Duality -important results

Useful for both NET and GATE exam

1. If the primal problem has finite optimal feasible solution then it's dual has also optimal feasible solution and conversely.
2. If the primal problem has an unbounded objective function, then it's dual has no feasible solution and conversely.
3. The problem has finite optimal solution iff there is a feasible solution to it's dual problem.

Review of book - Csir - Net General Aptitude - A New outlook

Book Name
CSIR - NET GENERAL APTITUDE - A NEW OUTLOOK
Author- Christy Varghese a
Publisher- Lilly publishing house
This book has two sections-
Section 1.
Theory and questions of following topics
1. Numerical ability ( numbers, probability and arrangements, distance and directions)
2. daily life problems ( finding the X , average, monetary problems)
3. Geometry type problem's
( Geometry, mensuration and quantitative comparison)
4. Logical reasoning ( Data interpretation, observational ability, logical puzzles)
5. Typical problems ( calendar problem, clock problem, moving locomotive problem, series formation)
6. General science
Section 2
Previous year's exam question papers
From June 2012 to Dec 2017
( Mathematical sciences, chemical sciences, earth sciences, physical sciences, life sciences).
Each and every solution is properly solved in this book
Model question papers
Total 7 model question papers are given in the book ( along with answers ).
Review- If your part-A is very weak, you take much time in solving questions then you can purchase this book. It has full explanation of previous year papers
You can get guidance  and trick  to solve them.
Including both previous years papers and model papers there are enough papers to practice through.
Although I found this book somewhat expensive.
It's approximate price is Rs 330 ( may vary)
It is available in Amazon, Flipkart, Paytm, ebay .

IMPORTANT TOPICS WHICH COVER MAJOR PORTION OF QUESTION PAPER

UNIT – 1,2 and 3

Analysis-

Topics- countability, supremum ,infimum, convergence of sequences and series , limsup, liminf,

Bw Theorem, continuity , uniform continuity, differentiability , mean value theorem ,

sequence and series of functions, uniform convergence , monotonocity , function of bounded variation ,

directional derivative , metric space – compactness and connectedness.

Linear Algebra

vector space and its subspace, L.D , L.I , Basis and dimension , Linear Transformation and its matrix transformation , Matrices, Rank of determinant of matrices, system of linear equations, eigen values and eigen vectors, Diagonalisation, triangularization, Jordan canonical form, orthogonality , Quadratic forms.

Complex Analysis

Power series, Analyticity, Cauchy Riemann equations, Cauchy integral formula, Maximum modulus principle, open mapping theorem, Taylor and Laurent series , residues, conformal mappings ,Mobius Transformation.

Algebra

Solution of Congruence equations, Euler phi function, primitive roots, groups , subgroups- Normal , Quotient. Homomorphisms , Isomorphisms, cyclic , permutations and dihedral groups, class equations, sylow theorems, Maximal and prime ideals , finite fields , field extension , polynomial and Quotients rings, irreducibility, Euclidean domain , PID , UFD.

ODEs and PDEs

All topics

Numerical Analysis -

Newton Raphson method, Rate of convergence, Lagrange interpolation, Numerical differentiation, Picard method , Euler and modified Euler, RK methods.

Calculus of variations

Euler Lagrange equation , Necessary and sufficient conditions for extrema.

Linear Integral Equations

All topics