All Questions
Tagged with calculus-and-analysis piecewise
69
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Problem Derivative (D) of function defined with Piecewise or UnitStep functions - SIMPLE BEAM PROBLEM, 3 SUPPORTS
I am solving a simple structural beam problem using slope-deflection approach - 3 support A(left- fixed), B(middle- pin), C(right - pin). Beam AB - uniform load, Beam BC - concentrated load in ...
- 63
2
votes
1
answer
90
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1
vote
2
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55
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Strange behavior when integrating vector valued piecewise function
The following straightforward integral should clearly equal $\{0,0\}$ for any $R\in\mathbb R$:
...
- 156
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1
answer
39
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Piecewise integration doesn't evaluate
I'm trying to integrate the following function:
$$q(d, \theta) = q_x(d, \theta) + q_y(d, \theta) - 2q_x(d, \theta) q_y(d, \theta)$$
where $q_x(d, \theta) = \min\left(2 - d\cos\theta, d\cos\theta\right)...
4
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1
answer
67
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Confusing cases in Piecewise
The following
FullSimplify[Integrate[Exp[I ω t] Sin[ω x]/ω, {ω, 0, ∞},
Assumptions -> t > 0 && x > 0]]
gives a piecewise output of the form
I ...
- 63
3
votes
2
answers
95
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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
<...
- 479
1
vote
1
answer
116
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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\...
- 123
3
votes
2
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96
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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: ...
0
votes
1
answer
343
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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 ...
- 101
4
votes
1
answer
148
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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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2
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317
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Using Piecewise to create a periodic waveform
I want to create a piecewise function that repeats after t=T.
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4
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2
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102
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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 ...
- 41
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votes
1
answer
78
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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}}];
...
1
vote
1
answer
83
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NDSolve with embedded piecewise function for state-variable
Given ODE:
$\dot{x}=-2 e^{-x^2} x + U$
where:
$U=-u_{as}$
$u_{as} = \begin{cases} \frac{e}{\psi_+-e}, & \mbox{if } e\mbox{>=0} \\ \frac{e}{e-\psi_-}, & \mbox{if } e\mbox{<0} \end{cases}$
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1
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Solving a complicated time-dependent function
I want to solve the following time-dependent system of equations:
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