pde and integral equation previous questions and answers
27 videos • 2,562 views • by msc mathematics
1
msc mathematics 3 rd sem pde calicut university 2023 question paper
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2
duhamels principle, rankie hugoniot condition, poisonns formula
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3
state mean value principle of harmonic functions
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4
Derive the general solution of 1 dimensional wave equation (2021.3)
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5
solve Ux=1 subject to the condition u(0,y)=g(y)
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6
solution of vibrating string
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7
utt−4uxx=0|find u(x,1)|limt→∞ u(5,t)|points with singular solution|points solution not continuous
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8
solve non linear eikonal equation p²+q²=n⁰² subject to the initial condition u(x,2x)=1
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9
CU MSc mathematics 3rd semester PDE and integral equation previous year question & detailed answers
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10
find the characteristic numbers and characteristic fumction
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11
solve Ux+Uy=2 subject to the condition u(x, 0)=x²
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12
solve the pde Ux+3Y⅔Uy=2 subject to the initial condition u(x, 1)=1+x
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13
describe the condition for a first order quasilinear pde to have a unique solution
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14
discuss greens function for the differential equation [d\dx[p d\dx]q]y+Ψ(x)=0
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15
describe the cauchy problem for non homgeneous Wave Equation also ST it has at most one solution
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16
show that Ym(x) and Yn(x) are orthogonal
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17
find the Canonical form of X²Uxx-2XYUxy+Y²Uyy+XUx+YUy=0 and find the general solution on half plane
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18
u(x, t) be a solution for Wave Equation Utt-C²Uxx=0 u is constant on the line x=2+ct. PT Ut+CUx=0
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19
state the strong maximum principle of harmonic function
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20
Let U(x, t) be the solution of the cauchy problem Utt-9Uxx=0,f(x)=1,|x|≤2,0 otherwise & g(x)=1,|x|≤2
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21
y''+xy=1,y(0)=0=y(1)
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22
transform the differential equation y''+λy=0 with y(0)=0 y(l)=0 to an integral equation
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23
the function u in c²(D) satisfying the mean value property at every point in D will be harmonic in D
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24
prove that characteristic number of a fredholm equation with a real symmetric kernal are all real
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25
dirichlet problem in a bounded domain Δu=f(x, y), (x, y)∈D, u(x, y)=g(x, y), (x, y)∈δD has atmost 1
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26
show that the Neumann problem for the vibrating string has a unique solution
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27
show that λ=[nπ\L]², n=1,2,3...are the only possible values for the eigen value problem d²X\dx²+λX=0
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