Questions tagged [piecewise]
Questions about the Piecewise function, which is represented by different expressions for different ranges of values of its independent variable.
453
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Derivative of piecewise function returns one more case
I define the following piecewise function:
U[c_,n_,g_,p_]:=Piecewise[{{c^(1-g)/(1-g)-n^(1+p)/(1+p),g!=1}, {Log[c]-n^(1+p)/(1+p),g==1}}]
When I take the derivative
<...
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2
votes
1
answer
71
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How to plot a function with different conditions (if or which or piecewise)
The given function is
This function is plotted to be
...
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7
votes
2
answers
239
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How to remove branches in Piecewise with measure 0
I am doing Convolve over UnitTriangle in 2 dimensions and the resulting piecewise function has conditions with measure zero (...
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-4
votes
1
answer
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I can't plot a certain solution
DSolve[{x''[ u] == -(1/ 2)*(2*1*(\[CapitalTheta] (u + a) - \[CapitalTheta] (u - a)))*x[u]}, {x[u]}, {u}];
x[u] /. {{x[u] ->
C[1] Cos[Sqrt[2] Sqrt[a] u Sqrt[[...
1
vote
2
answers
112
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NDSolve with piece-wise function and BVP
How to numerically solve a system of differential equation with boundary conditions and piece wise affine functions ?
Consider the following system of differential equations from some optimal control ...
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0
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1
answer
47
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How to plot the derivative of a piecewise discontinuous function (by excluding discontinuity points)
With the following code I am trying to get a plot for the derivative of the ftot1 function, which is a piecewise discontinuous function defined as the sum of other two piecewise discontinuous ...
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0
votes
0
answers
51
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Using DSolve, For A System With A Piecewise Function, And For Given Boundary & Continuity Conditions
I'm trying to solve a system of ODE's, analytically, to find the integration constants.
The system is the following (with zUpper=125 000 and zLower= 200 000).
For 0 <= z <= zUpper:
3 T''[z] == 0....
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1
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1
answer
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Derivative of long expression renders Piecewise[…<<…>>…] in Jupyter notebook
My mathematical problem is to solve the optimization problem:
$$ Max_{u} \quad \mathbb{E}[\gamma S-S^2]$$
where $$S= A_0 u X+a-\max(\alpha u X+b,0)$$
with $\gamma,A_0,a,\alpha,b$ some constants and $X\...
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1
vote
1
answer
57
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Vectorplot shows empty result
I've tried to draw a vector plot with piecewise functions, but it shows empty result.
When I don't use piecewise functions, Vectorplot works well..
I can't figure out what the problem is.
I would ...
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0
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0
answers
52
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Numerical integration of iterated integral with piecewise integrand
I need to plot the following integral:
$$
\Omega(t)=\int^{x_1(t)}_0 {4\pi x_i^2\rho(x_i,t=t_s)\int^\infty_04\pi x^2\rho_{reg}(x_i,x,t)dx}dx_i
$$
where
$$
\rho(x_i,t)=
\left\{
\begin{...
1
vote
0
answers
46
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A piecewise inequality not simplified to True [closed]
In = Simplify[-a + Piecewise[{{-b, t > c}}] < 0, {a > 0, b > 0, c > 0}]
Out = Piecewise[{{-b, t > c}}] < a
Why the result is not evaluated to ...
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3
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2
answers
65
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How do I integrate this piecewise function with Mathematica?
I came across the question of what percent of numbers from 0 to 1 have a logerithm whose floor is even. What I did was I made a piecewise function: ...
3
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2
answers
142
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FunctionPeriod for functions defined in a Piecewise manner
To create a minimal example, consider a piecewise function:
...
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7
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1
answer
130
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Plot discontinuities use Piecewise
how can I get a plot like this?
I tried with in Mathematica 13.0:
...
3
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1
answer
55
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Piecewise Functions from List of Functions
I have multiple functions from two different NDSolves that I would piece together. Here is a working minimal example:
...
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1
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5
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1
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How can I remove the outermost pair of brackets enclosing a Piecewise function when it occurs in an equation?
Recently I have been annoyed by an automatic formatting in MMA, that is when a Piecewise function occurs in an equation, it will be enclosed by a pair of brackets automatically by MMA, although when ...
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2
votes
2
answers
72
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Piecewise based on the length of the list
I want to create a piecewise function that depends on the length of the list.
Let's say I have a list, and a corresponding piecewise function:
...
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4
votes
4
answers
189
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Parts of a Piecewise Matrix Function in NDSolve
First time posting.
Reproducing the Problem
I'm relatively new to Mathematica (using v.12.3), and working on a project. My problem can be reproduced with this.
...
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votes
1
answer
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How to convert traditional form of piecewise output into input piecewise function? [closed]
I have an output in this form. Let's say the f[s_,t_]:=output; When I try to calculate points at s, t e.g f[0.1,0.1], the output is still the same instead of any point.
but if I convert this output ...
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0
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35
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Using the recursion index to compare with a value in another list
I am trying to generate an arrivals and departures plot for a signalised junction with the following parameters:
lambda: rate of arrival
c: cycle length of traffic lights
g: length of time signal is ...
1
vote
2
answers
188
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Is there a way to fit a piecewise linear function to a list?
I need to find a piecewise linear function that is a proper approximation for sunrise/sunset times of each day of year. Due to some limitations, I cannot use any trigonometric functions. So the sine-...
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2
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1
answer
116
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Piecewise smooth rectangular pulse
I am wondering how to create a rectangular pulse with a non linear falling edge on one side, and straight line sloping from the falling edge (the red line).
So far I have managed to get the plot ...
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0
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48
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How to plot Piecewise function using symbols as axis
I want to make a plot of V(r) vs r with my x-axis being in units of R, and my y-axis in units of q/(4πqεR). I used discrete values of q and R to get the plot to work but I would prefer if they could ...
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0
votes
2
answers
81
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Mathematica Issue [closed]
I'm completely new to Mathematica, and I'm facing an issue.
So basically, I know that Out[43]'s answer is 1+2a+3b. And out[44] is a+b. I dont know why it's giving me a different answer here. Can ...
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0
votes
1
answer
123
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How to obtain the convolution of these functions?
I am starting to use Mathematica. I wanted to compute
$$\nabla F*\phi(x),\;x\in\mathbb{R^2}$$
where $F(x)=\ln\|x\|$ and $\phi(x)=\chi_{B(0,2)}(x)$.
I am a new user of this software, so I don't know ...
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4
votes
1
answer
133
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Mathematica 12.1 integrates functions individually but not their sum
I found something odd in MMA 12.1 when symbolically integrating DiracDelta and Piecewise. These functions are integrated individually but not their sum. The following code
...
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1
vote
1
answer
128
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System of ODE with piecewise functionals
I am trying to solve a system of ODE. I am new to Mathematica
What I am trying to get is the plot labelled 1 & 2.
...
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0
votes
1
answer
31
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Manipulate plot with Eplilog where location of Point is given by a function outside of the Plot/Manipulate command
Consider a piecewise function such as
f = Piecewise[{{x, 0 <= x <= x1}, {Sin[\[Pi] x], x1 < x <= x2}}]
I want to plot f using Manipulate and add a ...
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1
vote
1
answer
97
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Colour plot based on x-axis value
I am trying to adapt [this solution for colouring the different sections of a Piecewise function]
I want to colour based on the x-axis value. I have two functions I want to do this for, one is ...
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1
vote
1
answer
83
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NSolve for Piecewise function
I have a piecewise function. I want to find the root of this function with the NSolve command. But, it does not give me any result and it just prints the equation. I can find the root with FindRoot, ...
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3
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1
answer
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How to use ConvexOptimization on a piecewise function?
I define a simple piecewise convex function, but ConvexOptimization does not take it as a valid input:
...
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5
votes
2
answers
143
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Using Piecewise to create a periodic waveform
I want to create a piecewise function that repeats after t=T.
...
- 19.3k
4
votes
2
answers
100
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Plot and differentiate a piecewise vector function [closed]
Consider the map $f:\mathbb R^2\to \mathbb R$ defined as
$$ f(x,y)=\begin{cases}
\|(x,y)\|^2\sin(1/\|(x,y)\|) & (x,y)\neq0 \\
0 & (x,y) =0\\
\end{cases}$$
I am trying to get a ...
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0
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1
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Plotting a piecewise multivariable function [closed]
I want to plot the following function :
\begin{equation}
f(x,y)=\begin{cases} \frac{xy(x^2-y^2)}{x^2+y^2}, \; (x,y)\neq(0,0)\\ 0, \; (x,y)=(0,0)\end{cases}
\end{equation}
I tried the following :
<...
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1
answer
49
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Difficult on integration the normalization of a piecewise function
I have a little problem; I have defined the following Piecewise-function in the variables {x,L,w}:
f[x_, L_, w_] := Piecewise[{{x w (L - x), 0 <= x <= L}}];
...
0
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0
answers
86
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piecewise vector field and composition of piecewise functions
I have the following vector field
...
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0
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1
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I have a variable error and was curious to see if it's due to piecewise functions?
So I have a displacement function sigx as a function of "t" (time) and sig.pre (pre-stress). At some time "dx": force "fo" goes to 0, and the same displacement function ...
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0
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1
answer
70
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NIntegrate seems to not recognize multiplication of Piecewise function and f[t_]:= function, Why?
Considering inputs:
vti={0, 1.5, 2.4, 5.0675, 7.735, 10};
Vscc=1.5; PSA=0.025; f=0.6; m=10;
I defined a function "pwtemp2", using "FC1" and &...
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1
answer
78
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how to find and b piecewise function mathamatica [closed]
how would i find a,b for
how would i write this in Mathematica to get a and b
0
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0
answers
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Piecewise[ ] for joining InterpolationFunction objects?
I want to combine InterpolationFunction objects, results of an NDSolve in a loop, into one function. This is my code:
...
0
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0
answers
96
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Summing `Piecewise` function with many cases efficiently
Schematics of the question: I have two piecewise functions $f_1$ and $f_2$ as
$$f_1 = \begin{cases}
\textrm{value 1}, & \textrm{case 1}, \\
\vdots & \vdots \\
\textrm{value 1024}, & \...
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1
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2
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100
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Simplifying expressions with `Sign` functions to a single piecewise format
I have the following expression with many Sign functions:
...
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1
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57
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Single computation is fast, but 6 computations are extremely slow
I have an expression that involves many Sign functions. I want to expand this in the piecewise format.
My function is:
...
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1
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59
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4
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2
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What is the scope of the bug where Piecewise breaks DSolve?
Bug introduced after 9.0.1, persisting through 12.3.1. Fixed in 13.0
I have identified a bug in DSolve when differential equation includes a ...
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0
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68
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NDSolve with Piecewise function consideres some value inside Piecewise as Indeterninate
I'm solving a PDE, with one coefficient being piecewise. The issue appears to be that NDSolve somehow consideres piesewise boundary as ...
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Piecewise Function Definition
I am new to Mathematica, and I am unsure on how to do this.
I am working with piecewise function
$$
f_N(x) := \begin{cases} 1 & \text{if}\;\;x = j\sqrt{3}, \quad j=1,...,N \\
0 & \text{...
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Did Mathematica make a mistake or was it me?
I'm having a little trouble with Mathematica. There are two expressions that should be equal over a given region. Each of which consists of three terms that should be equal individually:
term1 of ...
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1
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3
answers
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How solve this nonlinear equations system by 12 unknowns?
We consider the following integral equation of mixed type:
$x[t]=\frac{t^4}{6} -\frac{t^3}{3} +t+\Sigma_{\mu=1}^2\int_{0}^t k_\mu[t,s]G_\mu[s,x[s]]ds
,0\leq t\leq 1 $ ; (1)
where
$k_1 [t, s] = s^3$...
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