings: Measurement of Wavelength and Refractive Index.


    Michelson’s Interferometer: (1) Idea of form of fringes (No Theory required), (2) Determination of Wavelength, (3) Wavelength Difference, (4) Refractive Index, (5) Standardization of Meter and (6) Visibility of Fringes.
    Coherence: Temporal and Spatial Coherence. Theory of Partial Coherence. Coherence Time and Coherence Length. Purity of a Spectrum Line.


    Diffraction: Fresnel diffraction: Fresnel’s Assumptions. Fresnel’s Half-Period Zones for Plane Wave. Explanation of Rectilinear Propagation of Light. Theory of a Zone Plate: Multiple Foci of a Zone Plate. Comparison of a Zone plate with a Convex lens. Diffraction due to (1) a Straight Edge and (2) a Rectangular Aperture (Slit), (3) a Small Circular Aperture and (4) an Oopaque Circular Disc. Fresnel’s Integrals, Cornu’sSpiral: Fresnel Diffraction Pattern due to (1) a Straight Edge, (2) a Slit, and (3) a Wire (Qualitatively using Cornu’s Spiral).


    Fraunhoferdiffraction: Diffraction due to (1) a Single Slit, (2) a Double Slit and (3) a Plane Transmission Grating. Rayleigh’s criterion of resolution. Resolving Power and Dispersive Power of a Plane Diffraction Grating.
    Holography: Principle of Holography. Recording and Reconstruction Method. Theory of Holography as Interference between two Plane Waves.

    • 1. Fundamentals of Optics By Francis Arthur Jenkins and Harvey Elliott White (McGraw- Hill, 1976)
    • 2. Optics by Ajoy Ghatak (Tata McGraw Hill, 2008)
    • 3. Optics By Eugene Hecht and A R Ganesan (Pearson Education, 2002)
    • 4. Light and Optics: Principles and Practices by Abdul Al-Azzawi (CRC Press)
    • 5. Contemporary Optics by A. K. Ghatak& K. Thyagarajan.(Plenum Press,1978).
    • 6. Introduction to Optics by Khanna and Gulati
  • JBCH-201

    Organic Chemistry:


    Alkanes, Alkenes, Dienes and Alkynes, cycloalkanes:

    • a. Alkanes: Methods of formation (with special reference to Wurtz reaction, Kolbe reaction, Corey-House reaction and decarboxylation of carboxylic acids), chemical reactions (nitration and halogenation. Mechanism of free radical halogenation of alkanes- orientation, reactivity and
    • b. Alkyenes: Structure and bonding in alkynes. Mehtods of formation, chemical reactions, and acidity of alkynes. Mechanism of electrophilic and nucleophilic addition reaction, hydroboration oxidation, selectivity.
    • c. Alkenes: Methods of formation, mechanisms 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-mechanisms involved in hydrogenation, electrophilic and free radical additions, Markownikoff’s rule. Hydroboration-oxidation, oxymercuration-demercuration, epoxidation, ozonolysis, hydration, hydroxylation and oxidation with KmnO4. Polymerization of alkenes.
    • d. Dienes: Nomenclature and classification- isolated, conjugated and cumulated dienes. Structure of allenes and butadiene, method of formation. 2- and 1, 4-additions, Diels-Alder reaction.
    • e. Cycloalkanes: Nomenclature, methods of formation, chemical reactions, Baeyer’s strain theory and its limitations. Stran in small rings (cyclopropane and cyclobutane), theory of strainless ring. The case of cyclopropane ring: banana bonds.


    Alchols, Ethers and epoxide:

    • a. Alcohols: preparation, properties and relative reactivity of 10, 20, 30 alcohols, Bouvaelt-Blanc Reduction; Preparation and properties of glycols: Oxidation by periodic acid and leadtetraacetate, Pinacol- Pinacolone rearrangement; Phenols: Preparation and properties; Acidity and factors effecting it, Ring substitution reactions, Reimer – Tiemann and Kolbe’s – Schmidt Reactions,
    • b. Ethers and Epoxides: Preparation and reactions with acids. Reactions of epoxides with alcohols, ammonia derivatives and LiAlH4.


    Carbonyl Compounds:

    Structure, reactivity and preparation; Nucleophilic additions, Nucleophilic addition-elimination reactions with ammonia derivatives with mechanism; Mechanisms of Aldol and Benzoin condensation, Knoevenagel condensation, Claisan-Schmidt, Perkin, Cannizzaro and Wittig reaction, Beckmann and Benzil-Benzilic acid rearrangements, haloform reaction and Baeyer Villiger oxidation, α-substitution reactions, oxidations and reductions (Clemmensen, Wolff-Kishner, LiAlH4, NaBH4, MPV, PDC and PGC); Addition reactions of unsaturated carbonyl compounds: Michael addition. Active methylene compounds: Keto-enol tautomerism. Preparation and synthetic applications of diethyl malonate and ethyl acetoacetate:


    Carboxylic Acids and their Derivatives:

    Preparation, physical properties and reactions of monocarboxylic acids: Typical reactions of dicarboxylic acids, hydroxy acids and unsaturated acids: succinic/phthalic, lactic, malic, tartaric, citric, maleic and fumaric acids; Preparation and reactions of acid chlorides, anhydrides, esters and amides; Comparative study of nucleophilic sustitution at acyl group - Mechanism of acidic and alkaline hydrolysis of esters, Claisen condensation, Dieckmann and Reformatsky reactions, Hofmann-bromamide degradation and Curtius rearrangement.


    • 1. Organic Chemistry by Morrison & Boyd, Printice-Hall.
    • 2. Organic Chemistry by L.G. Wade Jr. Prentice-Hall.
    • 3. Organic Chemistry by Fessenden & Fessenden, Brooks/Cole Publishing Company.
    • 4. Organic Reaction Mechanism by V.K. Ahluwalia and R.K. Parashar, Narosa Publishing House, New Delhi.
  • JBPH-251

    Optics Lab:

    List of Experiments:

    Note: Select any ten experiments from the following list

    • 1. To determine the wavelength of Sodium light by Newton’s rings.
    • 2. To determine the wavelength of Sodium light by Fresnel’s biprism.
    • 3. To determine the specific rotation of the cane sugar solution with the help of Polarimeter.
    • 4. To study the forward characteristics of a light emitting diode.
    • 5. To determine the resolving power and dispersive power by a prism.
    • 6. To determine the resolving power of grating.
    • 7. To study the elliptically polarised light.
    • 8. To determine slit width using He-Ne laser.
    • 9. To determine the Flashing & Quenching of Neon bulb.
    • 10. To determine the Resolving power of a telescope
    • 11. To determine the wavelength of the sodium lamp by Michelson interferometer.
    • 12. To determine the wave form and frequency of a given signal using C.R.O.
  • JBCH-251

    Organic Chemistry-I Lab:

    • 1. Checking the calibration of the thermometer.
    • 2. Purification of organic compounds by recrystallisation using the following solvents
      • a) Water
      • b) Alcohol
      • c) Alcohol-water
    • 3. Determination of the melting point of unknown organic compounds.
    • 4. Effect of impurities on the melting point - mixed melting point of two unknown organic compounds.
    • 5. Determination of boiling point of liquid compounds.
    • 6. Crystallization of the given organic sample.
  • Total Credits