Properties of Matter : Elasticity; moduli of Elasticity, Experimental determination of Young’s modulus, Bending of beams, Cantilever. Fluids: Steady and turbulent flow, Bernoulli’s theorem, Viscosity, determination of Coefficient of viscosity by Poiseuille’s method. Surface tension, Surface energy, Angle of contact, determination of surface tension by rise in a capillary tube.

Heat & Thermodynamics : Heat, Temperature, Theories of heat, Adiabatic and isothermal processes, The four laws of thermodynamics, Thermodynamic functions, Maxwell’s Thermodynamic relations. Efficiency of Heat Engines, Carnot’s Cycle, Entropy.

Optics : Waves and Oscillations, Simple Harmonic Motion, types of wave- motion, theories of light, Interference , Diffraction, Polarisation, Double refraction, Dispersion, Deviation.

Electricity and Magnetism : Electric charges, Electric field, Electric potential, Coulomb’s law, Gauss’s law, Capacitors and dielectrics, Electric current, Ohm’s Law, Magnetic field, Magnetic force on current, Ampere’s law, Faraday’s law, and Lenz’s law. Varying current, Alternating current, concept of phase, L-R, C-R, and LCR circuits. Magnetic properties of matter: dia, para, & ferromagnetism.

Methods of Integration: Definite and Indefinite Integrals,Riemann sum, Fundamental theorem of Integral calculus, Techniques of integration.

Improper Integrals : Definition, Convergence & Divergence, Beta and Gamma function and their properties.

Infinite Series : Limit of a sequence, Partial-Sums, COnvergence and divergence of series, Geometric and p-series, Ratio, Integral and comparision tests.

Analytic geometry of three dimension : Equations of straight line and plane (parametric and Symmetric form), Angle between two lines and two planes. Sphere and quadric surfaces. Polar, Cylindrical and spherical coordinate-system and their Jacobians.

Functions of several variables : Limit, Continuity, Partial derivatives, Chain rule, Maxima and Minima and method of Lagrange's multiplier.

Multiple Integrals : Double and triple integrals with their application in finding area and volume.

Linear Algebra : Algebra of matrices, Inverse of a matrix. Gauss-Jordan method for solution of a system of algebraic linear equations.

Vectors : Scalar and vector quantities, Differentiation and integration of vector functions. Gradient, divergence and curl. Gauss’ divergence theorem. Stokes’ theorem.

Ordinary Differential Equations : Formulation, Order, degree and linearity of differential equation. Complementary and particular solution. Initial and boundary value problems.

Solution of Ordinary Linear Differential Equations of First Order : Methods of solution. Bernoulli’s differential equation.

Linear Second Order Differential Equation : Characteristic equation and different types of it. Methods of solving homogeneous linear differential equations with constant coefficients. Particular solution by variation of parameters, method and solution by indeterminate coefficient method.

Laplace Transform : Definition and properties, Laplace transform of derivatives and integrals. Inverse Laplace transform. Solving the linear constant coefficient differential equation by Laplace transform.

Z-Transform : Definition, examples and properties. Solution of difference equation.

Thermodynamic Properties : Introduction, Working substance; System; Pure substance; PVT surface; Phases; Properties and state; Units; Zeroth Law; Processes and cycles; Conservation of mass.

Energy and its Conservation : Relation of mass and energy; Different forms of energy, Internal energy and enthalpy; Work; Generalized work equation Flow and non-flow processes; Closed systems; First Law of Thermodynamics; Open systems and steady flow, Energy equation for steady flow; System boundaries; Perpetual motion of the first kind.

Energy and Property Relation : Thermo dynamics equilibrium; reversibility; Specific heats and their relationship; Entropy; Second Law of Thermodynamics; Property relations from energy equation; Frictional energy.

Ideal Gas : Gas laws; Specific heat of an ideal gas; Dalton’s Law of Partial Pressure; Third Law of Thermodynamics; Entropy of an ideal gas; Thermodynamic processes.

Thermodynamic Cycles : Cycle work; Thermal efficiency and heat rate, Carnot cycle; Stirling cycle; Reversed and reversible cycles; Most efficient engine.

Consequences of the Second Law : Calusius’s inequality; Availability and irreversibility; Steady flow system.

Two-Phase Systems : Two-phase system of a pure substance; Changes of phase at constant pressure; Steam tables; Superheated steam; Compressed liquid; Liquid and vapour curves; Phase diagrams; Phase roles; Processes of vapours; Mollier diagram; Rankine cycle; Boilers and anciliary equipment.

Internal Combustion Engines : Otto cycle; Dual combustion cycle; Four-stroke and two-stroke engines; Types of fuels.

Reciprocating Compressor : Condition for minimum work; Isothermal efficiency; Volumetric efficiency; Multi-stage compression; Energy balance for a two-stage machine with intercooler.

Number Theory: Prime factorization of integers, Division Algorithm, Modular arithmetic, Application of Conruence, Chinese remainder theorem, Euler's and Fermat's theorem , Cryptology.

Groups Theory: Groupoid, Monoid, Semi-groups, Cyclic and abelian groups with examples, Cosets, Lagranges theorem, Cayley's theorem, Homomorphism and Isomorphism of groups.

Vector Spaces : Sub spaces, Bases and Dimensions.

Rings & Fields: Definition, Examples of Rings, Fields, Integral domains, Ideal and Modules. Statement of some useful theorems.

Graph and Trees: Graph Terminology and application, Algorithm and traversing graph.

Descriptive Statistics: Basic definitions, Measures of central tendency and variation, Chebychev's theorem, z-scores, Frequency distribution, Graphical representation of data stem & Leaf and Box Plots, Symmetry and skewness, Quintiles (Percentiles, Deciles & Quartiles)

Probability Theory: Basic definition and rules of probability, Conditional probability & Bayes's Theorem, Counting techniques.

Random Variable: Concept of random variable, Discrete & Continuous random variable and its probability distributions, means and variance of random variable and their properties.

Discrete & Continuous Probability Distributions: Uniform, Binomial, Multinomial, Hyper geometric, Negative binomial, Geometric, Poisson, Normal & Exponential distributions and their applications.

Sampling Theory: Sampling distribution of mean, t-distribution, and Sampling procedures.

Regression & Correlation: Linear, Exponential and Multiple regression models, and multiple correlation coefficient.

Lab work: Students will be expected to solve problems in the computer laboratory using MINITAB and SPSS.

Error Estimation in Numerical Computations: Errors, Absolute error, Relative error, Percentage error, Sources of errors, Significant digits, Error in function evaluation, Error in Arithmetic operations.

Solution of Non Linear equations: Bisection, Newton Raphson and Fixed point iterations methods.

Interpolation & Extrapolation: Newton divided difference formula, Lagrange Interpolating polynomials.

Solution of Linear system of equations: LU Decomposition & Gauss Siedal iteration method.

Numerical Differentiation & Integration: Various methods of differentiation and integration.

Solution of ODE's & PDE's: Numerical method of solving ODE's (first and second order) and PDE's.

Statistical Inference : Estimation of parameters such as mean and variance, Classical and Bayesian method of estimations.

Hypothesis Testing: Z-test, t-test, and Goodness of fit test.

Simulation: Random numbers and their generation, generation of random deviates from different distributions, special and general method of simulation. Simulation of probability models and test of goodness of fit.

Lab work: Students will be expected to solve problems in the computer laboratory using Matlab and Mathematica.