Find eigenvalue (?) and eigenfunction and evaluate orthogonality
from the given boundary value problem. ?2?′′ +...
Find eigenvalue (?) and eigenfunction and evaluate orthogonality
from the given boundary value problem. ?2?′′ + ??′ + ?? = 0, ?(1) =
0, ?(5) = 0. Hint: Use Cauchy-Euler Equation, (textbook
pp141-143).
Find the eigenvalues and eigenfunctions of the given boundary
value problem. Assume that all eigenvalues are real. (Let
n represent an arbitrary positive number.)
y''+λy=
0,
y(0)= 0,
y'(π)= 0
Describe the mathematical models of the boundary value problem
to evaluate the elastic deflection of the beam based on
Euler-Bernoulli and Timoshenko theories with finite difference
discretisation (for numerical integration and differentiation)
Describe the mathematical models of the boundary value problem
to evaluate the elastic deflection of the beam based on
Euler-Bernoulli and Timoshenko theories with finite difference
discretisation (for numerical integration and differentiation)
Find the eigenvalues λn and eigenfunctions
yn(x) for the given boundary-value problem. (Give your
answers in terms of k, making sure that each value of
k corresponds to two unique eigenvalues.)
y'' + λy = 0, y(−π) = 0, y(π) = 0
λ2k − 1 =, k=1,2,3,...
y2k − 1(x) =, k=1,2,3,...
λ2k =, k=1,2,3,...
y2k(x) =, k=1,2,3,...
Find the eigenvalues
λn
and eigenfunctions
yn(x)
for the given boundary-value problem. (Give your answers in
terms of n, making sure that each value of n
corresponds to a unique eigenvalue.)
y'' + λy = 0, y(0) = 0, y(π/6) = 0
λn =
,
n = 1, 2, 3,
yn(x) =
,
n = 1, 2, 3,
Find the eigenvalues
λn
and eigenfunctions
yn(x)
for the given boundary-value problem. (Give your answers in
terms of n, making sure that each value of n
corresponds to a unique eigenvalue.)
x2y'' +
xy' + λy =
0, y(1) =
0, y'(e) = 0
Find the eigenvalues
λn
and eigenfunctions
yn(x)
for the given boundary-value problem. (Give your answers in
terms of n, making sure that each value of n
corresponds to a unique eigenvalue.)
x2y'' + xy' + λy = 0, y'(e−1) =
0, y(1) = 0
λn =
n = 1, 2, 3,
yn(x) =
n = 1, 2, 3,
Write a program to solve the boundary value problem ? ′′ = ? ′ +
2? + cos ? for ? ? [0, ?/2] with ?( 0) = 0.3, ?( ?/ 2) = 0.1. Check
your numerical solution with actual using necessary
plot.(MATLAB)
Write and test MatLAB code implementing the mathematical models
of the boundary value problem to evaluate the elastic deflection of
the beam based on Euler-Bernoulli and Timoshenko theories with
finite difference discretisation (for numerical integration and
differentiation). The results must be plotted on a graph with
labelled local maxima and minima