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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3answers
213 views

How to express the function $a(t)$ knowing a parametrization $a(\eta)$ and $t(\eta)$?

I have this function : \begin{equation}\tag{1} a(\eta) = \sqrt{\sin{2 \eta}}, \end{equation} and this time variable : \begin{equation}\tag{2} t(\eta) = \int_0^\eta a(\eta') \, d\eta'. \end{...
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1answer
106 views

How can I find the domain of $x$ for which the function $g(x)\geq0\;$?

I have this function ($x>0$) $$f (x)=\frac{\sqrt{g (x)}+4 x \left(x^2+1\right) \sin (\pi x) \cos ((3+\pi ) x)}{x^4+2 x^2+1+\left(4 x^2+\left(x^2-1\right)^2 \cos (2 \pi x)\right)}$$ ...
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2answers
1k views

How to determine if a function is continuous?

I wish to write code for Riemann-Stieltjes integrals in Mathematica. A necessary condition for the theorem to hold is that the function must be continuous. The domain of the function is a closed real ...
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2answers
51 views

How to make derivative as a function

g[z_] := z^2 l[z_] := D[g[z], z] How to make the derivative of a function as a new function. Here I am showing the simple case.
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3answers
102 views

Get curve values at a given altitude

If I have the following data: ...
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0answers
76 views

Numerical integration of a function with singularity

I am trying to find the following integral numerically, ...
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3answers
80 views

Superimposed data on top of each other in a Do Loop

If I have 4 different types of data such (that I get from an Excel file) as: https://pastebin.com/j3Bgfxqm I am trying to implement a ...
5
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1answer
258 views

Bug: Wrong limit in Mathematica 11.1.1 and current WolframAlpha

Bug introduced around 11.1.1 and fixed in 11.2 ...
12
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1answer
335 views

Getting wrong limit with Bessel

Bug introduced in 7.0 or earlier and fixed in 11.3 I computed a following limit (related to the asymptotic expansion of the sequence A000009 - number of partitions ...
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0answers
62 views

Calculating the integral

The question is asked in the mathstackexchange. There is no answer. I can't solve it by hand, also. Maybe we can solve it with Mathematica. Appreciate all your help, effort. Best regards. ...
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1answer
148 views

Integration not working

Can't seem to get this integration to work. s, n, b, b, l are all constants. ...
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1answer
74 views

I'm getting 0 when I evalute an integral I know is non-zero [closed]

Here is my code: ClearAll[n, y]; Integrate[(1 - y^n)/(1 - y^2), {y, 0, 1}, Assumptions -> Re[n] > -1] When I evaluate it, Mathematica 12.0 is giving me $0$, ...
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1answer
104 views

Solving an equation with Reduce

In the equation shown in the code that follows, I must find or eliminate rb, but Mathematica is reluctant to work with my Reduce ...
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4answers
347 views

Solving Integral Equation -numerical solution

I am trying to find a (numerical) solution to the following integral equation: where $\epsilon$ is a real valued function and $\beta$ and $c_0$ are constants. MMA code: ...
2
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1answer
166 views

How do I draw a conformal mapping from the z-plane to the w-plane

I am total beginner in Mathematica. Don't know a thing. I need to draw some diagrams for showing the conformal nature of map $w=e^z$. I need to draw some contours in $z$-plane; e.g., horizontal line, ...
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1answer
66 views
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0answers
53 views

Solve method in Mathematica, symbolically solving method

I am looking for a way to solve this equation symbolically with Mathematica. ...
2
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1answer
161 views

(Numerical) calculation of nested integrals

The problem I'd like to (numerically) compute nested integrals of the type $$I(a;k) \equiv \left( \prod_{i=1}^k \int_0^\infty \mathrm{d}x_i \right) \exp \left( - \frac{1}{4a} \sum_{i=1}^k \left( x_i - ...
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0answers
64 views

How to simplifying the following integral that involves Bessel functions and Exponential integral function?

I have obtained the following as a solution of heat conduction equation of a semi-infinite model in cylindrical coordinates which is initially subject to non-homogenous initial condition and isolated ...
2
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3answers
132 views

Parametric equations and eq. of tangent plane

I have written the following code to determine the equation of a plane tangent to a surface at a given point: ...
0
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3answers
110 views

Again Integrate with singularities

Integrate[1/(a x + Sqrt[b x^2 - c]), {x, 1, d}] where a,b,c are positive values. Mathematica runs this forever.
1
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1answer
77 views

How to simplify the following integral to be in terms of Bessel functions?

I have evaluated the following integration using Mathematica. I obtained a solution in terms of Meijer G function. I wonder if it can be simplified to be in terms of Bessel functions. ...
0
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0answers
37 views

Picking elements from separate lists and multiplying them

So I'm doing some instruction items about surface integrals. I've written the following code. it calculates curl and partial derivatives of the surface. I now want to create the following function, ...
1
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1answer
52 views

Help with code on integration

I'm trying to do a surface integral through a vector field of a disc. The problem says there is a vector field $\langle 0, y, -z\rangle$ and the disc is $x^2 + z^2 \le 1, y = 1$. The answer is $\pi$ ...
0
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2answers
70 views

Problem with integral of the type (x^2-y^2)^a/2 x^2 Exp[-x]

I tried to calculate the following integral using Mathematica Integrate[(x^2 - y^2)^(3)/2 x^2 Exp[-x], {x, y, Infinity}] The answer was a conditional expression ...
0
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0answers
49 views

How to evaluate the following integrals using Mathematica?

I have the following integrals obtained during solving heat diffusion equation for semi-infinite system that is subject to non-homogenous initial condition in Laplace domain. I want to simplify the ...
14
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3answers
2k views

Calculate inertia tensors

Moments of inertia and inertia tensors are well-known characteristics of rigid bodies in physics and applied mathematics. How to calculate them in Mathematica? Is possible to use regions which was ...
4
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1answer
163 views

Moment Of Inertia of half cylinder

With cylinder I have: ...
1
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3answers
193 views

How to prove the following integration identity?

I have the following integration that I want to evaluate it using Mathematica. ...
4
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1answer
432 views

How to take derivative of a expression with respect to a function?

I want to program the Euler-Lagrange equations for continuous systems. But in this formulation I have to compute the derivative of the Lagrangian with respect to all the derivatives of the generalized ...
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0answers
41 views

Evaluating the sign of a derivative

I would like to know the sign of the derivative of a function (for instance whether it is always positive or not). Also, how can I specify that the parameter with respect to which I differentiate can ...
5
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2answers
235 views

Kuba's MoreCalculus package - an example

First of all, congratulations to @Kuba for this excellent package. I did not know where to report the following example, so I thought I would make a post about it. ...
2
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1answer
73 views

How to get the result from a RootSum?

While working on an integral, I got this scary-looking expression. I tried to use // Normal // ToRadicals // FullSimplify to get the answer, but it is taking lot of ...
3
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1answer
97 views

Parametric Surface Integral Boundary Code?

I am having trouble using MMA to calculate 2 parametrized surface integrals. I'd be grateful for any fixes people can offer. I usually calculate surface integrals with the following code, which works, ...
4
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3answers
164 views

Initial-boundary value problem of 2nd order linear PDE with variable coefficient

Today I was studying partial differential equations and I tried to check if my solution was correct, I thought Mathematica code would be easy, but it wasn't. Here is my problem: Solve $u_{xx}-2tu-u_t=...
1
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2answers
57 views

Problems with Dsolve[] and simple function

I'm trying to solve the following very simple differential equation, but it seems Mathematica cannot give me an answer, ...
0
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0answers
54 views

How to do a functional derivative with Exp and integration?

Define a functional derivative as: ...
6
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1answer
109 views

Keeping Phase Factors in Sqrt

I am trying to plot certain holomorphic functions that contain square and higher roots. In the complex analysis sense, the function $f:z\mapsto z^\alpha$ for some $\alpha\in\mathbb C$ has a phase ...
1
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1answer
50 views

How to force mathematica to take derivatives in a specific way? [closed]

I am attempting to take some derivatives of some Lagrange planetary equations. In this I have two types of anomaly which have derivatives that are found geometrically. I'm trying to force mathematica ...
5
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1answer
75 views

Derivative of a 3D Interpolated function

I cannot get the partial derivative of a set of data. I managed to get the accurate interpolation, but I cannot evaluate its derivatives. Here are my details: ...
0
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1answer
177 views

How to remove complex infinity

I have an equation for the effective potential for a neutral particle (non-spinning), i.e. VeffNonSPIN[r_, θ_] := (1 - 2/r)*(1 + LL^2/(r^2 Sin[θ]^2)); If I take ...
0
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1answer
119 views

Expand terms of series in denominator

I have equation: $a+bx+cx^2+dx^3= \dfrac{1}{f+gx+hx^2+ix^3} \dfrac{\partial}{\partial r}(ax+bx^2+cx^3+dx^4) +\dfrac{1}{(f+gx+hx^2+ix^3)^2} \dfrac{\partial^2}{\partial r^2}(ax^2+bx^3+cx^4+dx^5)$ ...
0
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3answers
221 views

An integral problem with Sin and Cos

I have a difficulty in calculating the following integral with Mathematica: $$ \int^{\pi}_{0}\rm d\theta_1\frac{ \sin^2\theta_1[2(2-\cos\theta_1\cos\theta)^2+(\sin\theta\sin\theta_1)^2]}{[(2-\cos\...
3
votes
2answers
378 views

Calculating a double integral

I want to calculate the following integral: $$\int^{10}_{0}\int^{\pi}_{0}\sqrt{(37-\frac{45\cdot37\cdot x^2}{74\cdot 150})^2\cdot \sin(t)^2-(40-\frac{27\cdot37\cdot x^2}{16\cdot 150})^2\cdot \cos(t)^2}...
1
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0answers
80 views

How reliable is AsymptoticIntegrate?

In new mathematica 12 there is a new function AsymptoticIntegrate. However, it seems that it gives me incorrect results in some cases. To be completely honest, it ...
0
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0answers
22 views

Can't plot derivative of Hankel function [duplicate]

I am trying to plot the first derivative of $H^{(1)}_3 (ix)$ with respect to its argument $ix$, where $H^{(1)}_3 (ix)$ is the Hankel function of the first kind with order $3$, $x \in \mathbb{R}$ is a ...
16
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3answers
519 views

Computing the surface area and volume of molecules

Here is a somewhat difficult problem I've had for a long while. Space-filling models of molecules can be easily generated by ChemicalData[], ...

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