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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2
votes
1answer
468 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 : ...
7
votes
3answers
526 views

Inverting a function in a certain region

InverseFunction works well for globally invertible functions, like f = 2*# + 2 &; InverseFunction[f] ...
4
votes
1answer
568 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
685 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
578 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 ...
7
votes
1answer
509 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
773 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
566 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
225 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: ...