## Monday, June 17, 2019

### SOLUTION - CSIR NET JUNE 2019 Q.26,Q.27,Q.28,Q.29, AND Q.30 SET- A MATHS SOLUTION

CSIR NET JUNE 2019 SET- A MATHEMATICS SOLUTION
Q.26 Real Analysis-Uniform  and Point wise
convergent
Q.27 Linear Algebra-Basis Problem
Q.28 Linear Algebra -Matrix problem
Q.29 Linear algebra-Digonalizable of matrix
Q.30 Rank of matrix

## Thursday, June 13, 2019

### Critical Points of System of Simultaneous Differential Equation | Critical Point at orgin (0,0)

Critical Point at origin (0,0)
Nature and Stability of Critical point.
Node,
stable and unstable condition,
Spiral point and centre,
Critical point of a simultaneous Differential Equation,
what is codition of stability of critical point,
Type of stability of critical point,
type of Nature of critical point,
Solve one problem,
Discuss the nature and stability of the differential equation,
dx/dt=2x- 7y
dy/dt=3x-8y

## Tuesday, May 7, 2019

### CSIR NET JUNE 2018 Q.61 Linear Algebra -Quadratic form of Matrix

CSIR NET JUNE 2018
Q.61            SET-C
LINEAR ALGEBRA
Quadratic Form of matrix

## Sunday, May 5, 2019

### LINEAR ALGEBRA HAND WRITTEN NOTES IN PDF FOR CSIR NET / GATE / IIT JAM /NBHM /TIFR | LECTURE NOTES OF LINEAR ALGEBRA | LINEAR ALGEBRA NOTES IN PDF

LINEAR ALGEBRA HAND WRITTEN NOTES IN PDF

CSIR NET / GATE / IIT JAM /NBHM /TIFR
|
LECTURE NOTES OF LINEAR ALGEBRA
Linear Algebra is most important topic for above examination.
*Thanks to this person made linear algebra notes*

SYLLABUS

*Vector spaces, subspaces,

* linear dependence,
*Basis and  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 Canonical forms.
*Inner product spaces, orthogonal basis.
*Reduction and classification of quadratic forms

## Friday, May 3, 2019

### ABSTRACT ALGEBRA HAND WRITTEN NOTES IN PDF FOR CSIR NET /GATE/IIT JAM , Lecture notes for abstract algebra

ABSTRACT ALGEBRA

ABSTRACT ALGEBRA HAND WRITTEN NOTES IN PDF
FOR CSIR NET /GATE/IIT JAM

SYLLABUS:

*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 and Sylow theorem.
*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.

## Sunday, April 28, 2019

### AKTU/UPTU Engineering Mathematics -III Practice Set -I and Practice Set-II , All Branches (ME/CS/IT/EE/EC/AG)

UNIVERSITY OF AKTU/UPTU

Engineering Mathematics-3 Practice Set-1 and 2 ,
ENGINEERING MATHEMATICS-III FOR ALL BRANCHES(ME'/CE/CS/EC/AG/IT) |
Topic
1) Complex Analysis -
analytic function, Cauchy Riemann equation,Cauchy Residue theorem,
Cauchy theorem and Cauchy Integral Formula
Laurent series problem and Infinite limit problem,

2)Statistics
Measure of central tendency,correlation of coefficients,Lines of regression,
curve fitting,probability, angle  between two lines
moment about central moment
3)Numerical Analysis-
difference operator and its properties,
Newton's forward and backwards,

Newton's Raphson method, Regula Falsi and bisetcion method,
Crout method, Decomposition method, picard method and euler's method,
Trapezoidal method, simson method

4)Fourier Trans form , Z-Transform and
solution of one dimensional Heat ,wave equation by Fourier Transform