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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0
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3answers
57 views
2
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1answer
86 views

Series approximation to integral

I would like to approximate the integral $$ \int_0^\infty dy\,\frac{1}{\sqrt{2\pi y\sigma^2}}\exp\left(-\frac{(x-y)^2}{2y\sigma^2}\right)f(y), $$ as a series expansion in the limit $\sigma\rightarrow ...
0
votes
1answer
27 views

Integration with changing parameter [on hold]

I want to calculate the integral of Rev for a = 0 to 1 by step 0.1. How can I do it? ...
1
vote
0answers
53 views

Calculate exact Probability of product of normal random variables

Find the value of $P[\Pi_{i=1}^{10}X_i > C]$ for $C=5$, where $X_{10\times 1}$ is a random vector with $10$ dimensional Normal Distribution having location parameter $\mu_{10\times 1} = ...
2
votes
0answers
39 views

Getting error messages from a Plot expression containing an integral [on hold]

This should be a really simple question, but I just got confused. Plot[Integrate[x, x], {x, -5, 5}] Integrate::ilim: Invalid integration variable or limit(s) ...
0
votes
0answers
23 views
-1
votes
1answer
65 views

Help me with sum [on hold]

good morning $$ \begin{array}{l} \left\{ \begin{array}{l} u_0 = 1 \\ u_n = 3 - \frac{4}{{1 - v_n }} \\ \end{array} \right.\quad \\ \;v_n = \left( { - 3} \right)^{n + 1} \\ s = v_{1436} ...
3
votes
2answers
125 views

Integral does not converge (when it should)

I was looking at integrals like: Integrate[HermiteH[50, x]*Exp[-x^2], {x, 0, Infinity}] which gave me a "does not converge on $(0,\infty)$" error. On the other ...
0
votes
1answer
59 views

Integrating spherical harmonics

I am trying to simply check the integration/normalization condition on the SperhicalHarmonic functions that are built into Mathematica. So basically, I just want to check that the following integral ...
-1
votes
0answers
27 views

Secant/tangent line of a function [closed]

Little confused on two concepts. a) how a specific problem gets simplified and b)how to actually solve. here is the problem (I apologize I do not know the math codes to do this properly): y=-4-8x^2; ...
2
votes
1answer
56 views

Double integral over normal pdf gives inconsistent answer

I am using Integrate function to do the following double integral ...
1
vote
1answer
42 views
1
vote
1answer
92 views
13
votes
4answers
621 views

How to make a Line[] with no end?

I'm trying to do this: In this graph, the secant points are aproximated in order to become the tangent, it seems I need some kind of function which plots a line based on two points and it's points ...
13
votes
4answers
3k views

Multivariable Taylor expansion does not work as expected

The basic multivariable Taylor expansion formula around a point is as follows: $$ f(\mathbf r + \mathbf a) = f(\mathbf r) + (\mathbf a \cdot \nabla )f(\mathbf r) + \frac{1}{2!}(\mathbf a \cdot ...
2
votes
0answers
68 views

How can I do multiple (double) integral with periodic boundary conditions?

I am trying to do a simple double integral $\int_0^l \left[\int_0^l h^3 h_{xxx}dx\right]dx$ with periodic boundary conditions $h[0,\tau]=h[l,\tau]$ $h_x[0,\tau]=h_x[l,\tau]$ ...
0
votes
0answers
6 views

Does anyone know names of some of Newton's THEOREM? [migrated]

Does anyone know names of some of Newton's THEOREM? any or a list of them would be great. I already know about the Shell method.
0
votes
2answers
53 views

Derivative after numerical Integration

So I have a function that I want to numerically integrate with respect to temperature, so the integral changes depending on the value of temperature being used as it is one of the bounds. After ...
4
votes
2answers
296 views

Probability: Calculating a multiple integral

Find the value of $P[\Pi_{i=1}^{10}X_i > C]$ for $C=2,5$, where $X_{10\times 1}$ is a random vector with $10$ dimensional Cauchy Distribution having location parameter $\mu_{10\times 1} = ...
2
votes
1answer
74 views

Limits and transformation rules

I can calculate this limit: Limit[(c^(1 - g) - 1)/(1 - g), g -> 1] and obtain the correct value: Log[c] but if I try ...
0
votes
1answer
155 views

Integration of linked PDFs over probability simplex

I'm trying to integrate the following expression: f[a1,p1+p2+p3+p4]*f[a2,p2+p3+p4]*f[a3,p3+p4]*f[a4,p4] Where ...
0
votes
2answers
116 views

What is the simplest way to plot x^(1/3) on the interval [-3,3]?

My question is: What is the simplest way to plot x^(1/3) on the interval [-3,3]?
1
vote
1answer
78 views

How to avoid complex terms in the results given by Integrate?

As shown by In1, integrating Sqrt[x^2 - 1]/(a + x^2) (1/x) returns a result with a complex terms; however, after I make a ...
2
votes
0answers
53 views

NDSolve is running an extremely long time: how can I save the existing data?

I am trying to solve a PDE by the following code. It takes 1 hour or so to reach t=25.72 but about 20 hours to reach t=25.72404031638060174049337306126853310997. Actually, the time step is extremely ...
1
vote
2answers
146 views

A regularized hypergeometric function related question

I'm interested in finding a way (if possible) of expressing this specific value of the regularized hypergeometric function in terms of known constants. How might I use Mathematica to check this ...
0
votes
1answer
99 views

Writing a Code to plot a function that includes a double integral [closed]

I am trying to write a code in Mathematica. Here are my steps: F[u_] = Some nontrivial and long expression in terms of u; Umax[x_, y_] = Some expression in terms of x and y; W[x_, y_] := integral ...
6
votes
1answer
189 views

Incorrect evaluation of integral involving a DiracDelta, whose argument has infinitely many zeros

Let's say $X>0$ is a random variable with probability density $p_X(x)={\rm e}^{-x}$. Define the random variable $Y=\sin(X)$. From the transformation theorem for probabilities we know that its ...
5
votes
2answers
234 views

Working with abstract vectors

I often need to compute derivatives or integrals involving N-dimensional vectors (where the dimension could be equal to 2 or 3 but is not particularly relevant for the sake of the derivation). The ...
1
vote
1answer
77 views

Strange timings of integrals involving Hermite's polynomials

I have used Mathematica to calculate tunneling for quantum harmonic oscillator. The code is simple: ...
1
vote
2answers
56 views

Integrating a compound expression

I have an integral of the form I[r]=∫(arExp[-r]-brSin[k(r-d)]Exp[-r])BesselJ[0,kr]dr where Besse1J[0,kr] is the modified ...
2
votes
1answer
120 views

Inverse gradient operator

I found a nice paper about inverse vector operators here. I have successfully implemented a Mathematica function for most of them, however I can't figure out how to do inverse gradient (page 7 in the ...
5
votes
3answers
362 views

Bug in complicated Limit

The code Limit[Log[2 - Sin[x]*Cos[x]], x -> Infinity] outputs Interval[{0, Log[3]}] in Mathematica 10.0.2.0 . It should ...
3
votes
2answers
482 views

Color a Function by its Derivative

Mathematica's ColorFunction seems to struggle with coloring a function "y" by its derivative D[y,x]. This is a seemingly simple task, but Mathematica can't handle it. While I can certainly evaluate ...
2
votes
2answers
236 views

After definite integration the result is still integration variable dependent!

This integral $\int _{-\infty }^{\infty }\int _{-\infty }^{\infty }\int _{-\infty }^{\infty }\frac{\exp \left(\frac{2}{x^2+y^2+z^2+1}-2\right)}{\left(x^2+y^2+z^2+1\right)^4}dzdydx$ or ...
0
votes
1answer
55 views

Integration of an expression yields wrong result

I'm trying to find a general expression for the definite integral of ...
1
vote
1answer
110 views

How to differentiate an integral on Mathematica?

I am so new on Mathematica. I try to find the first variation of this function according to $t$ on mathematica but I could not achieve. Here is the function ; ...
3
votes
1answer
197 views

Using WhenEvent for derivative of discontinuous function

I have a discontinuous function ($u(t)$, a square wave) and I would like WhenEvent to trigger when the signal goes high/low, i.e. when the value of $u(t)$ changes. ...
-4
votes
1answer
63 views
2
votes
1answer
177 views

Calculating the area under a curve

How can I calculate the area under a curve after plotting discrete data as per below? ...
1
vote
3answers
82 views

Speed up NIntegrate, which takes eigenvalues from another function

I have simplified my problem here, in my actual problem the matrix is much bigger which makes it impossible to find eigenvalues analytically. So, I chose standard BCS problem (2x2 matrix) to ...
8
votes
3answers
495 views
7
votes
3answers
306 views

Generating a polynomial that's accurate to within an error of no more than 1/10^5

I'm currently stuck on a question for class that asks... "Find a polynomial p[x] that you can use to calculate 6 ArcTan[x] to ...
0
votes
1answer
54 views

Derivatives of overscript variables

If we have an expression with terms of some variable and terms of the same variable with some overscript, the differentiation of this expression does not entirely function. The problem is that ...
0
votes
1answer
135 views

Mathematica does not solve this integral [closed]

I want to compute the integral of a polynomial in t, which I know an analytical solution exist. But Mathematica give me as result the input, not the result of the integral: I already know this ...
3
votes
2answers
91 views

Integration of a Rational Function returns RootSum[]

I am trying to solve an integral given below: Integrate[r^2/(-α r^3 + r^2 - 2 m r + Q^2), r] but since coefficients of this cubic polynomial are as parameters, ...
7
votes
2answers
261 views

Definite integral incorrectly giving a nonreal value

In Mathematica 10.0, when I enter N[Integrate[Sqrt[1+x^3],{x,-1,3}]] , I get a nonreal value. (I.e., the imaginary part is nonzero.) Why? This arose when I ...