Questions tagged [calculus-and-analysis]
Questions related to the calculus and analysis branches of Mathematica, including, but not limited to, limits, derivatives, integrals, series, and residues.
4,721
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Integral not simplifying
I specify a function in terms of an integral and then try to evaluate it with Simplify. However, the answer is not really simplified to what it should be.
...
- 403
16
votes
5
answers
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How can you compute Itō Integrals with Mathematica?
How can you compute Itō Integrals with Mathematica? I tried searching through the documentations but I didn't find anything.
P.S. I was not at all sure how to tag this question. I had to put in at ...
- 3,156
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votes
2
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How can the {x,y,z} points that fall on the outer boundary of a set of values be selected and smoothly surfaced?
For a given set of x,y,z values, that may, or may not form a uniform shape, how can the center of the data cloud be found, and the surface points be located and a solid smooth surface created from ...
- 4,466
3
votes
1
answer
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n-fold symbolic integral in Mathematica
I am trying to compute symbolically a n-fold integral (n is a parameter of a function) over, say, the cube [0,a]^n. My code looks like this
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- 215
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1
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Speeding up a slow indefinite integral
I have found an alternative way to express an old solution:
...
- 51
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2
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3k
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Plot Indefinite integral
I'm having a hard time to find a solution to a numerical limitation on mathematica:
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- 51
22
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2
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2k
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Why does Mathematica give the wrong answer when integrating?
Bug introduced in 8.0 or earlier and fixed in 9.0.0
I integrate
Integrate[Exp[I Cos[b - c]] Cos[b], {b, 0, 2 Pi}]
Mathematica gives:
...
- 983
13
votes
5
answers
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Finding critical points of a function
Let's say we'd like to find the critical points of the function $f(x)=\sqrt{x-x^2}$. Finding out where the derivative is 0 is straightforward with Reduce:
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- 919
15
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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 :
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- 6,288
9
votes
3
answers
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Inverting a function in a certain region
InverseFunction works well for globally invertible functions, like
f = 2*# + 2 &;
InverseFunction[f]
...
- 14.8k
6
votes
1
answer
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Definite and Indefinite integral give different results for piecewise function
I have the following function:
$$
f(q,y)=
\begin{cases}
\tfrac{11720+p}{37791360} & -11720<p<-7720 \\
0 & \text{True}
\end{cases}
$$
where $p = 443\ y-777600\ \sin^{-1}\left(\frac{q \...
- 435
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3
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recursive integration
I am trying to do multiple integrations recursively. For instance, I would like to do the following equation for arbitrary integer $n$:
$\displaystyle R_n(t) = \int_0^t \mathrm dt' R_0(t-t') R_{n-1}(...
- 2,765
9
votes
1
answer
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Hankel Transform integrals won't work in Mathematica
I'm trying to do this integral, which is shown on the Wikipedia page on the Hankel transformation:
$$\int_0^{2\pi}\mathrm d\varphi\;e^{\mathrm im\varphi}e^{\mathrm ikr\cos(\varphi)}$$
The answer is ...
user854688
5
votes
5
answers
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Using implicit differentiation to find a line that is tangent to a curve at a point
A few days ago I asked about using differentiation to find a line that is tangent to a curve at a given point. J.M. provided a very elegant way to solve these kinds of problems in Mathematica.
Now I'...
- 919
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2
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Is there any automatic differentiation package?
I'm wondering if an automatic differentiation package exists for Mathematica.
This is what I mean by automatic differentiation.
- 10.9k
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2
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9k
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Equation of a line that is tangent to a curve at point
A common problem in the derivative section of calculus texts is "find the equation of the line that is tangent to the curve $y = \ldots$ at the point $P$."
To find the line that is tangent to $y = 2 ...
- 919
13
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1
answer
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Kramers-Kronig relations
I am trying to calculate the change of the refractive index from the change of the absorption coefficient using the Kramers-Kronig relations, in Mathematica.
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- 633
14
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2
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Suppressing negative roots in Mathematica
Problem
Using Mathematica's Solve operator can sometimes lead to an output involving a positive and negative root (say when solving for a variable such as ...
- 345
11
votes
2
answers
1k
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Series expansion of an inverse
I have to find the series expansion of the inverse function of : $\arctan\left(\frac{\ln(1+x)}{1+x}\right)$
How do I find out the series expansion of any inverse ?
Note: The inverse of a function $f$...
- 2,449
30
votes
4
answers
12k
views
Implementing discrete and continuous Hilbert transforms
What is an efficient and accurate Mathematica implementation of the Hilbert transform, for both continuous and especially discretely sampled functions?
This transform relates phase and amplitude in ...
- 267k
34
votes
2
answers
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Symbolic derivatives are being calculated numerically
Update: (1) By V11, not sure of the exact version, the derivative IntegerPart' has been given a symbolic definition. (2) The numeric derivative computed has changed ...
- 115k