Questions related to the calculus and analysis branches of Mathematica, including, but not limited to, limits, derivatives, integrals, series, and residues.

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10
votes
2answers
892 views

Maximizing a function with assumptions

Using f[s_] := Log[(s/r)^α ((α - 2) n0 r^α + 2 π Pmax ρ r^2) /((α - 2) n0 s^α + 2 π Pmax ρ s^2)]/s When I run the following line: ...
7
votes
2answers
612 views

Integration with vector coefficients

I asked this same question in Mathematics, and it was suggested I might try here. I'm more comfortable with Maple, but if I can get Mathematica to do what I'm after, so much the better. Basically ...
4
votes
3answers
517 views

Integrating with multiple indicator functions

I am trying to calculate an integral involving multiple indicator functions, such as: $$ h(u,v,w) = -\int_0^1 J^{\prime\prime}(s) (I_{(0,s]}(u) - s)(I_{(0,s]}(v) - s)(I_{(0,s]}(w) - s)\, ...
9
votes
3answers
2k views

Derivative of real functions including Re and Im

When deriving functions using Re, Im or Arg (and probably some other functions as well), ...
13
votes
3answers
819 views

How to evaluate the 0/0 type limit in Mathematica?

When I use Limit to evaluate the $k \to 0$ limit of ((k + 2) (α^2 - Sqrt[α^4 + k]) + k)/(α^2 - Sqrt[α^4 + k] + 2 k) If ...
6
votes
5answers
744 views

Trying to prove that $x\sin(\frac{\pi}{x})\ge\pi \cos(\frac{\pi}{x})$ for $x\ge 1$

Consider the function f[x_] := x Sin[Pi/x] I want to prove that this function is increasing for $x\ge 1$. This can be done with the first derivative. We have to ...
8
votes
2answers
819 views

Bug in Integrate for Mathematica

Consider the following: ...
13
votes
5answers
732 views

Does $x>0$ imply that $x\in\mathbb{R}$?

Let’s assume I input Assuming[x > 0, expression] Is it assumed by Mathematica that $x$ is a real number? Or that the real part of $x$ is positive? Something ...
8
votes
5answers
496 views

simplifying $\frac{\log x^a}{a} = \log x$

If one makes the assumptions $x>0,a>0$, then $\frac{1}{a}\log x^a = \log x$. Thus, in Mathematica, Simplify[1/a*Log[x^a], {a > 0, x > 0}] returns ...
2
votes
1answer
199 views

Checking if first derivative is zero at a given point

I have a function V[a_, h_, tau_] := (Sqrt[3]/2) h (Sqrt[3] a + h/3 tau)^2 now I want to check, whether its first derivative is zero in a given point. Say for ...
2
votes
1answer
258 views

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. ...
12
votes
5answers
2k views

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 ...
16
votes
1answer
718 views

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 ...
3
votes
1answer
264 views

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 ...
2
votes
1answer
480 views

Speeding up a slow indefinite integral

I have found an alternative way to express an old solution: ...
9
votes
4answers
4k views

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: ...
11
votes
2answers
4k 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 : ...
8
votes
3answers
552 views

Inverting a function in a certain region

InverseFunction works well for globally invertible functions, like f = 2*# + 2 &; InverseFunction[f] ...
4
votes
1answer
575 views

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 ...
5
votes
3answers
688 views

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') ...
7
votes
1answer
585 views

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 ...
4
votes
5answers
2k views

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 ...
8
votes
1answer
519 views

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.
7
votes
2answers
3k views

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 ...
13
votes
2answers
787 views

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 ...
9
votes
2answers
571 views

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 ...
17
votes
2answers
235 views

Symbolic derivatives are being calculated numerically

Just found the following while debugging a problem. Mathematica is calculating the derivative of IntegerPart[x] in some odd way: ...