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I would like to have the syllabus for Physics candidates for the SLET examinations to be conducted in Tamilnadu this year i.e. 2011

Syllabus for SLET [State Level Eligibility Test] in Physics is as follows:

Section A:

1. Basic Mathematical Methods
2. Classical Dynamics
3. Electromagnetism
4. Quantum Physics and Applications
5. Thermodynamic and Statistical Physics
6. Experimental Design

Section B:

1. Electronics
2. Atomic and Molecular Physics
3. Condensed Matter Physics
4. Nuclear and Particle Physics
5. Nature of Nuclear Forces

Originally Posted by estherelis

I would like to have the syllabus for Physics candidates for the SLET examinations to be conducted in Tamilnadu this year i.e. 2011

Dear Friend

The syllabus for State Eligibility Test(SET) is same as that of CSIR-NET is same.

The syllabus for Physics is as under;

I. Mathematical Methods of Physics

Dimensional analysis; Vector algebra and vector calculus; Linear algebra, matrices, Cayley
Hamilton theorem, eigenvalue problems; Linear differential equations; Special functions
(Hermite, Bessel, Laguerre and Legendre); Fourier series, Fourier and Laplace transforms;
Elements of complex analysis: Laurent series-poles, residues and evaluation of integrals;
Elementary ideas about tensors; Introductory group theory, SU(2), O(3); Elements of
computational techniques: roots of functions, interpolation, extrapolation, integration by
trapezoid and Simpson’s rule, solution of first order differential equations using Runge-Kutta
method; Finite difference methods; Elementary probability theory, random variables,
binomial, Poisson and normal distributions.

II. Classical Mechanics

Newton’s laws; Phase space dynamics, stability analysis; Central-force motion; Two-body
collisions, scattering in laboratory and centre-of-mass frames; Rigid body dynamics, moment
of inertia tensor, non-inertial frames and pseudoforces; Variational principle, Lagrangian and
Hamiltonian formalisms and equations of motion; Poisson brackets and canonical
transformations; Symmetry, invariance and conservation laws, cyclic coordinates; Periodic
motion, small oscillations and normal modes; Special theory of relativity, Lorentz
transformations, relativistic kinematics and mass–energy equivalence.

III. Electromagnetic Theory

Electrostatics: Gauss’ Law and its applications; Laplace and Poisson equations, boundary
value problems; Magnetostatics: Biot-Savart law, Ampere's theorem, electromagnetic
induction; Maxwell's equations in free space and linear isotropic media; boundary conditions
on fields at interfaces; Scalar and vector potentials; Gauge invariance; Electromagnetic waves
in free space, dielectrics, and conductors; Reflection and refraction, polarization, Fresnel’s
Law, interference, coherence, and diffraction; Dispersion relations in plasma; Lorentz
invariance of Maxwell’s equations; Transmission lines and wave guides; Dynamics of
charged particles in static and uniform electromagnetic fields; Radiation from moving charges,
dipoles and retarded potentials.

IV. Quantum Mechanics

Wave-particle duality; Wave functions in coordinate and momentum representations;
Commutators and Heisenberg's uncertainty principle; Matrix representation; Dirac’s bra and
ket notation; Schroedinger equation (time-dependent and time-independent); Eigenvalue
problems such as particle-in-a-box, harmonic oscillator, etc.; Tunneling through a barrier;
Motion in a central potential; Orbital angular momentum, Angular momentum algebra, spin;
Addition of angular momenta; Hydrogen atom, spin-orbit coupling, fine structure; Time-
independent perturbation theory and applications; Variational method; WKB approximation;
Time dependent perturbation theory and Fermi's Golden Rule; Selection rules; Semi-classical
theory of radiation; Elementary theory of scattering, phase shifts, partial waves, Born
approximation; Identical particles, Pauli's exclusion principle, spin-statistics connection;
Relativistic quantum mechanics: Klein Gordon and Dirac equations.

V. Thermodynamic and Statistical Physics

Laws of thermodynamics and their consequences; Thermodynamic potentials, Maxwell
relations; Chemical potential, phase equilibria; Phase space, micro- and macrostates;
Microcanonical, canonical and grand-canonical ensembles and partition functions; Free
Energy and connection with thermodynamic quantities; First- and second-order phase
transitions; Classical and quantum statistics, ideal Fermi and Bose gases; Principle of detailed
balance; Blackbody radiation and Planck's distribution law; Bose-Einstein condensation;
Random walk and Brownian motion; Introduction to nonequilibrium processes; Diffusion
equation.

VI. Electronics

Semiconductor device physics, including diodes, junctions, transistors, field effect devices,
homo and heterojunction devices, device structure, device characteristics, frequency
dependence and applications; Optoelectronic devices, including solar cells, photodetectors,
and LEDs; High-frequency devices, including generators and detectors; Operational
amplifiers and their applications; Digital techniques and applications (registers, counters,
comparators and similar circuits); A/D and D/A converters; Microprocessor and
microcontroller basics.

VII. Experimental Techniques and data analysis

Data interpretation and analysis; Precision and accuracy, error analysis, propagation of errors,
least squares fitting, linear and nonlinear curve fitting, chi-square test; Transducers
(temperature, pressure/vacuum, magnetic field, vibration, optical, and particle detectors),
measurement and control; Signal conditioning and recovery, impedance matching,
amplification (Op-amp based, instrumentation amp, feedback), filtering and noise reduction,
shielding and grounding; Fourier transforms; lock-in detector, box-car integrator, modulation
techniques.

Applications of the above experimental and analytical techniques to typical undergraduate
and graduate level laboratory experiments.


VIII. Atomic & Molecular Physics

Quantum states of an electron in an atom; Electron spin; Stern-Gerlach experiment; Spectrum
of Hydrogen, helium and alkali atoms; Relativistic corrections for energy levels of hydrogen;
Hyperfine structure and isotopic shift; width of spectral lines; LS & JJ coupling; Zeeman,
Paschen Back & Stark effect; X-ray spectroscopy; Electron spin resonance, Nuclear magnetic
resonance, chemical shift; Rotational, vibrational, electronic, and Raman spectra of diatomic
molecules; Frank – Condon principle and selection rules; Spontaneous and stimulated
emission, Einstein A & B coefficients; Lasers, optical pumping, population inversion, rate
equation; Modes of resonators and coherence length.

IX. Condensed Matter Physics

Bravais lattices; Reciprocal lattice, diffraction and the structure factor; Bonding of solids;
Elastic properties, phonons, lattice specific heat; Free electron theory and electronic specific
heat; Response and relaxation phenomena; Drude model of electrical and thermal conductivity;
Hall effect and thermoelectric power; Diamagnetism, paramagnetism, and
ferromagnetism; Electron motion in a periodic potential, band theory of metals, insulators and
semiconductors; Superconductivity, type – I and type - II superconductors, Josephson
junctions; Defects and dislocations; Ordered phases of matter, translational and orientational
order, kinds of liquid crystalline order; Conducting polymers; Quasicrystals.

X. Nuclear and Particle Physics

Basic nuclear properties: size, shape, charge distribution, spin and parity; Binding energy,
semi-empirical mass formula; Liquid drop model; Fission and fusion; Nature of the nuclear
force, form of nucleon-nucleon potential; Charge-independence and charge-symmetry of
nuclear forces; Isospin; Deuteron problem; Evidence of shell structure, single- particle shell
model, its validity and limitations; Rotational spectra; Elementary ideas of alpha, beta and
gamma decays and their selection rules; Nuclear reactions, reaction mechanisms, compound
nuclei and direct reactions; Classification of fundamental forces; Elementary particles (quarks,
baryons, mesons, leptons); Spin and parity assignments, isospin, strangeness; Gell-Mann-
Nishijima formula; C, P, and T invariance and applications of symmetry arguments to particle
reactions, parity non-conservation in weak interaction; Relativistic kinematics.

Thank You

The syllabus is given in the prospectus and also in the website of the SLET.
the syllabus is;
The syllabus for State Eligibility Test.doc

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Syllabus for SLET (Tamilnadu) examination for mathematical science paper

Originally Posted by Unregistered

Syllabus for SLET (Tamilnadu) examination for mathematical science paper

SLET ( State Level Eligibility Test):-

MATHEMATICAL SCIENCES

UNIT – 1
Analysis: Elementary set theory, finite, countable and uncountable sets, Real number system as a
complete ordered field, Archimedean property, supremum, infimum.
Sequences and series, convergence, limsup, liminf.
Bolzano Weierstrass theorem, Heine Borel theorem.
Continuity, uniform continuity, differentiability, mean value theorem.
Sequences and series of functions, uniform convergence.
Riemann sums and Riemann integral, Improper Integrals.
Monotonic functions, types of discontinuity, functions of bounded variation, Lebesgue measure,
Functions of several variables, directional derivative, partial derivative, derivative as a linear
transformation, inverse and implicit function theorems.
Metric spaces, compactness, connectedness. Normed linear Spaces. Spaces of continuous functions
as examples.

Linear Algebra: Vector spaces, subspaces, linear dependence, basis, dimension, algebra of linear
transformations.
Algebra of matrices, rank and determinant of matrices, linear equations.
Eigenvalues and eigenvectors, Cayley-Hamilton theorem.
Matrix representation of linear transformations. Change of basis, canonical forms, diagonal forms,
triangular forms, Jordan forms.
Inner product spaces, orthonormal basis.
Quadratic forms, reduction and classification of quadratic forms

Unit 2:-

Complex Analysis: Algebra of complex numbers, the complex plane, polynomials, power series,
transcendental functions such as exponential, trigonometric and hyperbolic functions.
Analytic functions, Cauchy-Riemann equations.
Contour integral, Cauchy’s theorem, Cauchy’s integral formula, Liouville’s theorem, Maximum
modulus principle, Schwarz lemma, Open mapping theorem.
Taylor series, Laurent series, calculus of residues.
Conformal mappings, Mobius transformations.

Algebra: Permutations, combinations, pigeon-hole principle, inclusion-exclusion principle,
derangements.
Fundamental theorem of arithmetic, divisibility in Z, congruences, Chinese Remainder Theorem,
Euler’s Ø- function, primitive roots.
Groups, subgroups, normal subgroups, quotient groups, homomorphisms, cyclic groups, permutation
groups, Cayley’s theorem, class equations, Sylow theorems.
Rings, ideals, prime and maximal ideals, quotient rings, unique factorization domain, principal ideal
domain, Euclidean domain.
Polynomial rings and irreducibility criteria.
Fields, finite fields, field extensions, Galois Theory.

Topology: basis, dense sets, subspace and product topology, separation axioms, connectedness and
compactness.

UNIT – 3

Ordinary Differential Equations (ODEs):

Existence and uniqueness of solutions of initial value problems for first order ordinary differential
equations, singular solutions of first order ODEs, system of first order ODEs.
General theory of homogenous and non-homogeneous linear ODEs, variation of parameters, SturmLiouville boundary value problem, Green’s function.

Partial Differential Equations (PDEs):

Lagrange and Charpit methods for solving first order PDEs, Cauchy problem for first order PDEs.
Classification of second order PDEs, General solution of higher order PDEs with constant
coefficients, Method of separation of variables for Laplace, Heat and Wave equations.

Numerical Analysis :
Numerical solutions of algebraic equations, Method of iteration and Newton-Raphson method, Rate
of convergence, Solution of systems of linear algebraic equations using Gauss elimination and
Gauss-Seidel methods, Finite differences, Lagrange, Hermite and spline interpolation, Numerical
differentiation and integration, Numerical solutions of ODEs using Picard, Euler, modified Euler and
Runge-Kutta methods.

Calculus of Variations:
Variation of a functional, Euler-Lagrange equation, Necessary and sufficient conditions for extrema.
Variational methods for boundary value problems in ordinary and partial differential equations.

Linear Integral Equations:

Linear integral equation of the first and second kind of Fredholm and Volterra type, Solutions with
separable kernels. Characteristic numbers and eigenfunctions, resolvent kernel.

Classical Mechanics:

Generalized coordinates, Lagrange’s equations, Hamilton’s canonical equations, Hamilton’s
principle and principle of least action, Two-dimensional motion of rigid bodies, Euler’s dynamical
equations for the motion of a rigid body about an axis, theory of small oscillations.

UNIT – 4

Descriptive statistics, exploratory data analysis
Sample space, discrete probability, independent events, Bayes theorem. Random variables and
distribution functions (univariate and multivariate); expectation and moments. Independent random
variables, marginal and conditional distributions. Characteristic functions. Probability inequalities
Markov chains with finite and countable state space, classification of states, limiting behaviour of n-step probabilities,
stationary distribution, Poisson and birth-and-death processes.
Standard discrete and continuous univariate distributions. sampling distributions, standard errors and
asymptotic distributions, distribution of order statistics and range.
Methods of estimation, properties of estimators, confidence intervals. Tests of hypotheses: most powerful
and uniformly most powerful tests, likelihood ratio tests. Analysis of discrete data and chi-square test of
goodness of fit. Large sample tests.
Simple nonparametric tests for one and two sample problems, rank correlation and test for independence.
Elementary Bayesian inference.
Gauss-Markov models, estimability of parameters, best linear unbiased estimators, confidence intervals,
tests for linear hypotheses.

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