"Ode: Intimations of Immortality from Recollections of Early Childhood" (also known as "Ode", "Immortality Ode" or "Great Ode") is a poem by William Wordsworth, completed in 1804 and published in Poems, in Two Volumes (1807). The poem was completed in two parts, with the first four stanzas written among a series of poems composed in 1802 about childhood. The first part of the poem was completed on 27 March 1802 and a copy was provided to Wordsworth's friend and fellow poet, Samuel Taylor Coleridge, who responded with his own poem, "Dejection: An Ode", in April. The fourth stanza of the ode ends with a question, and Wordsworth was finally able to answer it with seven additional stanzas completed in early 1804. It was first printed as "Ode" in 1807, and it was not until 1815 that it was edited and reworked to the version that is currently known, "Ode: Intimations of Immortality".
The poem is an irregular Pindaric ode in 11 stanzas that combines aspects of Coleridge's Conversation poems, the religious sentiments of the Bible and the works of Saint Augustine, and aspects of the elegiac and apocalyptic traditions. It is split into three movements: the first four stanzas discuss death, and the loss of youth and innocence; the second four stanzas describes how age causes man to lose sight of the divine, and the final three stanzas express hope that the memory of the divine allow us to sympathise with our fellow man. The poem relies on the concept of pre-existence, the idea that the soul existed before the body, to connect children with the ability to witness the divine within nature. As children mature, they become more worldly and lose this divine vision, and the ode reveals Wordsworth's understanding of psychological development that is also found in his poems The Prelude and Tintern Abbey. Wordsworth's praise of the child as the "best philosopher" was criticised by Coleridge and became the source of later critical discussion.
Modern critics sometimes have referred to Wordsworth's poem as the "Great Ode" and ranked it among his best poems, but this wasn't always the case. Contemporary reviews of the poem were mixed, with many reviewers attacking the work or, like Lord Byron, dismissing the work without analysis. The critics felt that Wordsworth's subject matter was too "low" and some felt that the emphasis on childhood was misplaced. Among the Romantic poets, most praised various aspects of the poem however. By the Victorian period, most reviews of the ode were positive with only John Ruskin taking a strong negative stance against the poem. The poem continued to be well received into the 20th century, with few exceptions. The majority ranked it as one of Wordsworth's greatest poems.
Hi,
I have a set of ODE's represented in matrix format as shown in the attached file. The matrix A has algebraic multiplicity equal to 3 and geometric multiplicity 2. I am trying to find the generalized eigenvector by algorithm (A-λI)w=v, where w is the generalized eigenvector and v is the...
The Coupled ODE Model
Below are my coupled differential equations, where the only variable I try to meddle with is the ITMblood. The motivation here is if I try to increase ITMblood (in the next section I will show how I do it), at some concentration of ITMblood (most likely a very huge one) ...
Hi!
I'm trying to solve ODE system with 2 equations
Here is a result from dsolve. How can i get R(t) out of it
And how to substitute initial conditions in it?
Hi PF!
Given the ODE system ##x'(t) = A(t) x(t)## where ##x## is a vector and ##A## a square matrix periodic, so that ##A(t) = A(T+t)##, would the following be a good way to solve the system's stability: fix ##t^*##. Then
$$
\int \frac{1}{x} \, dx = \int A(t^*) \, dt \implies\\
x(t) =...
Homework Statement
This question relates to a very large project I have been assigned in a course on mathematical methods in structural engineering. I have to solve the following equation, in a specific way:
(17)
Now we have to assume the following solution:
(18)
It wants me insert...
Hi!
\begin{cases} \dot{q} = a \left( 1 - q^2 \right) \\ \dot{a} = - \alpha - a^2 q\end{cases} \qquad \alpha \in (0, 1 )
I've looked into this ODE system about 7 months now, but I've not got anything promising how to write down the solution. I'm mostly interested in q-serie. (To those of you...
Hey there! I was trying to plot a ODE solution, but am not getting what I should be. It is actually plotting the orbit of Earth with Sun at the origin.
My equations
The (-0.00011847) is GM.
The Initial Conditions:
The plot I get:
Should not I be getting a elliptic/circular plot as the...
I have been solving system of homogeneous ODE numerically using Crank-nicolson (CN) method but now I have a system of non-homogeneous ODE. It would seem that CN would not work since the rank of the matrix will be less than the dimension of the matrix. Is there any other method that can...
dx/dt = x-y^2 dy/dt= x^2 -xy -2x
For each critical point, find the approximate linear OD system that is valid in a small neighborhood of it.
I found the critical points which are (0,0),(4,2),(4,-2) but have no idea how to do the above question! please help!
Hi everyone
I have a system of ODE as follows
x1_dot=f1(t)-ax1
x2_dot=f2(t)-ax2
x3_dot=f3(t)-ax3
f1,2,3(t) are unknown nonlinear functions of time, a is constant and unknown, x1,2,3 and their derivatives are given. How can I estimate the parameter a from the given information?
Thanks
I need to find a trapping region for the next nonlinear ODE system
$u'=-u+v*u^2$
$v'=b-v*u^2$
for $b>0$.
What theory i need to use or which code in Mathematica o Matlab could help me to find the optimal trapping region.
Homework Statement
Solve the following system for 0<t<5
u^\prime = u-e^{-2t} v, u(0) = 1
v^\prime = u+3v, v(0) = -2
using Forward Euler method and implement the numerical scheme into a MATLAB code.
Homework Equations
Forward Euler : \vec x^(\prime)_{n+1} = \vec F(t,\vec x)...
Question:
Show that the system
x'= x-y-x[x^2 + (3/2)y^2]
y'= x+y -y[x^2 + (1/2)y^2]
has at least one periodic orbit.
I know that I need to apply Poincare-Bendixson Theorem. I can prove the first three points of it easily, but to create a trapping region, I believe that I need to...
Hi.
If I have a homogeneous ODE with constant coefficient system in the form of 2x2 matrix:
X'=A X, A is a 2x2 matrix.
How do I solve this using wolfram or matlab?
Problem:
The following two-dimensional system of ODEs possesses a limit-cycle solution for certain values of the parameter$a$. What is the nature of the Hopf bifurcation that occurs at the critical value of $a$ and state what the critical value is.
$\dot{x}=-y+x(a+x^2+(3/2)y^2)$...
Homework Statement
The following two-dimensional system of ODEs possesses a limit-cycle solution for certain values of the parameter a. What is the nature of the Hopf bifurcation that occurs at the critical value of a and state what the critical value is.
Homework Equations...
I have:
$\dot{x}=4x+y-x(x^2+y^2)$
$\dot{y}=4y-x-y(x^2+y^2)$
And I need to find $\dot{r}$ and $\dot{\theta}$
I got as far as:
$\dot{x}=r(\text{sin}(\theta)-\text{cos}(\theta)(r^2-4))$
$\dot{y}=r(-\text{sin}(\theta)(r^2-4)-\text{cos}(\theta))$
How do I go from here to $\dot{r}$ and...
Hello all.
I am studying a system and want to investigate how the frequency of y(3) varies under different conditions. However, my the fft I perform on it tells me the frequency is zero, which must be incorrect. I have tried a stack of things but can't see what the problem is. I'm relatively...
hi
suppose we have this equation :
d/dt(X)=A(t)*X
x is a n by 1 column matrix and A is a n by n matrix that is the matrix of coefficients.
coefficients of equations and consequently A are depend on t which is time.
how i Solve this equation ?
thanks
Hello all,
I don't have much experience with ODEs.
I have a simple system, which I believe is first order linear, similar to the following:
dA/dt = 2A + 3B - C
dB/dt = A + 2B - C
dC/dt = -2A + 5B - 2C
Now I would like to include the constraint that A + B + C = 1. How do I do this...
Homework Statement
A 3-storey building can be modeled as a system of coupled masses and springs as showen in attached document. Where mi is the mass of each floor, ki is the spring constant, xi is the displacement of each floor, and ci is the damping coeffcient.Homework Equations
I understand...
Hi to everyone, I have some problem in implementing a ODE system in matlab.
function dC = Model(x,C)
dC = zeros(2,1);
dC(1) = -2/C(1) -3*dC(2);
dC(2) = -3/C(2) -4*dC(1);
[x,C] = ode23(@Model(x,C),[0 300],[56.9 0]);
plot(x,C)
The debugger says
"? Input...
Given the ODE system:
v' = u(u2-1)
u' = v-u
Define w=u2+v2. Compute w'.
Find the largest radius R for which u2+v2<R so that the if the solution curve (u,v) is inside that circle the solution tends to (0,0) as t--> +\infty
Any guidance would be appriciated !
Homework Statement
I have 3 masses in 1-D connected by two springs. A driving force is exerted on the first mass and i need to derive the equation of motion of the last mass. I have worked out the Lagrangian to determine the equations of motion but cannot solve for z.
Homework Equations
The...
Homework Statement
Hello.
I want to study the stability of the origin of the following problem:
dx/dt = -2y
dy/dt = x + 2y
dz/dt = -2z
So the eigenvalues of this 3 x 3 matrix are -2, 1 + i, 1-i.
The eigenvectors are (0,0,1) , (2,-1-i,0), (-2,-1+i,0)...
Hi,
I need to solve very large complex ODE system. It is about time evaluation of system, which is at time t=0 in eigenstate with the smallest eigenvalue. For my test case I am trying to solve smaller similar problem, the ODE system is like:
C^{'}_{m} = - i \sum^{N-1}_{n=0} C_{n}(t) Exp[...
Hi
i got a question trying to solve some problems from my schools webpage and encountered a problem where I am given 2 RLC-Circuits and the corresponding dgls for the oscillation ( no problem so for all the standart basic E/M stuff)
But then I am asked to transform this system of 2 dgl´s of...
I have a system of spatial ODEs to solve... Actually a DAE system, but here's the issue:
The equations are vaild over a specific domain, x = 0..L
The equations are only bound at one point (thier "initial point") but at either 0 or L
f1(0)=0
f2(0)=100
f3(L)=0
f4(L)=100
(also an...
In order to solve the near field description of a round jet, I want to work out the variables F(\eta) , \rho(\eta) and Y(\eta) which represents the self similar stream function, density, and mass fraction respectively. The system obtained is...