06:18
f is differentiable and f'(z) = 1/(g'(f(z)))
03:14
G⊂C is open&connected, totality of branches of log z = functions f(z)+2πki, k ∈ Z.
06:41
If G is open and connected and f:G→C is differentiable with f'(z) = 0 for all z in G,f is constant.
06:28
f(z) =∑ an(z-a)^n have R ›0 (a) k ≥ 1 ; ∑ n(n-1)... (n - k + 1) an(z - a) ^(n-k) has R
02:11
mg university 5 th sem differential equation previous year question and answers
03:53
g•f is analytic on G and (gof)'(z)=g'(f(z))f'(z)
01:11
If f: G→C is differentiable at a point a in G then f is continuous at a
02:57
power series ∑ (an+bn) (z-a)^n and ∑ cn(z-a)^n have radius of convergence ≥r.
06:58
if ∑(z-a)^n is a given power series with radius of convergence R=lim|an/an+1|if this limit exists.
08:36
2.Σan(z-a)^n & 1/R=lim sup |an|^(1/n),(a)|z-a|‹R cnvrgs absltly (b)|z-a|›R unbndd & dvrgs (c)|z|≤r
03:18
if ∑ an converges absolutely then ∑ an converges
02:42
convergence of discrete topology
02:50
5.convergence of indiscrete topology
02:03
4.Discrete topology and indiscrete topology
02:02
3.define TOPOLOGY and HAUSDROFF space
08:09
2.φ,entire set,union and intersection of open set are open, if x, y ∈ X & x ∈ U, y ∈ V and U ∩ V = φ
04:51
1.open set, bounded set, a sequence convergence to y, a function f is continuous at x° in X
00:48
example for a proper and non trivial idea of zxz which is not prime ideal
02:58
R is a community Ring with Unity and N is a prime ideal of R if and only if R/N is a integral domain
01:08
maximial ideal of Z of the form pZ
01:04
a commutative Ring with unity is a field if and only if R has no proper and non trivial ideal
06:37
R is a commutative ring with unity and M is a ideal of R then M is a maximal ideal ⟺ R/M is a field
02:01
A field has no proper and non trivial ideal
01:51
R is a ring with unity and N is an ideal of R containing a unit, then N=R
01:11
expected questions for viva from multivariable
01:15
expected questions for viva from complex analysis
01:31
expected questions for viva from functional analysis 3rd sem
04:34
basic questions asked for my viva
07:12
all expected viva questions from real analysis 1
06:11
expected questions for viva algebra 1 general concepts
04:52
expected questions for viva from algebra 1 module 3
05:49
expected questions for viva algebra 1 module 2
05:43
expected questions for viva from algebra 1 module 1
02:35
examples of countable and uncountable sets
06:33
fuction, domain, range, one-one, onto, image of f, equivalence relation
07:24
ring, factor ring, integral domain
03:51
Evaluate the weingarten map Lp for X2²+X3²=a² in R³
01:58
why weingarten map is called sphere operator
03:43
prove that the weingarten map is self adjoint
04:43
state and prove inverse function theorem for n surfaces
06:58
let c be an oriented plane curve. then ∃ a global parameterization of C iff C is connected
02:18
prove that the gradient of f at p ∈ f-¹(c) is orthogonal to f-¹(c) at p
05:45
Δf(p)⊥ = α •(t)
07:29
s be an n-surface in Rn+1.PT ∃ an I containing 0 and a geodesic α:I→S st α(0)=p & α •(0)=v and β:I→S
03:03
define level set andgraph of a function.sketch it for the function f(x1,x2)=x1²-x2²
01:24
Find and sketch the gradient field of the function f(x1,x2)=x1+x2
02:17
describe the spherical image f(x1,x2,..,xn)=x1²+x2²+...+x(n+1)²
01:45
Define (¡) differential 1 form and (¡¡) exact 1 form
01:30
sketch the level set of the function f(x1,x2,x3)=x1²+x2²+x3²at heights 0 and 4
01:54
sketch the following vector field on R²X(p)=(p, x(p))where X(x1,x2)=(x2,x1)
02:26
Define Guass map. illustrate with an example
02:05
Find the normal curvatureof -x1²+x2²+x3²=1 at a point on the surface in the direction of V
00:55
Define parametrized n-surface
03:31
Σ [σp,σp-1][σp-1,σp-2]=0
02:29
Bp(k) ⊂ Zp(k)
01:10
Define reflection of a sphere with respect to an axis
01:08
whether unit disk is contractible? Justify
01:40
Define barycentric subdivision of Cl(σ)
01:11
state the Hopf classification theorem
00:49
Define Euler characteristic of a complex
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