IGNOU Syllabus www.ignou.ac.in Ph.D Entrance Exam 2013 Civil Engineering : Indira Gandhi National Open University

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Name of the Organisation : Indira Gandhi National Open University (ignou.ac.in)
Type of Announcement : Syllabus
Designation : Ph.D Entrance Examination 2013 (Civil Engineering)
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SYLLABUS FOR Ph.D ENTRANCE EXAMINATION 2013 (CIVIL ENGINEERING)

Part-I is compulsory for all students. Any two sections are to be selected from Part-II.

PART-I (Compulsory Section)
SYLLABUS FOR ENGINEERING MATHEMATICS

Linear Algebra :
Algebra of matrices, inverse, rank, system of linear equations, symmetric, skewsymmetric and orthogonal matrices. Hermitian, skew-Hermitian and unitary matrices. eigenvalues and eigenvectors, diagonalisation of matrices, Cayley-Hamilton Theorem.

Calculus :
Functions of single variable, limit, continuity and differentiability, Mean value theorems, Indeterminate forms and L'Hospital rule, Maxima and minima, Taylor's series, Fundamental and mean value-theorems of integral calculus. Evaluation of definite and improper integrals, Beta and Gamma functions, Functions of two variables, limit, continuity, partial derivatives, Euler's theorem for homogeneous functions, total derivatives, maxima and minima, Lagrange method of multipliers, double and triple integrals and their applications, sequence and series, tests for convergence, power series, Fourier Series, Half range sine and cosine series.

Complex variables :
Analytic functions, Cauchy-Riemann equations, Application in solving potential problems, Line integral, Cauchy's integral theorem and integral formula (without proof), Taylor's and Laurent' series, Residue theorem (without proof) and its applications.

Vector Calculus :
Gradient, divergence and curl, vector identities, directional derivatives, line, surface and volume integrals, Stokes, Gauss and Green's theorems (without proofs) applications.

Ordinary Differential Equations :
First order equation (linear and nonlinear), Second order linear differential equations with variable coefficients, Variation of parameters method, higher order linear differential equations with constant coefficients, Cauchy- Euler's equations, power series solutions, Legendre polynomials and Bessel's functions of the first kind and their properties.

Partial Differential Equations :
Separation of variables method, Laplace equation, solutions of one dimensional heat and wave equations.

Probability and Statistics :
Definitions of probability and simple theorems, conditional probability, Bayes Theorem, random variables, discrete and continuous distributions, Binomial, Poisson, and normal distributions, correlation and linear regression.

Numerical Methods :
Solution of a system of linear equations by L-U decomposition, Gauss-Jordan and Gauss-Seidel Methods, Newton's interpolation formulae, Solution of a polynomial and a transcendental equation by Newton-Raphson method, numerical integration by trapezoidal rule, Simpson's rule and Gaussian quadrature, numerical solutions of first order differential equation by Euler's method and 4th order Runge-Kutta method

PART-II (Any two sections optional)
SYLLABUS FOR FLUID MECHANICS (SECTION A) (Optional Section)

Fluid Properties : Relation between stress and strain rate for Newtonian fluids.

Hydrostatics : Buoyancy, manometry, forces on submerged bodies. Eulerian and Lagrangian description of fluid motion, concept of local and convective accelerations, steady and unsteady flows, control volume analysis for mass, momentum and energy.
Differential equations of mass and momentum (Euler equation), Bernoulli's equation and its applications.
Concept of fluid rotation, vorticity, stream function and potential function.

Potential flow : elementary flow fields and principle of superposition, potential flow past a circular cylinder.
Dimensional analysis :
Concept of geometric, kinematic and dynamic similarity, importance of non-dimensional numbers. Fully-developed pipe flow, laminar and turbulent flows, friction factor, Darcy-Weisbach relation. Qualitative ideas of boundary layer and separation, streamlined and bluff bodies, drag and lift forces. Basic ideas of flow measurement using venturimeter, pitot-static tube and orifice plate

SYLLABUS FOR MATERIALS SCIENCE (SECTION B) (Optional Section)
Structure : Atomic structure and bonding in materials. Crystal structure of materials, crystal systems, unit cells and space lattices, determination of structures of simple crystals by x-ray diffraction, miller indices of planes and directions, packing geometry in metallic, ionic and covalent solids. Concept of amorphous, single and polycrystalline structures and their effect on properties of materials. Crystal growth techniques. Imperfections in crystalline solids and their role in influencing various properties.

Diffusion : Fick's laws and application of diffusion in sintering, doping of semiconductors and surface hardening of metals.

Metals and Alloys : Solid solutions, solubility limit, phase rule, binary phase diagrams, intermediate phases, intermetallic compounds, iron-iron carbide phase diagram, heat treatment of steels, cold, hot working of metals, recovery, recrystallization and grain growth. Microstrcture,properties and applications of ferrous and non-ferrous alloys.

Ceramics : Structure, properties, processing and applications of traditional and advanced ceramics.
Polymers : Classification, polymerization, structure and properties, additives for polymer products, processing and applications.
Composites : Properties and applications of various composites.

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Could you please the syllabus for Ph.D Entrance Exam?

You can get the syllabus for Ph.D Entrance Exam from the below link
http://www.ignou.ac.in/upload/civile...ngsyllabus.doc