All Questions
Tagged with calculus-and-analysis piecewise
15
questions
10
votes
2
answers
263
views
Problem with Integrate with Piecewise and PrincipalValue
Bug introduced in 8.0.4 or earlier and persisting through 11.3
In the course of developing an alternative solution for question 127301,
With,
...
- 61.8k
6
votes
2
answers
3k
views
Derivatives of piecewise functions of functions
Background
Derivatives of piecewise functions in Mathematica are computed according to special rules. According the Piecewise documentation (see Possible Issues),
...
- 3,447
6
votes
2
answers
1k
views
Derivative of piecewise function
I tried to find $f'(0)$ of this function:
$$f(x) = \begin{cases} x\cdot\sin(\frac{1}{x}) & \text{if $x\ne0$} \\ 0 & \text{if $x=0$} \end{cases}$$
This is what I tried in Mathematica:
...
- 2,341
3
votes
2
answers
690
views
Derivative of Continuous and Differentiable Piecewise function is indeterminate
I'm attempting to analytically stitch together two linear functions with two quadratic functions. The function I'm considering, then, is a piecewise function consisting of 4 parts. Below are the ...
- 75
0
votes
1
answer
1k
views
Finding the tangent to a piecewise function
I'm new to Mathematica and I am trying to calculate the expression of the tangent to the curve
...
5
votes
2
answers
317
views
Using Piecewise to create a periodic waveform
I want to create a piecewise function that repeats after t=T.
...
- 56k
4
votes
1
answer
395
views
Integration of a piecewise function
Define
f[x_, i_] := Piecewise[{{1/n,
0 < x < (i - 1)/n}, {(i/n - x), (i - 1)/n < x < i/n} , {0,
i/n < x}} ];
I would like to compute
...
- 43
4
votes
3
answers
1k
views
Most efficient way to integrate a linear piecewise function
I am having a lot of trouble integrating a simple function. Here's the context: I generate data from two distributions, and I want to calculate the overlap coefficient of representing those datasets ...
- 967
2
votes
2
answers
1k
views
Piecewise Integration
I am trying to integrate a piecewise defined function twice. It represents the acceleration of a projectile. I am obtaining it's position as a function of time if it starts from rest at the ground, ...
- 123
2
votes
0
answers
540
views
Piecewise functions Integration with symbol
I want to integrate one piecewise functions as following,
...
- 21
2
votes
2
answers
178
views
Integrate over a piecewise function [closed]
I want to calculate the indefinite Integral of
$$f(x)=\begin{cases}
2x\cos(\frac{1}{x})& \text{ if } x\ne 0 \\
0& \text{ if } x=0
\end{cases}.$$
I use the following code:
...
- 149
1
vote
2
answers
414
views
Integration over a (non-parametric) curve defined by indicator function
I want to integrate the real function myFun defined on a 2D plane over the line locus, defined as the solution of a set of ...
- 572
0
votes
0
answers
242
views
Implicit function: derivative of piecewise function that has a FindRoot in one of the pieces
I have a piecewise function that has as one piece the result of a numerical approximation, like in the example below:
...
- 393
0
votes
1
answer
142
views
Strange behavior of derivative when using Abs[] [duplicate]
This code where I try to visualize Newton's Method on the function $f(x)=\sqrt{|x|}$ works fine when I define $f(x)$ piecewise. Then why doesn't it work when I define ...
- 2,341
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