TN SET Maths - Complex Analysis PYQ| Tamil | Prof. Suresh

Real Analysis - Continuity Definition | Theorem in Tamil

Real Analysis - Continuity Definition | Theorem in Tamil.

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Trainer @ Madura Coaching Centre, Madurai, Tamilnadu.

ONLINE Courses offered: CSIR NET/JRF , SET , TRB PG Assistant, TRB Polytechnic Lecturer. 

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CSIR NET & SET EXAM MATHS SYLLABUS

NOTE: 

THERE IS NO SEPARATE SYLLABUS FOR TN SET (& ALL OTHER STATES SET EXAM) MATHS. 

  
MATHS SYLLABUS IS SAME FOR SET & CSIR NET 

CSIR-UGC National Eligibility Test (NET) for Junior Research Fellowship and Lecturership

CSIR NET COMMON SYLLABUS FOR PART ‘A’ 

Joint CSIR-UGC NET for JRF and Elegibility for Lectureship

General Aptitude with emphasis On logical reasoning, graphical analysis, analytical and numerical ability, quantitative comparison,  series formation, puzzles etc.

There will be 20 questions and the candidates shall be required to answer any 15

CSIR NET - COMMON SYLLABUS FOR PART ‘B’ AND ‘C’ 

SET EXAM SYLLABUS - PAPER 2 

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,
Lebesgue integral. 
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,
Sturm-Liouville 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
(Tchebyshef, Markov, Jensen). Modes of convergence, weak and strong laws of large numbers, Central
Limit theorems (i.i.d. case). 
Markov chains with finite and countable state space, classification of states, limiting behaviour of n-step
transition 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. Analysis of variance and covariance. Fixed, random and mixed effects models.
Simple and multiple linear regression. Elementary regression diagnostics. Logistic regression. 
Multivariate normal distribution, Wishart distribution and their properties. Distribution of quadratic
forms. Inference for parameters, partial and multiple correlation coefficients and related tests. Data
reduction techniques: Principle component analysis, Discriminant analysis, Cluster analysis, Canonical
correlation. 
Simple random sampling, stratified sampling and systematic sampling. Probability proportional to size 
sampling. Ratio and regression methods.
Completely randomized designs, randomized block designs and Latin-square designs. Connectedness and
orthogonality of block designs, BIBD. 2K factorial experiments: confounding and construction. 
Hazard function and failure rates, censoring and life testing, series and parallel systems.

Linear programming problem, simplex methods, duality. Elementary queuing and inventory models. 
Steady-state solutions of Markovian queuing models: M/M/1, M/M/1 with limited waiting space, M/M/C, M/M/C with limited waiting space, M/G/1.

NOTE:

1. All students are expected to answer questions from Unit I. 
2. Students in mathematics are expected to answer additional question from Unit II and III.  
3. Students with in statistics are expected to answer additional question from Unit IV.

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TN SET EXAM 2018

*TN SET EXAM 2018*
To view the TNSET 2018 Final Answer Key for All the Subjects click the below Official Mother Teresa Women's University website link

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http://www.motherteresawomenuniv.ac.in/TNSET%202018%20Ans%20Keys/All%20Papers.html


Exam date 4.3.2018.


SS ACADEMY, Madurai
(BEST INSTITUTE FOR CSIR NET/SET Maths).

LAST YEAR TN SET 70% PASS RESULT

Subject: Maths
Classes start from 24.12.2017.

PLACE:
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Ph: 8838037215.
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Classes taken by
Prof Suresh NET & SET PASSED.

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தற்போது கல்லூரிகளில்
I M.Sc or II M.Sc maths பயில்வோரும் இத்தேர்வில் பங்கேற்கலாம் என்பதால் அனைவரும் பயன்பெறும்படி கேட்டுக்கொள்ளப்படுகிறது.

தேர்வுக்கு மிக குறுகிய காலமே உள்ளதால் உடனடியாக தொடர்பு கொள்க.
தொடர்புக்கு:
Prof SURESH (NET, SET QUALIFIED)
8838037215, www.SSacademymdu.tk


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Tamilnadu SET EXAM MATHS COACHING CLASSES.. @ Madurai by PROF SURESH,

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*BEST RESULT last year

*Study materials, Assignments
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*Important note:
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So YOU MUST CLEAR SET THIS TIME.
2. IF NOT IT WILL TAKE LONG TIME FOR NEXT SET EXAM.
ALL THE VERY BEST - Prof Suresh.

Tips for SET EXAM

TN SET EXAM TOMORROW 23.4.2017:
MY Tips:
1)Revise what you have prepared, don't study new topics hereafter .
2} Be confident, no tension
3) if u Dont know the answer, try to find best option from options itself (as other 3 might be equivalent)
4) use trial & error method, finding example,...
5) Don't shade OMR in hurry, think twice before shading.
6) Attend 50/60 in Paper I , 50 in Paper II & 75 Qns in Paper III as NO NEGATIVE MARKS.
7) Sit full time in exam hall.
8) Time management very important.
Don't take LONG time for single question, if you don't know the answer move to next question..
9) HAVE FAITH IN YOU. YOU CAN DO ANYTHING...
10) All the best  for Success in SET -
Prof Suresh, NET, SET MATHS COACH, MADURAI.
Ph: 8838037215
www.SSacademymdu.tk

SET EXAM Q & A ,NOTES, Materials

TN SET 2017 MATHS
SAMPLE Q & A ,
MATERIAL will be uploaded to this website.

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TN SET EXAM 2017

இந்த ஆண்டு செட் தேர்வை நடத்துவதற்கு, தெரசா பல்கலை துணை வேந்தர் வள்ளி தலைமையில், புதிய கமிட்டி அமைக்கப்பட்டுள்ளது.

உறுப்பினர் செயலராக, தெரசா பல்கலை பதிவாளர் கீதா, தேர்வு கட்டுப்பாட்டு அதிகாரியாக விமலா ஆகியோர் நியமிக்கப்பட்டு உள்ளனர். உறுப்பினர்களாக, சேலம் பெரியார் பல்கலை துணை வேந்தர் சுவாமிநாதன் மற்றும் திருவள்ளுவர் பல்கலை துணைவேந்தர் முருகன் நியமிக்கப்பட்டு உள்ளனர்.

 

இந்த ஆண்டுக்கான செட் தேர்வு தேதி, பிப்., முதல் வாரத்தில் அதிகாரபூர்வமாக அறிவிக்கப்பட உள்ளது.

Prof SURESH.

MATHS COACHING ADMISSION OPEN...@ MADURAI

Contact: 9790356826