All Questions
19 questions
1
vote
1
answer
153
views
How to assume "much greater than" when there are multiple assumptions? [closed]
Assume $r_{o1} \gg R_S, r_{o2} \gg R_S, g_{m1} r_{o1} \gg 1, g_{m2} r_{o2} \gg 1$.
$$Z_{out} = \frac{r_{o1} (R_S + r_{o2})} {r_{o2} + R_S (1- g_{m1} g_{m2} r_{o1} r_{o2})}$$
Here is what I tried to ...
- 1,892
3
votes
1
answer
179
views
2
votes
1
answer
155
views
Evaluation of integral with parameters
I am trying to solve the following integral having two strictly positive parameters:
...
- 23
0
votes
1
answer
73
views
What is the most efficient/optimal way to simplify the given function? Does the given code need more assumptions?
I have a very long function for $\{x,b\}\in\mathbb{R}$ and $n=\{1,2,3,4,5,6,7,8,9,10\}$; here, I have only mentioned a short part of that. The function is a sum of the complex exponentials (a picture ...
- 1,159
2
votes
1
answer
72
views
Identical integral evaluating differently
I am trying to compute an integral but am getting two different answers using two near-identical methods. I wish to know why they differ.
...
- 95
0
votes
1
answer
233
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The derivation and simplification of the functions HeavisideTheta and Dirac
I encounter some problems, can you help me? Thanks.
Step (1) gives the expected result 3 DiracDelta[x], why (2) and (3)
can not give expected result ...
- 693
1
vote
1
answer
91
views
3
votes
1
answer
122
views
Mathematica and its default assumptions
I am a bit surprised that evsluating
Integrate[Exp[I n x],{x, 0, Pi}]
gives
$\qquad \frac{-i(e^{in\pi}-1)}{n}$.
What if $n = 0$? I didn't assume anything about $n$ ...
- 613
1
vote
0
answers
44
views
Why does Mathematica miss some solutions for my integral?
When computing the integral of two orthogonal sine functions
$\qquad \sin(n\,\pi\,x)\,\sin(m\,\pi\,x)$, where $n,\,m$ are integers > 0
Mathematica seems to miss the solution where $n=m$. I don't ...
- 33
0
votes
1
answer
193
views
Why are some of my assumptions ignored?
In my opinion Mathematica should be able to further calculate and simplify the output of G1[...].
...
- 335
6
votes
1
answer
310
views
Integrate under assumptions
I am trying to solve the following integral:
$$\int_0^\infty u^{\sigma-1} \exp\left[-c u^\sigma\right] \mathrm{d}u$$
under the assumptions $\sigma \in (0,1)$ and $c>0$.
I know the result is
$$\...
- 239
3
votes
1
answer
106
views
1
vote
3
answers
191
views
Incorrect sinc limit
I'm trying to compute in Mathematica 11.0 the limit of the $\mathrm{sinc}$ function at integers:
Assuming[k ∈ Integers, Simplify[Limit[Sin[π x]/(π x), x -> k]]]
...
- 233
1
vote
1
answer
79
views
Assumptions not working with Trianglewave or Floor functions
The assumption below:
Simplify[Integrate[Sin[2 n π x], {x, 0, 1}], Assumptions -> n ∈ Integers]
simplifies the integration and gives $0$ as the correct answer....
- 529
2
votes
1
answer
129
views
Getting wrong result when Integrating under an assumption [duplicate]
The simple integral
$$\int_0^b \cos\left(\frac{2\pi m(y-\eta)}{b}\right) \cos\left(\frac{2\pi \eta}{b}\right)\mathrm{d}\eta$$
can be easily evaluated by Mathematica as,
...
- 605
2
votes
1
answer
3k
views
Dealing with indicator functions
I am calculating the integral of two indicator functions with Mathematica. I'm having difficulty in imposing assumptions. What I have done so far:
To define an indicator function:
...
user21766
27
votes
4
answers
1k
views
An apparently "simple" limit?
Let $c$ and $h$ be real values.
I was using Mathematica to compute the limit $(h \rightarrow \infty)$ of the following expression:
$$
\frac{\left(h^2 +c^2 h^2 + \sqrt{4 h^2+\left(h^2+c^2 h^2\right)^2}...
- 12.1k
1
vote
1
answer
264
views
Assumptions are not being applied to integral
I am trying to use assumptions to simplify an integral, but I can't seem to get the assumptions to apply themselves. Here is the code I am using:
Note the expressions in the assumption can be found ...
- 227
16
votes
2
answers
18k
views
How to specify assumptions before evaluation?
If I request mathematica evaluate an integral for me, I'll often get a more general ConditionalExpression than I want. Example :
...
- 6,488