B. Sc. III Mathematics
76 videos • 1,098 views • by Doctor of Mathematics
1
Find the residue of 1/(1+z^2)^n at z=i
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2
Find the residue of (1+e^z)/(sinz+z.cosz) at the pole z=0.
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3
Show that all singular point of 1/z(e^z-1) are poles. Find the order of poles and find the residue
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4
Evaluate ∫c(z^2+3z)dz alog the circle|z|=0 from (2,0) to (0, 2) in a counterclockwise direction.
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5
Evaluate ∫c(5z^4-z^3+2)dz around the circle |z|=1.||Best mathematics channel on YouTube
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6
Evaluate ∫c(5z^4-z^3+2)dz around the |z|=1,square (0, 0), (1, 0), (1, 1),(0, 1) ;along y=x^2 (0, 0)
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7
Evaluate ∫c(5z^4-z^3+2)dz around the square with vertices (0, 0), (1, 0), (1, 1) and (0, 1).TOP chan
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8
dz/dw=del z/del u (TOP mathematics channel on YouTube)
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9
Show that del gik/del xj=[k, I j]+[I, j k] Tensor Analysis (Top mathematics channel on YouTube)
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10
Bilinear or Linear Fractional Transformation Definition || Top mathematics channel on YouTube
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11
Prove that the resultant of two bilinear transformation is a bilinear transformation. ||Top Maths
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12
Find the supremum and infimum, if they exist, of the set:{1+(-1)^n/n:n belong to N}.Best Mathematics
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13
The intersection of an arbitrary collection of open sets is:||Unique solution ||Best mathematics||
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14
Find the analytic function of which the real part is e^-x[(x^2-y^2)xcosy+2xysiny]
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15
Show that |z|^2=z.z̄
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16
A uniform circular plate is supported horizontally at three points A, B, C of its circumference.
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17
Show that the necessary and sufficient conditions for a non empty subset S of a ring R to be a
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18
The series 1/1^p+1/2^p+1/3^p+...+1/n^p+.....is convergent if p greater than 1 and divergent if p les
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19
State mathematical form of a general L. P. P. and explain it
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20
A manufacturer of a line of patent medicines is preparing a production plan on medicines A and B.
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21
Prove that set Q if all rational number is countable.
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22
Position of Equilibrium:Stable, Unstable and Neutral Equilibrium
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23
Find the differential equation of the central orbit in polar coordinates. d^2u/dθ^2+u=f/h^2u^2
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24
Test the convergence of the series whose general term is given by 1/n.(logn)^p
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25
Solve the following linear programming problem graphically:maximize:z=2x1+3x2, subject to 4x1+3x2 le
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26
Solve LPP: min z=2x1+3x2,s.t.
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27
Prove that E=(1-∇)^-1
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28
Prove that Δ x^(n)=nhx^(n-1) #numericalanalysis
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29
Find the value of Δ^2(x+cosx)
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30
Prove that √2 is irrational number.
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31
The value of x and y are given as below:x: 5 6 9 11,y:12 13
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32
Find the form of the function y=Ux,given that U0=8,U1=11,U4=68,U5=123.
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33
General Quadrature Formula (Newton-Cote's Quadrature Formula)
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34
Euler Maclaurin Formula
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35
The velocities of a particle along and perpendicular to the radius vector from a fixed origin are λr
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36
Show that the sequence defined by xn=√5+xn-1 and x1=1 tend to definite limit.Find the limit.
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37
A particle is describing a plane curve.If the tangential and normal accelerations are each constant
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38
Show that the function f(z)=xy^3/x^2+y^6, z≠0;f(0)=0, is not continuous at the origin.
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39
Find the bilinear transformation which maps z=2,1,0 respectively onto w=1,0,i.
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40
An Example of Rotation transformation|Consider the transformation w=ze^i/4 and determine the region
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41
Inversion Transformation|Conformal Mapping|Complex Analysis
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42
For a common catenary x=clog (y+s/c)
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43
Find the centre of gravity of hemishpeical shell.
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44
Find the C.G. of a plane lamina of uniform density in the form of a quadrant of an ellipse.
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45
Find the C.G. of the area included between the curve y^2(2a-x)=x^3 and its asymptotes.
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46
Find the C.G. of an arc of catenary y=ccoshx/c.
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47
Use Cauchy's integral formula to evaluate ∫(z^2+1)/(z^2-1)dz Where C has radius 1 with centre at z=1
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48
Evaluate the integral ∫C1/z.coszdz, where C is the ellipse 9x^2+4y^2=1
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49
Consider the transformation w=2z and determine the region R' of w-plane into which the triangular re
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50
Find five terms in the Lauren's expansion of 1/z(e^z-1) for the region |z| greater than 0 and less
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51
Using Newton -Raphson method, establish the iterative formula for finding the reciprocal of a positi
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52
In a plane triangle, find the maximum value of u=cosAcosBcosC.
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53
Find the value of ∫Cdz/sinhz,where C is the circle |z|=4 described in the positive sense.
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54
Find the minimum value of x²+y²+z² subject to the condition ax+by+cz=p.
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55
Cartesian Equation of Common Catenary. y=ccoshx/c
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56
For a common catenary s=csinhx/c
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57
Find the span of common catenary
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58
Prove that the function |z|^2 is continuous every where but nowhere differwntiable except at the ori
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59
A uniform chain of length 2a and weight 2W is suspended from two point in same horizontal level.A w
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60
If the length of a uniform chain ,suspended between two points at the same level,is adjusted so as t
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61
find the billinera transformation of the points which maps the points -1,0,1 onto the points 0,i, 3i
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62
Use Cauchy's integral formula to evaluate z/(z^2-3z+2)dz where C is a circle |z-2|=1/2.
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63
∫e^z/z^2(z+1)^3dz,C: |z|=2
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64
Show that the function f(z)=x-iy is not analytic at any point.
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65
Expand f(z)=1/(z+1)(z+3) in a Laurent's series valid for the regions (i) 1 less than|z| leas rhan 3
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66
Evaluate ∫z^2+6z-1/(z-4)dz over the closed curve C ,where C is the circle|z|=5.
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67
Find the stationary value of u=x^2+y^2+x^2 subject to condition ax^2+by^2+cz^^2=1 and lx+my+nz=0.
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68
Evaluate by using Cauchy's Integral formula ∫c (z-1)dz/(z-2)(z+1)^2, where C is |z-i|=2.
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69
Use Cauchy's Integral Formula to evaluate ∫C(2z+1)dx/z^2+z where C is |z|=1/2.
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70
By using Cauchy's Integral formula Integral, evaluate ∫Ce^-zdz/z+1 , where C is the circle|z|=2.
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71
Evaluate by Cauchy's Integral formula Integral evaluate ∫Cdz/z(z+πi) ,where C is the circle|z+3i|=1
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72
Find the length of the circular helix r(t)=(a cost,a sint,ct) from (a,0,0) to (a,0,2πc).
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73
If aijxixj=0 for all values of the variables x1,x2,x3,...xn show that aki+aik=0. L-15
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74
If n^3 quantities Bi,jk are connected with the n^3 quantities Ai,jk by equations of the from Bi,jk=A
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75
Using Cauchy's Integral formula to evaluate ∫C e°3zdz/(z+1)^4 where C is the circle |z|=2.
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76
Evaluate by Cauchy's Integral Formula ∫3z^2+z/z^2-1dz along C ,where C is the circle |z-1=1.|
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