Questions tagged [piecewise]

Questions about the Piecewise function, which is represented by different expressions for different ranges of values of its independent variable.

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36 views

Plotting iterates of a piecewise defined map

This is a follow up question to the one I asked here. I’ve succeeded in figuring out how to plot the first image of my piecewise defined transformation $T: [-1,1]^2 \to [-1,1]^2$, but now I want to ...
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1answer
44 views

Plotting image of piecewise-defined transformation

I have a transformation $T : [-1,1]^2 \to [-1,1]^2$ that is piecewise defined in the following way: \begin{align*} T(x,y) &= \big(a(x-1)+1,\:\left(b-cx\right)(y-1)+1\big) \quad \textrm{if } y > ...
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2answers
134 views

Approximate the piecewise constant with a smooth function

Let us first define a two regions as follow : inner=1;outer=2; reg1 = Disk[{0, 0}, inner]; reg2 = Annulus[{0, 0}, {inner, outer}]; glass=1.5;air=1; Now let's say I ...
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1answer
269 views

How to illustrate the optimal solution with kinked constraint?

I have a simple optimization problem with a linear, continuous constraint or a kinked constraint. The optimal solution is either a tangent point with f*<T or at the kink with f*=T. The standard ...
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54 views

Manipulate and Plot of Tangent Point in Optimization Problem with Kinked Constraint: Solve and PieceWise Problems

I'm trying to illustrate an optimization problem with a piecewise constraint creating a kink at the maximum value of T if n>0. ...
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18 views

Assumptions with piecewise problem?

I am trying to apply the assumpion of 0<s<1 throughout the calculation however the piecewise condition does not accept it automatically. Is there any way to avoid the manual choice of x>0. ...
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2answers
101 views

Benefits/pitfalls of defining function that is discontinuous at a point “explicitly” vs using piecewise?

For example, suppose I wanted to define a function, f that is $f(x)=x^2$ except at $x=1$, where $f(x)=5$ Two ways I can define this are ...
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1answer
51 views

How to convert a Piecewise function in a HeavisideTheta function?

I want to convert a Piecewise function in a HeavisideTheta function in order to correctly evaluate its derivatives at the point of abrupt change and then integrate the result along the axis. How can I ...
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1answer
48 views

Both Dsolve and NDsolve for a differential equation failed

I tried both Dsolve and NDsolve for the following differential equation, it failed: It contains piecewise function ...
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2answers
68 views

How to plot HeavisideTheta with y=0.5 at x=0, and similar piecewise functions

How does one plot piecewise functions, with the ability to plot individual points along with open points to clearly show how values are defined at discontinuities? Example: Image Credit with the ...
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53 views

How to get Integrate to determine units

In a similar fashion to the question asked here, I am having trouble trying to get Integrate to correctly determine the units of the integrand: Here I have plugged in specific values into the general ...
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39 views

Piecewise function inside ProbabilityDistribution causing errors

I'm using a complicated Piecewise function to create a probability distribution and draw random points from it. ...
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2answers
66 views

How to take limits in Fourier series?

I have a Fourier series which produces an impulse train of period j+1. In principle, it is given by ...
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1answer
84 views

Continuity and derivability of a multivariable function at a specific point

I have this function: f = Sqrt(Abs(x^2 - x*y)) So, how can I prove that it is derivable and/or continue in a point, like (0,0)?
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1answer
29 views

Plotting an iterated piecewise function with endogenous nodes

I am trying to plot a piecewise function that I can define recursively, where the nodes are endogenous as well. Basically, $f(l)=a^{t}$ when $l \in \left( \frac{\mu}{\alpha^{t-1}(1-\alpha)+\mu(1-\...
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1answer
53 views

Error in drawing a Piecewise function!

I want to plot the piecewise function (FP), which is define as: $$FP=\cases{1,&$\text{Eta}<J$\\ \frac{1-\left| \text{Gam}\right| }{2}, &$\text{Eta}=J$\\ \frac{\left| \text{Gam}*J\...
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1answer
85 views

Limit of multivariate piecewise function

Let's say we have a multivariate piecewise function f[x1_,x2_]:=Piecewise[{{Sin[x1]/x1,x1>x2},{Sin[x2]/x2,x1<=x2}}] Now we want to determine the limit in f(0,...
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1answer
57 views

How to evaluate a multidimensional NIntegral in a range where certain conditions must be satisfied by the variables

I have a function f which looks similar to this : f[a_, b_, c_] := NIntegrate[sigma[a, b, c], {a, -valueA, valueA}, {b, -valueB, valueB}, {c, -valueC, valueC}] and ...
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1answer
54 views

How do I introduce an assumption when defining a piecewise function?

Define m as an integer. I want to specify a Piecewise function f[x,n] that takes value ...
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0answers
35 views

Find edges of a piecewise curve

I have a continuous function f[x], and I want to calculate the coordinates of the discontinuities in Round[f[x]]. My code needs ...
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1answer
37 views

Should be a Piecewise function, a ConditionalExpression or Indeterminate, but it is a number

I apologize in advance for the lack of focus of my question. Consider the function: f[x_, y_] := x/(x + y); f[0,0] evaluates to ...
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0answers
93 views

How do I create a piecewise function using Do[] or While[]?

The following non-linear circuit is an uncontrolled three-phase full-wave 6-pulse rectifier. The inputs are $v_{an}(t) = V_m \sin (\omega t)$, $v_{bn}(t) = V_m \sin (\omega t-120°)$ and $v_{cn}(t) = ...
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2answers
157 views

Finding the maximum of a piecewise function

I have the following piecewise function of the variable $e_f$: $$g(a,b,c,w,F,e_h,e_f)=\begin{cases} \frac{(c-a e_f) (e_f (4e_f w-a)+c)}{8 b e_f^2} & \left(e_f=e_h\land e_f>\frac{c}{a}\...
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1answer
59 views

Piecewise function not evaluating properly

I have a simple Piecewise function that defines a square pulse: ...
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1answer
58 views

ParametricNDSolve “delayed time” error message

Issue reported to Wolfram, Inc as a possible bug in Version 12.1; CASE:4554034. When trying to solve a system of delay-differential equations with ParametricNDSolve...
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2answers
65 views

Double integration with a piecewise function gives wrong result

I am attempting to solve a double integral $$I(t) = \int_0^t dt' \int_0^{t'} dt'' f(t'')$$ of a piecewise function of the type $$f(t) = \begin{cases}1 & \text{for } 0 \leq t < a \\ -1 & \...
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1answer
87 views

How to plot a thermodynamic cycle? [duplicate]

I try to plot a thermodynamic cycle with the data displayed using the tool, "Piecewise", but in the case of isochoric and isobaric processes, Mathematica shows nothing. Could someone please tell me ...
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47 views

Piecewise function and NDSolve [duplicate]

I'm trying to solve a system of differenial equations involving a piecewise function with NDSolve. I tried to define this function using Piecewise but the kernel ...
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1answer
50 views

Understand output of Integration

Could someone help me understand the output of the following Integration in Mathematica? Specifically, (a) what is the meaning of "True"? (b) Why is the answer in two parts which seem to overlap ...
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1answer
31 views

Export data from NIntegrate and Piecewise

I use the following to calculate my Integral. ...
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2answers
140 views

Best 5 segment piecewise linear fit

I'm trying to get a piecewise linear best-fit for the closing price of one of the stocks I'm interested in. The logic seems ok, and the workflow works for a straight-line (ie 2 pts, ie 1 segment) ...
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2answers
69 views

HeavisidePi Plot

how could i change This Plot to something like this plot each two plots are concatenation of HeavisidePi The code for the first plot is : ...
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1answer
51 views

Why does HeavisideTheta not have an implicit piecewise expansion?

The Heaviside step function implicitly expands to a piecewise function: UnitStep[t - 3] // PiecewiseExpand $$ \begin{cases} 1 & t\geq 3 \\ 0 & \text{...
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1answer
72 views

TransformedRegion with piecewise function

Is it possible to use TransformedRegion with a Piecewise defined function? I tried the following, but it doesn't work and I don'...
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33 views

Plotting a piecewise function MRI problem

I have this M.R.I. question, and i need to plot a function with some 'a' and 'b' parameters and 't' as a variable: ...
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35 views

Solving a Piecewise ODE [closed]

I am attempting to solve a piecewise ODE. $y' = \begin{cases} -1 & \text{for $y \geq 0$}\\ 1 & \text{for $y < 0$} \end{cases}, \qquad y(0)=0, \qquad x \in [0,1]$ I have attempted solving ...
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21 views

```PiecewiseExpand``` doesn't work as expected with a recursive function

In an effort to examine this question on Math.SE, I defined the following functions ...
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25 views

Find and indicate the minimum of a piecewise function in the `Plot3D` diagram

I'm trying to indicate in my Plot3D diagram the minimum level of the dependent variable and the corresponding levels of two independent variables. More specifically,...
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1answer
50 views

Using subscripted symbol affects integration — why?

Below is a sample program that shows that Integrate is giving different results depending on whether I name the variable duration1 or ...
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1answer
43 views

Why do Integrate and DSolve/DSolveValue yield such complex expressions for Piecewise functions?

This code uses two different methods for integrating a very simple piecewise function but yields surprisingly complicated integrals: ...
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1answer
60 views

Piecewise integration not giving continuous result

I'm trying to integrate a piecewise function symbolically and I'm ending up with discontinuities which is surprising since the help mentions that constants are determined to ensure continuity. If I ...
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2answers
241 views

Graphing a Fourier Series

First off, I have created the following Fourier series for the below equation/condition: $$f(t) = \begin{cases} 0, & 0<t<1 \\ 1, & 1<t<2 \end{cases} $$ My Fourier Equation for ...
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1answer
24 views

Limiting the Domain of a Function

Currently, I am trying to plot (using Mathematica) the following function: $$f(t) = \begin{cases} 0, & 0<t<1 \\ 1, & 1<t<2 \end{cases} $$ And, to try to plot this, I did some ...
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41 views

Bad Integral evaluation for Piecewise function

I have been trying to evaluate this symbolic function: f[ρ_, R_, α_, yp0_, yp_] := R*((ρ - R*Cos[α])^2 + (R*Sin[α])^2 + (yp-yp0)^2)^(-(1/2)); Mathematica can ...
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1answer
70 views

Plot of Piecewise function is slow

While working on answer for question (here) I found out that the Plot is incredible slow for Piecewise function: Some preparations: ...
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1answer
56 views

Plotting Piecewise function?

I am facing a problem in plotting the Piecewise function. I simplified my problem to take the following form: where \[Sigma][i] are Pauli matrices. My code is: <...
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1answer
65 views

How do I combine a piecewise function within a parametric plot?

I'm trying to combine two functions together piecewise style, but nest that within a ParametricPlot function. Here's my code right now: ...
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3answers
119 views

count conditional items in list

I have a list of the form: {1,1, (1 if x>y, -1 if y>=x), -1} I want to count the number of 1's in the list. The output I'm looking for is something of the ...
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1answer
79 views

Forcing the fit of a nonlinear piecewise function to be continuous

I am trying to fit some data ...
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2answers
83 views

IVP Piecewise ODE: Changing the Domain outside region of interest changes result dramatically

Good afternoon, I am attempting to solve the following ODE: ...

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