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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Double angular integration in D dimensions and Hypergeometric functions [closed]

I am currently in Ph.D and trying to work out some calculations in HTLpt (Hard Thermal Loop perturbative theory) which involves a lots of nasty integrals. Especially, the one I am currently trying to ...
2
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1answer
124 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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51 views

Solve method in Mathematica, symbolically solving method

I am looking for a way to solve this equation symbolically with Mathematica. ...
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0answers
72 views

Log(x-1) replaced by Log(1-x)

Consider the following input Integrate[1/(-1 + x) + 2/(2 + x), x] Using step-by-step to calculate an integral, I get the following answer Why does ...
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37 views

Why does this code fail sometimes [closed]

I found this helpful code on MMA SE, which tells you the equation of a plane from three known points: ...
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0answers
58 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 ...
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3answers
107 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.
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36 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
48 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 $\pi$ ...
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3answers
64 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 ...
1
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1answer
71 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. ...
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46 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 ...
3
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1answer
139 views

Moment Of Inertia of half cylinder

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

How to prove the following integration identity?

I have the following integration that I want to evaluate it using Mathematica. ...
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0answers
40 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 ...
3
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1answer
83 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, ...
5
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2answers
210 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. ...
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0answers
41 views

How to solve the attached integral analytically? [closed]

How to solve this integral analytically as well as numerically
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2answers
56 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, ...
2
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3answers
125 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: ...
4
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3answers
148 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=...
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0answers
48 views

How to do a functional derivative with Exp and integration?

Define a functional derivative as: ...
1
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1answer
46 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
100 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 ...
2
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3answers
292 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: ...
5
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1answer
56 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
171 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 ...
4
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2answers
289 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}...
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0answers
78 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 ...
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2answers
50 views

Plot Parametric f(x), inverse f(x) and f'(x) and then f(x)/f'(x) and inversef'(x)/inversef(x)

I want to plot f(x), inverse f(x) and f'(x) and then f(x)/f'(x) and inversef'(x)/inversef(x) f[x_] := 2 a ArcTanh[(# a)/Sqrt[-1 + #^2 b]] + a Log[1 + #^2 (a^2 - b)] - 2 Log[# b + Sqrt[-1 + #^2 b]] &...
6
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4answers
294 views

NIntegrate Oscillating kernel

I have a finite highly oscillating integral of the type: NIntegrate[x^2 Exp[I f[x] s] , {x, 0, 1}] where f is a simple function ...
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1answer
94 views

More help on surface integrals

I've searched MMA SE and read all of the posts on surface integrals, and several people have helped on various pieces of code to evaluate them. I seem to have found a simple and correct code from ...
3
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1answer
68 views

InverseFunction and Plot them

I'm trying plot an inverse function ...
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1answer
77 views

How do I ensure the substitution happens after I take the first derivative before taking my second derivative

The title may be a little confusing so let me explain what I mean: I am using lagrange brackets to produce some equations of motion for orbital mechanics, where the motion is split between oscillating ...
1
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2answers
131 views

Right code for solving Stoke's Theorem problem

In solving Stoke's Theorem problems, I have developed a step by step method. I'm now trying to write a MMA script to help me solve these problems. But I'm a little stuck. Here's my step by step method,...
3
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4answers
421 views

How to explain these results of integration of DiracDelta?

Let us consider ClearAll["Global`*"]; Integrate[DiracDelta[1 - x^2 - y^2], {x, -1, 1}, {y, -1, 1}] (*\[Pi]/2*) Let us verify it, making use of ...
2
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1answer
55 views

Help on script for parametric surface integral

I'm working on a short script that I can repeatedly use to solve parametric surface integrals. There is a post on this elsewhere on MSE, but it is a complicated doublecontourintegral function. It is ...
11
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2answers
404 views

Cubic equation and tangent circle

I have a cubic equation as below, which I am plotting: Plot[(x + 1) (x - 1) (x - 2), {x, -2, 3}] I like Mathematica to help me locate the position/equation of a ...
5
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1answer
142 views

Integral of a function defined with a loop

I have defined a function g as ...
2
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1answer
104 views

Cannot understand the meaning of Derivative[1, 0][BesselK][-M, 2]?

When I do the following integration Integrate[(Log[x]/x)*x^M*Exp[-x-1/x],{x,0,\[Infinity]},Assumptions->Element[M,PositiveIntegers]] Mathematica return a very ...
4
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1answer
138 views

Is this second solution to this ODE correct?

Mathematica V 12.2 on windows 10. I was using Mathematica to check my solution for this ODE. Mathematica gives 2 solutions. Any idea where the second solution came from? and is it correct? Here is ...
1
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2answers
87 views

Why Mathematica is giving “Indeterminate form”

I have an equation for effective potential (Veff). For SS=0, Mathematica gives output, if I take derivate of Veff with respect to r, then I take SS=0, Mathematica gives infinity (indeterminate form). ...
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0answers
60 views
3
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1answer
84 views

Limit takes too long

I want to compute the following limit Limit[ Integrate[BetaRegularized[(2 h - h^2), (d - 1)/2, 1/2], {h, 0, 1}], d -> Infinity ] However, surprisingly, it ...
0
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1answer
42 views

Fit and find fitting parameters of data given an equation

If I have the following data: ...
1
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1answer
45 views

How to find integrals including certain expression

how do I find some terms in an integral containing some expression, e.g. in $$ \int \int \int \beta\phi(x,y,z) + \gamma\omega(x,y,z)\,\textrm{d}x\textrm{d}y \textrm{d}z +\int \int \alpha\phi(x,y,z) + \...
1
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0answers
75 views

How to plot integral of a gradient function

For $f : \mathbb{R} \longrightarrow \mathbb{R}$ continously differentiable and $\phi \in [0,\pi/2]$ let $$F(x) = \int \frac{f'(x)-\cot \phi}{1+ f'(x) \cot \phi} d x$$ be a clockwise 'rotation' of $f$. ...
0
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2answers
101 views

Asymptotic behavior of $n^2-n$

I recently became familiar with the Power of Wolfram. As a part of the problem I'm working o, I need to find which of the following is closer to $n^2-n$ $O(n \sqrt n)$ or $O(n \log n)$ or $O(n^2)$. ...
0
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1answer
35 views

Finding the x coordinate of a point in the solution of NDSolve from its y coordinate

Using NDSolveValue, we can know the y coordinate of the function from an x coordinate. Is it possible to do the reverse, where the input is the y coordinate and ...

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