# Questions tagged [linearization]

On the many different ways to turn non-linear systems of equations into linear ones.

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### How to linearize a max function about a small change??

My question is the following: Given a vector field $\mathbf{v}$, we have the following functional: $f\{\mathbf{v}\}=1/|\mathbf{v}|_{\text{max}}$, where $|\mathbf{v}|_\text{max}$ is the maximum of the ...
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### Linear Instability vs. Nonlinear Stability

I have an N-body system that I can simulate directly. For certain initial conditions, this system is unstable to a buckling behavior (exponential growth in an angle), and for others it's stable (...
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### Help in expressing in McCormick Envelope

The statement which I want to express in McCormick envelope is $\sum_ix_iM_{ij}\leq F_j$ for all $j$ The initial McCormick envelope I wrote where $w_{ij}=x_iM_{ij}$, is: $\sum_iw_{ij}\leq F_j$ for all ...
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### Taylor series for linearization

I need to apply Taylor series to linearize following equation $$f_{dr}= Au'+ Bu + C u^2 +D$$ Here, $A$, $B$, $C$, $D$ are constants and $$u'=\frac{{\rm d}u}{{\rm d}t}, u=\frac{{\rm d}x}{{\rm d}t}$$ ...
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### Linearization of a Second Order Nonlinear Differential Equation

I am in need of help with the linearization of this equation around the initial condition u=pi My main confusion lies in the middle term .5xdotx. I cannot for the life of me figure out what to do with ...
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### Find the linearization of the following curves at a suitably chosen integer near a [closed]

Find the linearization of the following curves at a suitably chosen integer near a $f(x) = x^2 + 2x$ $a=0.1$ in this i used the formula $L(x)=f(a) + f'(a)(x-a)$ and solved and got $L(x)=2.2x-0.01$ is ...
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### Can Linearization from Calculus I be used as a Multivariable function?

In my math class yesterday we learned about linearization of a function to approximate values in a small range of x values (followed by Newton's method of approximating the zeros of functions). We ...
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### Linearising an inverse exponential function $A\exp(-C*x) + B$

I am doing a math-intensive Physics IA experiment, which is looking at the relationship between pressure and bounce height of a ball. With all the data, I came across a best-fit line, which is in form ...
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### Linear problem with min of hyperbolic functions as the objective [closed]

I am trying to convert the problem below to linear programming problem and solve it with simplex algorithm. I am aware that converting max and min in goal function usually means adding proper ...
From my previous questions, I have a variable : $Q$, which is function of a discrete known vector, $P$ and a binary variable $x$ : $Q=f(P,x)$. I know, we can linearize the products of (a) two / ...
I have the following nonlinear and non-autonomous system to solve ($a,b,c$ are specific constants): \begin{align} x^\prime &= -a\,\omega\,y+\frac{b}{\cosh t}\,\left(z-\frac{1}{z}\right),\\ ...