Inegral Transformation
105 videos • 764 views • by Doctor of Mathematics
1
Find the value of Laplace{integration from 0 to infinity t.e^-2t.sint}
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2
(D^2+2D+5)y=e^-t.sint;y(0)=0;y'(0)=1 y''+2y'+5y=e^(-x).sinx
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3
L-1[tan-1(2/1+p^2)]
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4
Apply the method of Laplace transforms to solve d^2y/dt^2+tdy/dt=y where y(0)=0 and dy/dt=1 at t=0.
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5
Find L{cosh2t.cos2t}.
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6
Explanation of Shab-e-miraj and Isra on basis on special theory of relativity
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7
Find Fourier Transform of F(x) =e^-|x| , |x| less than 1;0 if |x| greater than 1.
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8
Solve the p.d.e. delU/del t=2del^2U/delx^2;U(0,t)=0=U(5,t) , =10sin4πx-5sin6πx by Laplace trans.
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9
Solve the following differential equation by using Laplace transform:Y"(t)-tY'(t)+Y(t)=1
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10
Integral Transform and Laplace Transform
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11
Use Laplace transform to solve del^2/delt^2=9.del^2y/delx^2subject to the condition y(0,t) =0 y(2,)=
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12
Find the value of cosat*cosat. (convolution)
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13
Find inverse Laplace of 1/s^3(s^3+1)
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14
Find the Laplace Transform of F(t) =t, if t greater than and less than 4; 5 if t is greater than 4.
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15
Prove that F(t) =t^n is of exponential order t tends to infinite.
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16
Function of Exponential order.
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17
Solve d^2/dx^2+y=x.cos2x, y=0, dy/dx=0, when x=0 by using Laplace Transformation.
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18
To Prove L{1}=1/p, Laplace transform of 1
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19
Laplace transfor of t^n.
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20
Laplace transform of cosh(at)Laplace transform of cosh(at)
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21
To Prove L[sinhat] or L{sinhat}
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22
Find L{4cos7t} Laplace transform problem
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23
Determine Laplace transform of (t^2+1) ^2
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24
Find out the Laplace transform of cos^2(at) or co^2at.
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25
Find L[8e^3t+9e^-3t+5cos2t+7t^3+4]
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26
L{t^2-3t+5} Laplace transform
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27
L{2e^3t-e^-3t} Laplace transform
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28
L{(sint-cost)^2} Laplace transform
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29
L{sin5t+cos3t} Laplace transform
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30
L{5-3t-2e^-t} Laplace transform
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31
Application of First shifting Property
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32
64 L{3e^3t+5t^4}
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33
Find Laplace transform of following function t.cas(at)
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34
L{t.sinat} or Laplace transform of tsinat
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35
Find the Laplace Transform of the following function t. cosat.
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36
H-54:L{sin5t+cos3t}
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37
Solve d^2y/dx^2+y=x.cos2x by using Laplace transform
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38
Laplace transform Formlae. Maloom ho to inverse Laplace ke formulae kaise banayen
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39
L{t^2.cosat}
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40
L{t.sinat}=?
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41
Change of scale property
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42
Solve:(D^2+1)y=6cos2t if y=3, Dy=1, when t=0.
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43
Find the fourier complex transform of f(x) if: f(x)=e^iwx, a less than x less than b, f(x)=0, x less
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44
Find Fourier cosine transform of f(x)=1/(1+x^2) hence find Fourier sine transform of F(x)=x/(1+x^2)
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45
Find: L-1{p/(p^4+p^2+1)}
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46
Solve by Laplace transform (D+1)^2=t, y=-3 when t=0 and y=-1, when t=1.
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47
Find L-1[1/√p] ||Top mathematics channel on YouTube
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48
To Prove L-1[5p-2/p^2(p+2)(p-1)]=t+e^t+e^-2t-2
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49
Second derivative of {3/(s^2+9)} w. r. t. s
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50
Using Laplace transform to solve D. E. d^2y/dt^2-3dy/dt+2y=4t+e^3t
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51
Find the solution of initial value problem y'-2y=4, y(0)=0
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52
Solve: ty"+(t-1)y'-y=0 given that y(0)=5, y(infinity)=0
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53
Using Laplace teansform solve initial value problem utt=uxx, u(x, 0)=0, ut(x, 0)=sin(πx/l) , u(0,
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54
Solve:(D^2+m^2)x=acosnt, if x=x°, Dx=x1 when t=0, n≠m
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55
Determine Laplace transform of the following: 3e^3t+5t^4-4cos3t
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56
Find :L[3sin2t-5cos2t]
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57
Find Laplace transform of the 3e^2t+4e^-3t
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58
Determine Laplace of sint.cost
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59
Determine L[cosh^2(2t)]
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60
Find the Laplace transform of cosat/t
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61
Find the Laplace transform of sinat/t
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62
Solve:(x^2D^2+xD-1)y=x^2e^x
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63
For the Heaviside's unit step function f(t-a)={1,t greater than a;0,t less than a,prove that L[F(t
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64
Find L{sinht/t} Laplace transform
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65
Prove that ∫t^3.e^-t.sintdt from t=0 to t=♾️ infinity
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66
If L{2√(t/π)}=1/p^3/2,then prove that L{1/√(πt)}=1/p^1/2
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67
If F(t) is a periodic function with period w,then L{F(t)}=1/(1-e^-pw)∫e^-pt.F(t)dt, from t=0 to t=w.
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68
Find Laplace transform of ∫(1-e-2x/x)dx from x=0 to x=t.
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69
Find L-1{1/(s-2)+1/(s+5)+6/s^4}
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70
Evaluate:L-1{1/s^2(s^2+1)}
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71
Evaluate:L-1{(3p+1)/(p+1)(p^2+1)}.
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72
Prove that ∫e^-x^2dx=√π/2
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73
Find:L-1{1/(p^2+8p+16)}
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74
First Shifting Property:If L-1{f(x)}=F(t),then L-1{f(p-a)}=e^at.F(t).
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75
Find L-1{1/(p+3)^7/2}
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76
second shifting property: If L-1{f(p)}=F(t),then L-1{e^-ap.f(p)}=G(t),where G(t)={F(t-a), greater th
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77
L[4cos^2(2t)] का मान ज्ञात करो।
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78
L-1[1/√p] को हल करो।
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79
(2p^3+2p^2+4p+1)/(p^2+1)(p^2+p+1) काLaplace Inverse ज्ञात करो। Find Inverse Laplace transform of
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80
Show that L{(1+te^-t)^3}=1/s+3/(s+1)^2+6/(s+2)^3+6/(s+3)^4.
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81
Find the finite Fourier cosine transform of f(x),if f(x)=-cosk(π-x)/ksinkπ.
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82
If L{F(t)}=f(s), then prove that L{t^n.F(t)(-1)^n d^n/dx^n f(s)
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83
Find the Fourier series for the function f(x)=e^-x in x greater than and equal 0 and less than and
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84
Find the inverse Laplace transformation of p+2/(p^2-2p+5). in Hindi and Urdu
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85
Find the inverse Laplace transform of F(s)=(s+2)/(s^2-4s+13)
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86
For the Dirac delta function Fε(t)={1/ε if 0≤t≤ε, 0 , if ε less than t. in Hindi Urdu
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87
Find Laplace transform of f(t)=t² by use of definition of the Laplace transform.
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88
Calculate the Laplace transform of the function f(t)=sin(3t) using the definition of the Laplace tra
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89
L{t^2.cosat}
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90
Solve the initial value problem y"+y'=sint, where y'(0)=0,y(0)=0.
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91
If L{f(t)}=1/s(s²+a²),find f(t).
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92
Find L-1{1/s²+4s}
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93
Evaluate L-1[1/s^3+4s]
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94
Find L-1{1//s^2+25}
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95
If L{f(t)}=F(s) and c is any constant then shoe that L{f(t)}=1/saf(s/c).
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96
Find L(sin5t)=.....
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97
Find L-1(s/s^2+16)=......
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98
State first shifting theorem
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99
Write cosine Fourier integral formula
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100
State Convolution theorem
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101
Write sine Fourier Integral formula
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102
Find L{sin^2(3t)}
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103
Find Laplace t^2sin^2(3t)
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104
Find the inverse Laplace of s/s^4+s^2+1
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105
Find the Fourier transform of function f(x)=1+x/a when x greater than - infinity and less than -a ,
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