All Questions
Tagged with calculus-and-analysis piecewise
69
questions
4
votes
1
answer
390
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 ...
- 75
1
vote
2
answers
180
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
...
- 2,335
2
votes
1
answer
325
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,...
- 53
2
votes
2
answers
162
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 & \...
- 197
0
votes
1
answer
94
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 ...
- 79
0
votes
1
answer
54
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 ...
- 125
0
votes
1
answer
70
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:
...
- 125
2
votes
1
answer
120
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 ...
- 125
0
votes
0
answers
46
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 ...
1
vote
0
answers
81
views
Speed up Integrate around Max/Min or Piecewise
Integrate around a convex combination of two functions containing Min or Max or ...
- 447
5
votes
2
answers
630
views
Integration of a piecewise function with parameters
Here is a simple piece-wise and continuous function:
f[t_,a_,b_]:=Piecewise[{{a t,t<1},{a,t<1+b},{a(2+b-t),t<2+b}}]
When I integrate ...
- 1,515
0
votes
1
answer
63
views
Integrating a function "bit by bit"
I am trying to integrate a function. But for this task I need to do it
"bit by bit". I created a working example that shows the problem.
...
- 127
5
votes
1
answer
168
views
Reduce to Piecewise
There are some similar posts on SE, but none of them seems to exactly address my issue.
I need to integrate a rather complicated function (over $x>1$) separately over two domains defined as ...
- 19.2k
2
votes
0
answers
64
views
Make Mathematica evaluate an integral symbolically
The following integral has a symbolic solution, which MMA does not return.
$\kappa(x) \begin{cases}
\text{mod}(x,1)\le0.5: & 1\\
\text{mod}(x,1)>0.5: & 0
\end{cases}$
$f(z)=\int_0^1 \...
- 856
1
vote
0
answers
64
views
Piecewise function inside Integrate - Wrong result
I tried to evaluate the following integral:
...
- 959