• Statistical Methods: Measures of central tendency and dispersion: Standard
• Deviation, moments, measures of skewness and kurtosis. Simple Correlation, calculation ofcorrelation coefficient, probable error, Rank correlation.
• Regression: Linear regression,calculation of regression coefficients, Time series Model (Component, Uses, Moving AverageMethod, Least Square Method)

• Probability: Concept, Addition, Conditional Probability Baye’s theorem,
• Probability Distributions: Binomial, Poisson and Normal

• Decision Sciences & role of quantitative techniques. Linear Programming: Concept, Formulation & Graphical and Simplex Solution
• Assignment Models: Concept, Flood’s Technique / Hungarian Method, applications including restricted & multiple assignments.
• Transportation Models: Concept, Formulation, Problem types: Balanced, Unbalanced, Minimization, Maximization Basic initial solution using North West Corner, Least Cost & VAM, and Optimal Solution using MODI.

• Queuing Theory: Concept, Single Server (M/M/I,)
• Markov Chains & Simulation Techniques: Markov chains: Applications related to management functional areas, Decision Theory: Concept, Decision under risk (EMV) & uncertainty Game
• Theory : Concept, 2 zero sum game with dominance, Pure & Mixed Strategy.

The concerned faculty shall have the liberty to define the course contents under this module and teach students accordingly

• Meaning and significance of research.
• Importance of scientific research in decision making.
• Types of research and research process.
• Identification of research problem and formulation of hypothesis.
• Research Designs.

• Hypothesis testing; Z-test, t-test, F-test, Chi-square test.
• Analysis of variance.
• Non-parametric Test – Sign Test, Run test, Krushall – Wallis test

• Factor analysis, Multiple Regressions Analysis.
• Discriminant Analysis, Use of SPS Package.

Constraints, Classification of constraints, Principle of virtual work, D’Alembert’s principle and its application.

limitations of Newtonian formulation, degrees of freedom , generalized coordinates and velocities, Derivation of Lagrange’s equation, Calculus of variation, Euler – Lagrange equation, derivation of Lagrange’s equation from Hamilton’s principle , simple application of Lagrange’s equation, Cyclic coordinates , Symmetry and conservation theorems.

Phase Space and the motion of the system Hamiltonian Hamilton’s Canonical Equation of motion Physical significance of H Advantage of Hamiltonian approach Deduction of canonical equation from variational principle Hamiltonian canonical equation of motion in different co ordinate system Application of Hamilton’s equation of motion in different co ordinate system Application of hamiltonian’s equation of motion Hamiltonian for charged particle in an electromagnetic field Principle of least action.

Canonical or Contact transformations, Advantage of Canonical transformation, example of canonical transformation Solution of simple harmonic oscillator problem Condition for transformation to be canonical.

Particle Falling Freely, Hamilton Jacobi equation for Hamilton Characteristic function.

Poisson Bracket-Definition Invariance of poission bracket with respect to canonical transformation Equation of motion in poisson bracket form Jacobi’s identity Infinitesimal contact transformation interpretation in terms of poision’s bracket The angular momentum and poisson bracket Poisson bracket in quantum mechanics Lagrange bracket Relation in Lagrange and poisson bracket Liouvilies Theorem.

Michelson Morley experiment postulates of special theory of relativity Lorentz transformation length contraction time dilation Velocity transformation relativistic mass and momentum mass energy relation.

Thermodynamical system , Principles of thermodynamics , concept of thermodynamic state , Zeroth law of thermodynamics , work done in isothermal and isobaric processes, Heat and work ,Free energy and their application, internal energy function and the first law of thermodynamics , application to various processes , CP – CV , Equation of state for adiabatic process, work done in adiabatic process , Equations of state. Ideal gases and their PVT relations, Gas mixtures.

• Maxwell- Boltzmann formula for distribution of molecular speed (statement of formula and discussion), Average RMS and most probable speed, Mean free path, Degrees of freedom,
• The principle of equipartition of energy, The Vanderwaals equation of state, Evaluation of
• critical constants

Zeroeth law of thermodynamics, Heat capacity, Second law of thermodynamics, Carnot’s engine, Carnot theorem, The thermodynamic scale of temperature, Entropy, entropy change in reversible and irreversible processes, mathematical formulation of second law, Maxwell’s relations, first TdS equation, second TdS equation, Phase change, Clausius-Clapeyron equation

• Thermal conductivity, Conduction along a uniform bar, rectilinear flow of heat, Experimental determination of Thermal conductivity (Ingen-Hausz’s method).
• Blackbody radiation, Emissive and absorptive power, Kirchoff’s law, Stefan-Boltzmann’s law,
• Energy distribution in the blackbody spectrum, Wein’s law and Rayleigh-Jean’s law (Statement of formula and discussion). Planck’s radiation formula, derivation of Rayleigh-Jean’s formula, Wein’s formula and Stefan-Boltzmann law using Planck’s formula.

• Basic Concepts of Differential Equation
• Degree Equation
• Equations of First order but of Higher Degree

• Linear Equations with Constant coefficient
• Existence and Uniqueness of solution

• Series Solution and special function
• Gaseous state
• Liquid state
• Atomic structure
• Liquid state
• Atomic structure
• Periodic properties
• Chemical bonding