# Tagged Questions

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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### How to integrate with integer parameter in Mathematica?

I would like to integrate the following expression with N being Integer ...
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### How can the same Mathematica version give different symbolic results on different machines?

I'm testing the following code: ...
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### Replace higher order derivatives given lower order derivative

I have an unknown function f[x1,x2] whose partial with respect to x1 is identically zero. I would like to make sure that ...
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### Defining functions as derivatives

I'm working on a model that requires a sum over a function that uses various coefficients. In order to make the sum easier to perform, I am trying to keep things general through the use of a ...
108 views

### Problems with integrating over a region

Following the example of this answer: Find the volume of the region defined by $|x|+|y|+|z|<4$ I tried to compute the following integral over a region by using ImplicitRegion. However, when I ...
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### How to visualize Riemann surfaces?

In WolframAlpha we can easily visualize Riemann surfaces of arbitrary functions, can we plot the Riemann surface of an arbitrary function using Mathematica and ...
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### I would like to be able to get this integral evaluation to show up in terms of variables

this is very much a beginner question; I was hoping that someone may be able to take a look at this code and tell me why it outputs all of these crazy numbers instead of just the variables specified ...
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### Complex limit gives wrong answer

I'm evaluating $$\lim_{z\to e^{i \pi/2 n}} \frac{z-e^{i \pi/2 n}}{z^{2 n}+1}$$ with Mathematica 9.0.1: ...
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### Learning Mathematica for Math Majors [duplicate]

I just downloaded Mathematica and I'm taking a course in Multivariable Calculus. I realize there is a lot of complexity to Mathematica and there are Many types of learning resources out there. I was ...
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### Huge difference after changing a fraction to decimal

I have a limit to calculate. With[{p = 1/2, q = 0.1}, Limit[a^q Integrate[Sin[x]/x^p, {x, a, Infinity}], a -> Infinity]] gives correct result ...
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### Wrong limit involving sine?

Using Mathematica 9.0.0.0, I was trying to calculate the sum $$B_n = \sum_{i=1}^n \sin^4\left(\frac{(i-1)}{(n-1)}\cdot\frac{\pi}{2}\right).$$ where I thought it would be $B_n = \frac{3(n-1) + 4}{8}$....
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### How to perform this nth derivative operation in MMA?

I have to solve this following equation where I need to differentiate a function $n$ times. $$A=\sum_{n=0}^{m-1}\frac{s^n}{n!}(-1)^n\frac{d^nf(s)}{ds^n}$$ How to express the above equation in ...
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### Recycle boundary condition

I'm having the following issue that can not find a solution , by using this boundary condition u[0, t] == 2 u[1, t] that Mathematica does not understand, someone ...
117 views

### Numerical integration does excessive coarse-graining?

I am trying to perform numerically the following integral \int_0^8\text{d}x\,\text{Re}\left[\frac{e^{-\frac{a^2}{2}-\frac{x^2}{2}} x^4 \sin (b x)\left(e^{-i c x} \text{erfc}\left(\frac{-c +i x }{\...
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### Jump boundary conditions

I'm having the following issue that can not find a solution , by using this boundary condition ...
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### Why does the following integral generate an error message for Delete::partw and IntegrateImproperDumptmp

The following integral generates a couple of errors that I'm not sure what they mean or how to prevent them ...
157 views

### Strange DiracDelta integration results in 10.4.1

Integrate[DiracDelta[s (x - c)] x, {x, -Infinity, Infinity}, Assumptions -> {s > 0, c > 0}] gives me c/s in ...
242 views

### A power series expansion [closed]

Consider the function, $f(z) = z\, \tanh(\pi z) \log (z^2 + a^2)$ for some $a>0$. Now I am considering 3 different situations, $z = i(n+0.5) - i\epsilon + \delta - it$ for $n \in \mathbb{Z}$ ...
139 views

### The Disc and Washer Methods [closed]

How is it possible to demonstrate a visual solid of revolution utilizing the washer method? For example to show the shape formed by rotating the region bounded by $y=(x-2)^4, 8x-y=16$ about $x=10$? ...
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### Inconsistent Integrate behavior?

Evaluating the following integral with Mathematica Integrate[q0/(-1 + q0^2), {q0, 0, A}] gives a conditional expression ...