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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Function asymptotics showing different result after inter integration [closed]

I have a function fg[r_, t_, t2_, \[Phi]_, DR_]. I want to do the following Integrate it for t2 from 0 to t Then take the asymptotic limit r-> 0 The result of ...
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Plotting an integral with solving for a specific constant [closed]

Given an Integral I(t) which is a function of a constant tc, this constant is determined with the condition I(tc)=0, how can I add this condition?
Med Ch's user avatar
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Numerical Integration without giving all values

Is there a way to solve expressions numerically, while keeping other variables. For example, I want to Integrate the expression below for $\theta p,\theta q$ while keeping other things as it is. The ...
Lelouch's user avatar
2 votes
1 answer
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How to linearize these terms in many different variables?

How to linearize these terms in q[t] and p[t,y] ...
Dr. phy's user avatar
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Seeking Wolfram Mathematica Techniques for Detailed Step-by-Step Solution of Integral Equation Transformation

Hello Mathematica Community, I am working on a mathematical problem where I need to transform an integral equation into a simpler form using Euler's Formula and the Error Function. My current ...
Rob_'s user avatar
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Derivative of a function in euclidean distance [closed]

differentiate W in (Z=XW, D1=distance(Z[, 1]), D2=distance(Z[, 2]), D3=distance(Z[, 3]) exp[-D1/theta _1 -D2/theta _2 -D3 /theta _3]) where W is 5 by 3 matrix, Z is 100 by 3 matrix and X is 100 by ...
Eric Herrison Gyamfi's user avatar
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44 views

How do I find roots of a third degree polynomial? [closed]

expr = G^2 X^3 - 2 Δ G X^2 + Δ^2 X + ((ℏ *G*η* k*Subscript[E, l]^2)/(m*Subscript[Ω, m]^2)) == 0
abdul wahab's user avatar
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2 answers
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Integrate with `Max` and `Min` under assumptions runs forever

I'm trying to solve an integral under certain conditions on the parameters. The following is my code. ...
ppp's user avatar
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Leading significant digits

Given that the initial area in a Sierpinski triangle is A_0 and the subsequent areas $$(A_n) =A_0 (3/4)^n$$ , what is the formula to calculate the leading ...
Rubens Vilhena Fonseca's user avatar
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What does "{True,True}" mean in the result of IntegrateChangeVariables?

I want to change variables in the following integral: Integrate[q*D[z[x, y],x]^2, {x, -∞, ∞}, {y, -∞, ∞}] as follows: ...
Alexei Boulbitch's user avatar
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Integral of complex exponential with assumptions

I feel confident this problem has been posed before but alas I cannot find it. ...
David G. Stork's user avatar
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Time derivatives not working [closed]

I have the following code: ...
Saim Ehtesham's user avatar
2 votes
3 answers
141 views

Find Generalized Series with Symbolic Variable

CoefficientList[Series[Exp[x], {x, a, 3}], x] Gives the following expression, $$ \left\{-\frac{1}{6} e^a a^3+\frac{e^a a^2}{2}-e^a a+e^a,\frac{e^a a^2}{2}-e^a a+e^...
Torkoal's user avatar
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Express the double integral in terms of the function values at discrete nodes

Consider the following integral: $$ \mathcal{I}[p_{1},t] = \int \limits_{0}^{p_{1}}dp_{2}\int \limits_{0}^{p_{2}}dp_{3} \ \text{integrand} $$ where ...
John Taylor's user avatar
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Lagrangian density and Christoffel symbols [closed]

According to this article (equation 3.2) the Lagrangian density can be calculated by $$ 2 \mathcal{L} = \left\{\begin{array}{c} a \\ b c \end{array}\right\}(g b c \sqrt{-g})_{, a}-\left\{\begin{array}{...
Soliton-104's user avatar
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How to linearize this equation in two different variables?

How to linearize this equation in two different variables p[t] and q[t,y]: ...
Dr. phy's user avatar
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First order differential equation with two conditions

I want to produce all possible solutions for this equation: ...
Mathecis's user avatar
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Limit giving indeterminate result

I have a function $r_h(v)$ given by, $$r_h (v) = \left(\frac{m_0}{2 g} e^{-g v_f} \left(-1+e^{-g(v - v_f)} \right) \right)^{1/5}$$ where $m_0$ and $g$ are just numbers. I want to take the limits of ...
mathemania's user avatar
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Integrate function differing from RUBI's Int function in version 13.3.0

I had Mathematica Version 12.3.1 Student Edition and Integrate and RUBI's Int functions produced the same answers for my purposes with good results. I updated my version to 13.3.0 Student Edition and ...
Tom00496's user avatar
1 vote
1 answer
100 views

Plot after applying NIntegrate

I'm trying to integrate and graph $I$ vs $b$ the following integral (eq. 24 in this paper) in wolfram mathematica $$ I = \int_{2}^{\infty} \frac{g_i^3 \mathcal{K}_t \mathrm{~d} r}{r^2\left|\mathcal{K}...
Soliton-104's user avatar
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1 answer
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Incorrect results for Integrate[Cosh[x]/(Sinh[x] + Cosh[x]), x] [closed]

Input: ...
Boris's user avatar
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1 answer
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Change of variable of a numerically solved integral

I have the following function that numerically integrates a function on the interval $\left[ 2, 100 \right]$ ...
Soliton-104's user avatar
1 vote
0 answers
81 views

Intensity pattern [closed]

I'm trying to get the following intensity pattern from this paper In the Newtonian case, the equations for the intensity (eq. 9 and 10 in the article), I put them in Mathematica with the change $b^2 =...
Soliton-104's user avatar
1 vote
1 answer
87 views

Definite integral of real function outputting complex values

I'm trying to integrate the function $f(\omega)$ from $-\infty$ to $\infty$, where $$ f(\omega) = \begin{cases} \frac{(1-2 \omega )^2}{64 \cos (\tau (-\omega +\phi +1))-80} & 0<\omega \leq ...
peep's user avatar
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1 answer
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How to chose appropriate finite limits for NIntegrate?

I want to NIntegrate a function using finite limits so it gives a result as close as possible to a result which I would get making the limit ...
Patrycja's user avatar
1 vote
1 answer
257 views

Plot solution of an integral with parameter

In this article, they solve the following integral $$ \mathcal{I}_{o b s}\left(\nu_0\right)=\int_{\gamma_i} \frac{(A(r))^{3 / 2}}{r^2} \sqrt{\frac{1}{A(r)}+r^2\left(\frac{d \varphi}{d r}\right)^2} d r ...
Soliton-104's user avatar
2 votes
2 answers
85 views

How to prevent evaluation without simplification?

I am trying to compute a sequence of terms, which have a form similar to $g(z)$ at different points $z$. For $z$ close to 0, I have observed that the terms are evaluated as 0/0 (indeterminate form) ...
sai's user avatar
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8 votes
3 answers
3k views

Why doesn't Mathematica recognise two integrals as equal?

The following expression $$\int_{0}^{t} f(t_0) \,dt_0 - \int_{0}^{t} f(t_1) \,dt_1 = 0$$ is zero because it is just a change of integration variable. Why doesn't Mathematica give zero in this case? <...
Luca's user avatar
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4 votes
1 answer
182 views

Implementation of SINC filter using Integrate results in incorrect output

Bug introduced in 6.0, persisting through 13.3.1. This is SINC filter, integrate $|H|^2$ from $-\pi/2$ to $\pi/2$. MMA CODE, Result = 7.27956e-12 ...
Ring's user avatar
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2 answers
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How to find the roots of an equation for different wave numbers?

I have a equation nn which is a function of t and k. I want to find the maximum of the ...
Lohrasb's user avatar
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1 vote
2 answers
186 views

Sum $\sum _{k=0}^{\infty } \frac{(-z)^k}{\text{IteratedLog}(k+2)}$ [closed]

The following result can be obtained by means of succession acceleration. Can this result also be calculated in Mathematica? $$\sum _{k=0}^{\infty } \frac{(-z)^k}{\text{IteratedLog}(k+2)}=\frac{z+2}{2 ...
Capeamate's user avatar
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1 answer
132 views

How to speed up this integration?

I try to evaluate this integral: ...
Dr. phy's user avatar
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0 answers
59 views

Plotting list of points to a special graph

Given Mathematica code of eigenvalues in different variable-paths , I want to add experimental data in the path Gamma-X ; X-Gamma ; and M-Gamma . Here is the code : ...
Med Ch's user avatar
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2 votes
0 answers
271 views

Symbolic integral with UnitStep functions

I want to symbolically evaluate the following integral (with real positive parameters L1, L2, ...
Giancarlo Creanza's user avatar
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0 answers
68 views

How to make NIntegrate with large integration limit?

I try to double integrate this equation with respect to $b$ and $f$ ...
Dr. phy's user avatar
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1 vote
1 answer
78 views

Minimization of an implicitly specified function

exp - an experimental data, where expT - temperature, expChi - magnetic susceptibility I ...
Mam Mam's user avatar
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0 votes
1 answer
58 views

Syntax error trying to rewrite expression using rules

I want to use Mathematica to calculate derivatives of some long, complicated expressions. I have an integral with integrand $I_*$ which is a functional that depends on $h(x,t)$ and $\phi(x,t)$. The ...
Mjoseph's user avatar
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0 votes
1 answer
70 views

Divergent series $\sum _{k=0}^{\infty } (2 k+1)^{3 k+1} z^k$ and LambertW function [closed]

I can get values from the following function, $$\sum _{k=0}^{\infty } (2 k+1)^{3 k+1} z^k $$ could you tell me how you could check those values using the Lambert function in integral form or if you ...
Capeamate's user avatar
1 vote
1 answer
151 views

Why does Mathematica fail to compute $\int_{0}^{\infty} \sin(ax^2) dx$ whereas Wolfram Alpha seems to be able to do it? [closed]

I was symbolically computing $$ \int_{0}^{\infty} \sin(ax^2) dx $$ Via the command: Integrate[Sin[a*x^2], {x, 0, Infinity}] But it seems to fail with mathematica, ...
Sidharth Ghoshal's user avatar
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1 answer
50 views

Different integral values for analytically same integrals

Consider a function $L$ with parameters $h=0.1,\ D=1.5$ $L(m,x):=e^{-\frac{2\ (\frac{x}{h}-m)^{2}}{D}}$. While the integrals $\int_{-\infty}^{+\infty}L(0,x)dx$ and $\int_{-\infty}^{+\infty}L(40,x)dx$ ...
chintan's user avatar
0 votes
3 answers
137 views

Finding the area enclosed by two curves

I am trying to find the area enclosed between two curves (i.e., two datasets). The challenge is to estimate the cross-sectional area. as indicated in blue. The first dataset represents the bathymetry ...
Mehmet's user avatar
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3 votes
6 answers
447 views

Galactic rotation speed

Rotation speed vc[R] in reduced units for M33 looks like 0.342331 Sqrt[R^2/(0.728117 + R^2)^0.87955] Knowing ...
Rémy Galli's user avatar
2 votes
0 answers
142 views

Finite sum of complex exponentials giving wrong result [closed]

I was playing with the following sum: $$ \sum_{k=0}^{2} e^{\frac{2\pi i k^2}{3}} = e^{0} + e^{\frac{2\pi i}{3}} + e^{\frac{8\pi i}{3}} \ne 0, $$ which is non-zero, at least according to Wolfram|Alpha. ...
Sidharth Ghoshal's user avatar
2 votes
2 answers
88 views

How can I find maximums of a function without Table and FindPeaks?

I have the following equation $$\pi_{xx} = \exp(-2 k_x^2 \sin^2(\frac{t}{2})) k_x^2 \theta(t) \times \bigg[ -\frac{\sin(2t)}{2} - \cos(t) \sin(t) (1 - k_x^2 \sin^2(\frac{t}{2})) + 2 ...
Lohrasb's user avatar
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1 vote
2 answers
84 views

How can Mathematica merge $(1/t)^{1/3} t^{17/3}$ in an expression?

(1/t)^(1/3) t^(17/3) How to let Mathematica simplify it?
dessert's user avatar
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1 vote
3 answers
206 views

Integration giving unknown messages

I am trying to integrate the following Integrate[(Log[1 - t] t^(-(1/2) + eps))/(1 + t),{t,0,1}] To simplify this I am doing a further transformation ...
BabaYaga's user avatar
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0 votes
2 answers
79 views

How to find the maximum of an equation based on a variable? [duplicate]

I have the following periodic function, as a function of K and t. I need to know what is the maximum of each recurrence as accurate as possible for k={10,20,40,60,80} The equation is as follows, $pixx ...
Lohrasb's user avatar
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2 votes
0 answers
106 views

Why does Area produce finite values for this area? [closed]

Let us consider in 13.3.1 on Windows 10 the region reg = ImplicitRegion[{x*y >= 8, y >= 8 x^3, y <= 27}, {x, y}]; and its area ...
user64494's user avatar
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21 views

The relationship between dependent decision variables in a function

Given objective function f(x1,x2,x3) in a optimization problem, and don't know if all these variables are independent or not. How to know if dx2/dx3 is greater/less than/equal to zero. I could
Doublehappy Tough's user avatar
1 vote
2 answers
252 views

How to interpolate an implicit function?

chi(t) is implicit function. The implicit function can be plotted by ContourPlot. Is it possible to obtain chi(t) explicitly using function interpolation? ...
Mam Mam's user avatar
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