B.Sc. (Hons) Maths
Semester III

COURSE CODECOURSE NAMECREDITS

JBMH301
Differential EquationII:
UNITI
Introduction, solution of first order, Lagrange’s linear PDE with constant coefficients of 2nd order and their classificationsparabolic,elliptic and hyperbolic with illustrative examples, geometrical interpretation of first order PDE.
UNITII
Method of separation of variables for solving PDE,wave equation up to two dimensions, Laplace equation in two dimensions, Heat conduction equation up to two dimensions, Equation of transmission line.
UNITIII
Heat conduction problem, existence and uniqueness of solution of heat conduction problem,Laplace and beam equation, nonhomogeneous problem.
UNITIV
Cauchy problem for second order PDE, generalsolutions, onhomogeneous boundary condition, finite strings, Goursatproblem, spherical and cylindrical wave equation, initial boundary value problems.
Books:
 1. Dennis G. Zill, A first course in differential equations,
 2. Tyn MintU and Lokenath Debnath, Linear Partial Differential Equations
 3. D.A. Murray: Introductory Course on Differential Equations, Orient Longman India.
 4. A.S. Gupta: Calculus of variations with applications, Prentice Hall of India, 1997.
 5. I.N. Sneddon: Elements of Partial Differential Equations, McGraw Hill Book Company, 1988.
04 
JBMH302
AnalysisI:
UNITI
The algebraic and order properties of R, suprema and infima, the completeness properties of R, the archimedian property, density of rational numbers in R, characterization of intervals, neighborhoods, open sets, limit points of a set, isolated points, closure, complements, idea of uncountabilty of R.
UNITII
Sequences, bounded sequence, limit of a sequence, convergent sequences, monotone sequences, monotone convergence theorem.
UNITIII
Subsequences, convergence and divergence criteria, existence of monotonic subsequences(idea only),BolzanoWeirstrass theorem for sequence and sets, definition of cauchy sequence, Cauchy convergence criterion, limit inferior and limit superior of a sequence.
UNITIV
Definition of infinite series, sequence of partial sums, convergence of infinite series, Cauchy criterion, absolute and conditional convergence, convergence viaboundedness of sequence of partial sums, tests of convergence: comparison test, limit comparision test, ratio test, Cauchy's nth root test(proof based on limit superior), integral test (without proof), alternating series, Leibnitz test.
 1. R.G. Bartle and D.R. Shebert, Introduction to Real Analysis, John Wiley and Sons (Asia) Pt. Ltd., Singapore.
 2. K.A.Ross, Elementary Analysis.
 3. Real Analysis, MittalPundir, Pragati Prakashan.
 4. Real Analysis, Shanti Narayan, S.Chand Publication.
04 
JBPH301
Electromagnetism:
UNITI
Electric Circuits AC Circuits: Complex Reactance and Impedance. Series LCR Circuit: Resonance, Power Dissipation, Quality Factor and Band Width; Parallel LCR Circuit; Network Theorems: Thevenin theorem, Norton theorem, Superposition theorem, Reciprocity theorem, and Maximum Power Transfer theorem.
UNITII
Alchols, Ethers and epoxide:
Electric Field: Electric Field and Lines. Electric Field E due to a Ring of Charge. Electric Flux. Gauss’s law. Gauss’s law in Differential form. Applications of Gauss’s Law : E due to an Infinite Line of Charge, a Charged Cylindrical Conductor, an Infinite Sheet of Charge and Two Parallel Charged Sheets,Electric Potential: Line Integral of Electric Field. Electric Potential Difference and Electric Potential V (Line integral). Conservative Nature of Electrostatic Field. Relation between E and V; Potential and Electric Field of a Dipole, a Charged Disc. Conductors in an Electrostatic Field.
UNITIII
Dielectric Properties of Matter: Dielectrics: Electric Field in Matter. Dielectric Constant. Parallel Plate Capacitor with a Dielectric. Polarization, Polarization Charges and Polarization Vector. Electric Susceptibility. Gauss’s law in Dielectrics. Displacement vector D. Relations between the three Electric Vectors.
UNITIV
Magnetic Field Magnetic Effect of Currents: Magnetic Field B. Magnetic Force between Current Elements and Definition of B. Magnetic Flux. BiotSavart’s Law, Magnetic Dipole and its Dipole Moment Ampere’s Circuital law Gauss’s law of magnetism. Relative Permeability of a Material. Magnetic Susceptibility.B‐H Curve and Energy Loss in Hysteresis.
UNITV
Electromagnetic induction: Faraday’s law (Differential and Integral forms). Lenz’s Law. Self and Mutual Induction. Energy stored in a Magnetic Field Ballistic Galvanometer Potential Energy Current Loop. Ballistic Galvanometer: Current and Charge sensitivity & Damping.
Books:
 1. Electricity and Magnetism By Edward M. Purcell (McGraw Hill Education.
 2. Fundamentals of Electricity and Magnetism By Arthur F. Kip (McGraw Hill
 3. Electricity and Magnetism by J.H. Fewkes & John Yarwood. Vol. I (Oxford Univ. Press.
 4. Electricity and Magnetism. By D C Tayal (Himalaya Publishing House).
 5. David J. Griffiths, Introduction to Electrodynamics, 3rd Edn, (Benjamin Cummings).
04 
JBCH301
Physical ChemistryI:
UNITI
Ionic Equilibria: Strong, moderate and weak electrolytes, degree of ionization, factors affecting degree of ionization, ionization constant and ionic product of water. Ionization of weak acids and bases, pH scale, common ion effect; dissociation constants of mono, di and tri protic acids (exact treatment).Salt hydrolysiscalculation of hydrolysis constant, degree of hydrolysis and pH for different salts. Buffer solutions; derivation of Henderson equation and its applications; buffer capacity, buffer range, buffer action and applications of buffers in analytical chemistry and biochemical processes in the human body. Solubility and solubility product of sparingly soluble salts – applications of solubility product principle. Qualitative treatment of acid – base titration curves (calculation of pH at various stages). Theory of acid – base indicators; selection of indicators and their limitations.Multistage equilibria in polyelectrolyte systems; hydrolysis and hydrolysis constants.
UNITII
A.Gaseous State: Postulates of kinetic theory of gases, deviation from ideal behavior, van der Waals equation of state. Critical Phenomena: PV isotherms of real gases, continuity of states, the isotherms of van der Waals equation, relationship between critical constants and van der Waals constants, the law of corresponding states, reduced equation of state. Problems Molecular velocities: 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. liquification of gases (based on JouleThomson effect). Problems
B. Solid State: Definition of space lattice, unit cell. Laws of crystallography  (i) Law of constancy of interfacial angles (ii) Laws of rationality of indices (iii) Law of symmetry. Symmetry elements in crystals. Xray diffraction by crystals. Derivation of Bragg equation. Determination of crystal structure of NaCl, KCl and CsCl (Laue's method and powder method).
UNITIII
Phase Equilibrium: Statement and meaning of the terms  phase, component and degree of freedom, derivation of Gibbs phase rule, phase equilibria of one component system water, CO2 and S systems. Phase equilibria of two component system solidliquid equilibria, simple eutectic BiCd, PbAg systems, desilverisation of lead.
UNITIV
ElectrochemistryI: Types of reversible electrodes gasmetal ion, metalmetal ion, metalinsoluble saltanion and redox electrodes. Electrode reactions, Nernst equation, derivation of cell E.M.F. and single electrode potential, standard hydrogen electroderefence electrodesstandard electrode potential, sign conventions, electrochemcial series and its significance. Electrolytic and Galvanic cells  reversible and irreversible cells, conventional representation of electrochemical cells. EMF of a cell and its measurements. Computation of cell EMF. Calculation of thermodynamic quantities of cell reactions (ΔG, ΔH and K), polarization, over potential and hydrogen overvoltage. Concentration cell with and without transport, liquid junction potential, application of concentration cells, valency of ions, solubility product and activity coefficient, potentiometric titrations.
Books:
 1. Atkins, P. W. & Paula, J. de Atkin’s Physical Chemistry 8th Ed., Oxford University Press (2006).
 2. Castellan, G. W. Physical Chemistry 4th Ed. Narosa (2004).
 3. Engel, T. & Reid, P. Thermodynamics, Statistical Thermodynamics, & Kinetics
 4. Pearson Education, Inc: New Delhi (2007).
04 
JBPH351
Electromagnetism Lab:
List of Experiment
Note: Select any ten experiments from the following list
 1. To determine acceleration due to gravity (g ) by Bar Pendulum.
 2. To determine acceleration due to gravity (g ) by Kater’s Pendulum.
 3. To study the Motion of a Spring and calculate
 a) Spring Constant
 b) Acceleration due to gravity (g ) and
 c) Modulus of Rigidity
 4. To determine the Frequency of an Electrically Maintained Tuning Fork by Melde’s experiment.
 5. To determine a Low Resistance by Carey Foster’s Bridge.
 6. To determine High Resistance by Leakage of a Capacitor.
 7. To determine the
 a) Charge Sensitivity and
 b) Current Sensitivity of a B.G.
 8. To determine the Ratio of Two Capacitances by de Sauty’s Bridge.
 9. To determine Self Inductance of a Coil by Anderson’s Bridge using AC
 10. To determine Self Inductance of a Coil by Rayleigh’s Method.
 11. To determine the Mutual Inductance of Two Coils by Absolute method using a B.G.
 12. To study the response curve of a Series LCR circuit and determine its
 a) Resonant Frequency,
 b) Impedance at Resonance and
 c) Quality Factor Q, and
 d) Band Width.
02 
JBCH351
Physical ChemistryI Lab:
 I) Surface tension measurements
 a) The relative surface tension of a liquid with respect to water at room temperature by stalagmometer.
 b) The surface tension of methyl alcohol, ethyl alcohol at room temperature and also calculate the atomic parachors of carbon, hydrogen and oxygens.
 II) Viscosity measurement ( using Ostwald’s viscometer)
 a) Study the effect of the addition of solutes such
 (i) polymer
 (ii) ethanol
 (iii) sodium chloride on the viscosity of water at room temperature.
 b) The relative viscosity of a liquid with respect to water at room temperature by using viscometer .
 c) To determine the molecular weight of a polystyrene sample using viscometric method .
 a) Study the effect of the addition of solutes such
 III) pH measurements
 a) Measurement of pH of different solutions using pHmeter.
 c) To determine the pH value of a given solution by indicator method (using buffer solutions of known pH).
 d) pH metric titrations of
 i. Strong acid and strong base
 ii. Weak acid and strong base
02  I) Surface tension measurements

Total Credits20