What is Linearization: Definition and 72 Discussions
In mathematics, linearization is finding the linear approximation to a function at a given point. The linear approximation of a function is the first order Taylor expansion around the point of interest. In the study of dynamical systems, linearization is a method for assessing the local stability of an equilibrium point of a system of nonlinear differential equations or discrete dynamical systems. This method is used in fields such as engineering, physics, economics, and ecology.
Homework Statement
Finding the linearization of the function F(t) = t2 /2 + 2t at t = -1.
Homework Equations
F'(t) = t+2
The Attempt at a Solution
F(t) + F'(t)(t-a)
-3+1(t+1) = t -2
urgent help for Linearization
Dear All,
y" (t)+ y'(t)+y(t)=u2(t)-1
Linearize the system about y(t)=0, u(t)=1, for all t>= 0
can we say that this equation is already linear at the given point
which will be y" (t)+ y'(t)+0=1-1 => y" (t) + y'(t)= 0
and no need for linearization.
Hi,
I am trying to understand an example from a FEM software manual. The manual mentions a nonlinear equation http://aamir-pc:2080/v6.9/books/exa/graphics/exa_eqn00137.gif and this equation is linearized to obtain http://aamir-pc:2080/v6.9/books/exa/graphics/exa_eqn00152.gif .[/URL] Can...
Homework Statement
How should the variables ( l and T) be plotted to obtain k from the slope of a linear graph? Identify (write out) the constants correstponding to the slope and intercept of the linear graph.
Homework Equations
l = lambda
l = (k/f)*(T/u)^0.5
The Attempt at a...
Hi All,
Homework Statement
I have modeled a simple spring mass system in Matlab and trying to use linmod to linearize the system.
The system models a mass that hangs from ceiling with a spring and damper. So, the forces that act on the mass are gravity, spring force and damping force. I...
Homework Statement
I'm sure this is easy but I've been looking at it for an hour and can't get anywhere. I have an equation that I need a linear form of.
Homework Equations
y = a*b*(x1*x22-(x3*x44/c))/(1+b*x1)
That's the equation I have to write a linear form of.
The Attempt at a Solution...
Hi everybody,
could anyone help me in the linearization of the following non linear non-homogeneous ODE?
A*dy/dt+B*y^(4)=C
where A, B and C are constants. y is a function of t. is it possible to reduce this equation to a Riccati equation? do you know any analytical, approximate or...
If you have a water tank with an inflow u, and an outflow v, you have that
\frac{dV}{dt} = A \frac{dh}{dt} = u - v.
You can now linearize this expression so that you get
A \frac{d}{dt}(\Delta h) = \Delta u - \Delta v = (u-u_0) - (v-v_0),
where \Delta h = h-h_0.
I think I...
Homework Statement
Consider an ideal fluid large enough to experience its own gravitational attraction. If the fluid is initially at hydrostatic equilibrium with density \rho_{0} (r) and pressure p_{0}(r) , it can develop small amplitude pressure waves which may be analyzed as follows...
Homework Statement
find the linearization of L(x) at a.
f(x)=ln7x, a=1/7
Homework Equations
f(a)+f'(a)(x-a)
The Attempt at a Solution
i got f(1/7)=0 and f'(1/7)=9.12
then shouldn't it be 0+.9.12(x-0)=9.12x?
Homework Statement
Find the linearization of the equation y' = y(-1+4y-3y^2) about each of the fixed points
The Attempt at a Solution
I think this is correct for finding fixed points:
Set y' = 0 = y(-1+4y+3y^2), so the fixed points are y = 0, 1/3, 1
What exactly does it mean by...
do you understand what "linearization" means?
Homework Statement
Linearization
4x'' + 3 cos(x-y)y'' +2 y^2 sin(x-y) +3g sin (x) = 0
Homework Equations
initial condition x(0) = y(0) = 0
The Attempt at a Solution
pls tell me the relevant steps to solve this problem.thanx
This is a general question, but what is the difference between finding the linearization and the tangent line to the same curve? And what about at a specific point?
Find the linearization of f(x)= x^1/3 at a=-64
so i am trying to use f(x)=f(a)+f'(a)(x-a)
f(a)=-4
f'(x)=1/3(x^-2/3)
f'(a)=-1/48
so i get -4+1/48(x+64)
is that right?
Hello,
this is my situation: I've got some data from an experiment stored in matlab. So I plot the graph and get a x^2 curve. I plot the loglog graph and see a near-"perfect" line. Now I want to create the best approximation to it (in a least squares sense).
I don't want to do that...
Can someone point me in the right direction for this problem. I have no idea how to start on this. I know the linearization formula but i don't know if that's what i have to use here. can someone please help
problem: You want a linearization that will replace the function over an interval...
I am linearizing the function f(x,y,z) = tan^{-1}(xyz) at the point (1,1,1).
Since f(x_0,y_0,z_0)= \frac{\pi}{4} + \pi*n should I just take the first value or do I have to carry all the solutions through the linearization process?
Um, anybody remember this? I can put up some work if it...
Hello everyone,
I am stuck on a problem relating to graphical linearization. The way we did it in high school was much easier than here. Anyway here is the question:
There are many ways to graph equation (1) d=Vot+(1/2)at^2, depending on the arrangement of the variables d vs t. However...
Ok so here is the problem:
You have six steel bearing varying in size and you have their mass and diameter. When you graph the data you see that the mass (in Grams) goes up exponentially as diameter (in cm) goes up. Below is the table of the Mass and Diameters
M=.44 D=.4
M=2.04 D=.8...
the question is http://home.earthlink.net/~urban-xrisis/clip001.jpg
I got a different answer than what the book says...
so I need to find the formula of the graph.
H'(3)=f(3)=2
m=\frac{\Delta y}{\Delta x}
2=\frac{\Delta y}{x- \int^3_0 f(t)dt}
y=2(x+2)
y=2x+4
the book's answer...
Original question: Let f(x,y) = ln(xy) + yzcos(xz). Find the linearization of f at the point (1,1,pi/2). Use this linearization to estimate the change in the value of the function resulting from moving from (1, 1, pi/2) to (1.1, 1.2, pi/2 + 0.2).
I believe the first steps to completing...