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.

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66 views

Why is my integral with the error function not being evaluated?

I'm new to Wolfram Mathematica and I was trying to evaluate this integral in particular: $$\int_{0}^{x}\frac{e^t \operatorname{erf}(\sqrt{t})\sqrt{\pi t}+1}{\sqrt{\pi t x -\pi t^2}}\mathrm dt$$ The ...
2 votes
1 answer
54 views

Line integral around singular point (Residue theorem)

We have function $\frac{1}{x-\frac{i}{2}}$ which has one singular point $x=\frac{i}{2}$ so if we integrate around it we get by Residue theorem $2 \pi i$. ...
1 vote
2 answers
220 views

Evaluating a complicated integral

I am trying to integrate a function Gamma, but the output returns the input. I have the following code: ...
4 votes
1 answer
80 views

How to express the curvature in polar coordinates with DSolveChangeVariables (or without it)?

The curvature k[x] of a plane curve y==y[x] is given by ...
9 votes
1 answer
146 views

IntegrateChangeVariables producing incorrect result

Consider the simple quadratic function: ClearAll[f]; f[x_]:=x^2; Now let's set up the two identical integrals: ...
1 vote
0 answers
28 views

Integrate Differential Form with Parameter with DifferentialForms.m?

In this post, it is shown how to integrate a function with parameter(s) and output a function of the parameter(s). I am trying to do something similar with the DifferentialForms.m package. I have ...
0 votes
0 answers
21 views

HomotopyOperator in DifferentialForms.m Not Working

I'm trying to implement and check Faraday's tensor with the DifferentialForms.m package. I code this to implement the Faraday 2-form ...
6 votes
0 answers
62 views

Does IntegrateChangeVariables work with improper integrals?

Trying a new command of version 13.1 IntegrateChangeVariables, I obtain ...
2 votes
1 answer
92 views

Integrate ignoring assumptions

I want to evaluate an integral with all variables real and positive. Specifically, ...
1 vote
1 answer
67 views

Error propagation for multivariate polynomial

I am using a simple error propagation of a multivariate polynomial (of x[i_],y[i_],z[i_] ...). The way I am writing is as a symbolic expression and then ...
1 vote
3 answers
827 views

How to plot partial derivative of an integral vs. another variable?

Just to take an example, because my original numerical integral was too complex: T[t_] = NIntegrate[Exp[(eta - 1)*t], {eta, 0, 4}] But when I am using ...
3 votes
1 answer
927 views

Evaluation of Derivative in a Module

Can someone help me understand the evaluation procedure in the following two pieces of code? ...
2 votes
1 answer
100 views

Rewriting terms as perfect derivative

I am trying to find conservation laws of a system, and I'd like to rewrite terms of the form $$A\frac{dA^*}{dt}+A^*\frac{dA}{dt}$$ as $$\frac{d}{dt}|A|^2,$$ where $A$ is a complex valued function ...
2 votes
1 answer
359 views

Can Mathematica help a theorem to be alive?

We are used to do limits by means of $\epsilon, \delta$. This is the first step an student encounters limits. Using $\epsilon$ and $\delta$ leads him to be familiar to Logic. I have taught limits and ...
2 votes
2 answers
209 views

Solving an ODE with parameters and taking the limit of the solution

I am very new to Mathematica and already spent a lot of time trying to do this but failed. I am trying to solve an ODE: ...
0 votes
0 answers
133 views

Indefinite integral of x/(a + x ln(x))

My web version of mathematica (student version) can't provide an indefinite integral of $$\frac{x}{a+x\ln(x)}$$ where a is a positive constant. Specifically, I enter ...
3 votes
0 answers
137 views

Possible bug in ResidueSum

Trying a new command of version 13.1 ResidueSum, I obtain FunctionMeromorphic[{(x^2 - x + 2)/x, Abs[x] > 5}, x] ...
4 votes
3 answers
202 views

Behavior of Mathematica 12.3.1, 13.0.1 under certain integrations

I have a couple of modules (Laplace transformation of Plus-distributions) that were completely straightforward to integrate with version 12.0.0. However, recently ...
10 votes
7 answers
4k views

Is there a way to rewrite integrals in Mathematica using u substitution?

In Mathematica, can I give it an integral and a few substitution rules and have it rewrite the integral in terms of those variables?
1 vote
1 answer
42 views

Points, 3DPlots and symmetry of Multivariable functions using Mathematica

My doubts here are related to the construction of 3D plots of Multivariable functions. As a consequence of that, I am going to keep these questions in this single post rather than creating several ...
0 votes
0 answers
27 views

Taylor series two variables and CoefficientList [closed]

I have the code ...
1 vote
0 answers
71 views

How to simplify a formula with integrations by parts?

I have a huge expression to compute, which contains lots of different terms composed of multiplication of various functions, derived a certain number of times (non derived, derived once or twice). For ...
10 votes
3 answers
2k views

Change integration variable

Are there any automated procedures to change integration variables? For example by changing Sin[u]->x, I can change ...
10 votes
3 answers
4k views

How to change coordinates of integration?

Is there some built-in routine, some easier method to change variables of integration, without/before solving the integral? Say I have ...
1 vote
1 answer
77 views

Weird Infinite Limit results when dividing functions

I am getting 0 or 1 for the limit when dividing the two functions but Log of the same constant when taking the limit individually. ...
3 votes
0 answers
39 views

Get different results when evaluating indefinite integral multiple times

I'm trying to evaluate the following indefinite integral in Mathematica: Integrate[Exp[(k + g) t]/(1 + Exp[k t])^3, t] When evaluating the integral multiple times ...
0 votes
0 answers
57 views

Implementing the 3D Radon transform

I am wondering how to implement the Radon transform, the 3D Radon transform, that is, given a 'density' function $f: \mathbb{R}^3\to \mathbb{R}$ The Radon transform of $f$ is $$Rf(s,w)= \int_{x\cdot w=...
1 vote
0 answers
30 views

Using ReplaceAll to simplify derivatives

I'm struggling trying to simplify the derivative of a function. I know that ReplaceAll works like that: What I want is to replace the function itself that should ...
4 votes
1 answer
2k views

How to calculate the first derivative from experimental data

I have a set of experimental data and need to calculate the first derivative. What is the easiest way to do this? Many thanks in advance
0 votes
1 answer
70 views

How can I get the closed interval of a given function using W. Mathematica? [closed]

How can I get the closed interval of a given function using Wolfram Mathematica? f(x)= 3+2x-x^2
0 votes
2 answers
40 views

Additional line in the Plotting

I'm trying to plot a function, the problem is that the plot contains additional lines which originate from the solution itself, but at the same time removing the solutions will delete a whole portion ...
11 votes
0 answers
277 views

Series with ArcTan gives wrong symbolic answer in Wolfram Language

Bug introduced after 9 and persisting through 13.1 Recently, I have found a very bad problem with Wolfram Language. It gives the wrong answer for a quite simple expression! When calculating ...
4 votes
1 answer
165 views

Posible variable naming bug?

Bug introduced in 13.0 or earlier and persisting through 13.1 or later First integral and second integral are the same just replacing $\text{pb}$ <--> $x$. While Mathematica is not able to ...
6 votes
1 answer
160 views

Possible Mathematica bug

Fixed in 13.1 I believe the following two integrals should have the same value, since the Boole[] expression always evaluates to ...
10 votes
0 answers
142 views

Reduce: Var is not a valid variable

Bug introduced in 12.3 or earlier and persisting through 13.1 or later I am trying to integrate the following but it returns a Reduce::ivar warning message. ...
18 votes
5 answers
14k views

How to do implicit differentiation in Mathematica?

I have an equation which is K^(1/2)*L^(1/2)-(K+L) = 24 but I don't know how to do implicit differentiation to find dK/dL because I only know how to do the normal ...
0 votes
0 answers
50 views

Partial Derivative of Numerical Functions at a point not found

I have a complicated function of 4 different variables that was found using FindRoot and NumericQ?. When I plot the function for the different variables over the relevant range, it appears well ...
4 votes
2 answers
106 views

ComplexExpand no longer assumes Derivative[__][__][__] as real

Bug introduced after 11.3, in or before 12.3, persisting through 13.0. Consider the following sample: {Re, Im}[u'[t]] // Through // ComplexExpand In v9.0.1 ...
0 votes
0 answers
34 views

Is the integration feature of an interpolated plot/function supposed to have a much larger maximum and range values in general?

So, I have imported data from a software called NextNano, plotting electron density. My first step was to define the data within the desired domain data={,},.... ...
2 votes
1 answer
74 views

A complicated derivative problem

I have some equation,like this $$ \begin{aligned} &\hat{t}_{g o}=\frac{R}{V_{m}}\left(1+\frac{(n+2) \sigma^{2}+(n+1)^{2}(n+2) \sigma_{f}^{2}}{2(2 n+3)(2 n+5)}-\frac{(n+1) \sigma \sigma_{f}}{2(2 n+...
2 votes
2 answers
556 views

Defining the Hirota operator

The Hirota $D$-operator (derivative) is mathematically defined as follows: $$D_x^n f\cdot g=\left.\frac{\partial^n}{\partial s ^n} f(x+s)g(x-s)\right|_{s=0} $$ An example of this operator acting on ...
0 votes
1 answer
52 views

Real valued solution

I want to obtain the critical points or if you like a real solution for the first derivative of the function set to zero, and the second derivative also vanishes of the function : ...
6 votes
1 answer
180 views

Mathematica giving wrong answer for limit of LerchPhi[]

Mathematica is often frustrating to use, due to how it apparently get things wrong at times. It's giving me a totally wrong answer for this below limit (it gets it right though, if I pick a positive ...
3 votes
1 answer
1k views

Computing Christoffel symbols of the first kind

I am trying to compute the Christoffel symbols of the first kind. To keep the question short I am only computing the second term: $$\Gamma _{\text{ijk}}=\partial \text{Mg}_{\text{ik}}/\partial q_j $$ ...
0 votes
0 answers
37 views

Integer parameter assumption gives incorrect result when integrating

There are some dangerous pitfalls that can happen when evaluating some integrals, assuming that some parameters are integers. For example, consider the following: ...
1 vote
1 answer
107 views

How can I simplify the output after integration which is obtained in terms of hypergeometric function in Mathematica?

When I did the integration of the following function, I got the answer in terms of hypergeometric function. But when I did the same integration in MATLAB, a simplified form of expression is coming as ...
1 vote
1 answer
121 views

Simplification of Elliptic integrals

Consider an indefinite "elliptic integral”, $$ J_n(r):= \int^r_{r_0}\frac{x^n {\rm d}x}{\sqrt{f(x)}}, \quad f(x):=(x-x_1)(x-x_2)(x-x_3), $$ Here, $r_0>0, n=1,0,-1$, and $x_{1,2,3}$ are roots ...
0 votes
0 answers
43 views

Estimating a limit of a sequence by several values

Given first several values of a sequence, e.g., {0.291088365036517,0.34379330139259,0.370496101167372,0.383547058928976,0.389873503208829} I'd like to to find the ...
0 votes
0 answers
48 views

How to express elemental operations in matrix form?

I ran the following code: X = Array[x, {5, 4}]; W = Array[w, {4, 3}]; Y = Array[y, {5, 3}]; D[Norm[X.W-Y, "Frobenius"]^2, {W}]//MatrixForm However, mma ...
2 votes
2 answers
144 views

Getting fluctuations in the derivative of interpolated functions [closed]

The code I use is as follows ip = Interpolation[data, InterpolationOrder -> 3]; Plot[{ip[x], ip'[x], ip''[x]}, {x, 0.05, 0.5}] I get fluctuations for the first ...

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