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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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 ...
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63 views

Numerical solution of an iterative equation

I am trying to solve the following iterative equation: where the parameter tao (needed in the previous equation) is defined as: Here's the parameters and my approach to solving the equation in ...
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71 views

Plot of the derivative of a function

I have a function functionSL as a function of t (t<0) where I want to find the extremum ...
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0answers
57 views

1D Transient Heat Conduction Problem [closed]

I could really use some help with this problem regarding heat conduction through a steel bar Solve the one-dimensional transient heat conduction problem as follows. You insert a steel bar that had ...
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1answer
72 views

Fourier Series of ODE

I am having trouble finding the Fourier series of a 2nd order ODE. Should I be using the piecewise function as well to set up the range for t? Solve $ y'' + \omega^2 𝑦 = r(t) $, where $ r(t) = |t|, -\...
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63 views

zeros or minimum of a multivariable function

what is the most reliable method for finding the zeros or at least the minimum of $f(x,y,z,w,r)= - \frac{3}{96 \pi^{2}z^{4}} \int_{y}^{\infty}\sqrt{x^{2}-y^{2}}x^{2} e^{-x} dx+ \frac{3}{16 \pi^{2}(1-r^...
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1answer
68 views

Directional derivative of a function of three variables

I'm a Mathematica beginner and I'm and struggling with a problem concerning heat flow, not sure how to set it up with three variables. Any help with what I should input into Mathematica will be much ...
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116 views

Incorrect result by DSolve

For real $x$ consider the trivial equation $$|y'(x)|=-|x|.$$ Since the left side is always positive and the right always negative, there is no solution. Let's try ...
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1answer
46 views

Remove complex part of a solution

I have a function intSL[a,zl,zh] where I want to compute its derivative with respect to zl given some values of ...
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1answer
54 views

Derivative of a set of equations [closed]

I am a new learner of Mathematica, I think this question should be simple, but I just can't get the correct answer... This is my equations: p=x+y q=2x+y r=p+q And ...
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36 views

Mathematica outputs sin(Pi*t) as Pi*sin(t) [closed]

Im very new to Mathematica, so spare me if there is a very trivial solution to this. ...
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1answer
69 views

How to make Mathematica treat y/x as a one variable?

I would like to make for example: $\frac{\partial\frac{2y}{x}}{\partial\frac{y}{x}}$. However, when I put it into Mathematica as D[2y/x,{y/x}] it does not recognize ...
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3answers
116 views

Plot a set of complex numbers with given argument and absolute value bounds

I want to plot the following complex numbers $$z \in \text{(complex numbers)}:\pi/4 < \arg (z) \leq 5 \pi/4,\ 1 \leq |z| < 2 $$ I don't know how to graph it so that it would look like 2D without ...
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Integration using the change of variable formula [closed]

I am working on a project for my multivariate calculus class that is focused around using the change of variable formula to manipulate integrals in Mathematica, and I had some questions: How do you ...
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59 views

How can I analytically solve an integral which has some terms that do not converge in (-∞, +∞)? [closed]

It is to be integrated from -∞ to +∞ and clearly the terms with k1 and k2 don't converge in the interval.
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Solve differential equation with integral in Mathematica [closed]

I am reposting this question in hopes I can get some help. In the previous post I didn't put any thing regarding Mathematica So I hope this post is better. I want to solve the following equation: ...
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39 views

SystemException[“MemoryAllocationFailure”] in Integrate

Integrating products and ratios of piecewise linear functions throws the error ...
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1answer
18 views

Derivative of predictor function

Given some data dat, we would like to generate a predictor function. Therefore we use ...
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1answer
58 views

Analytical expression for a limit

I have the following equation $$\Delta v = -g I_\mathrm{SP} \left( 1 + \frac{1}{24} \frac{\mu}{r^3} \frac{g^2 {I_\mathrm{SP}}^2}{T^2} \frac{{m_p}^2}{n^2} \right) ^{-1} \sum _{k=1} ^n \log \left( \...
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1answer
44 views

Using Solution to Differential Equation in New Function

I am trying to feed the solutions from my differential equations into another function. I am using NDSolve to solve two differential equations simultaneously. It ...
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61 views

Solving a certain transcendental equation [closed]

I cannot make Mathematica solve the following transcendental equation using Solve with coefficients a, b, c, d, and ...
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75 views

Having trouble making a table of the derivative of a Bessel-function-based expression

Please suggest how I should correct the following code to plot the integral: ...
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1answer
100 views

Verify a conjectured formula for a modification of a 3D constrained integration successfully solved using Mathematica

I've acquired somewhat indirect--and not fully conclusive--evidence that the solution of a certain three-dimensional constrained integration takes the form ...
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0answers
52 views

Evaluate fractional derivative

I needed to evaluate the following fractional derivative of $f(t) = e^{t^2}$. The fractional derivative that I'm currently studying is the Grunwald-Letnikov fractional derivative, which is defined as ...
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1answer
168 views

Elliptical Integration

I have an integral which can be decomposed into three complete elliptical integrals. I want to know the method by which I can achieve this. The integration is the following: (4 (-1 + y)^2)/(c Sqrt[y (-...
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59 views

Derivative of a Definite Integral

I have two equations as follows, $$a = \int_0^1 dx \frac{c z_s^{d+1} x^d}{\sqrt{(1-(z_s/z_h)^{d+1} x^{d+1})(1-c^2 z_s^{2d} x^{2d})}} \tag{1}\label{1},$$ \begin{align} S &= \frac{1}{4 z_s^{d-1}}\...
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1answer
24 views

Calculating boundaries for a multiple integral from inequalities

I was trying to solve for the region enclosed by y=Sqrt[x], z=1+x+y, y=0, and ...
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2answers
92 views

Triple Integral boundaries and solution

So I'm working on triple integrals, specifically on those where I have a region bounded by various surfaces. (In other words, the ranges for each integrals are not given, but must be calculated.) I ...
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2answers
211 views

Hyperbola problem

I'm studying the hyperbola given by the implicit function $x^2/16-y^2/2=1$ I need plot the hyperbola and the asymptotes $y=b/a\,x$ and $y=-b/a\,x$. Then I need to select a point on the hyperbola and ...
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1answer
62 views

Half-life of a radioactive substance? [closed]

After 4.27 minutes 99.99% of a radioactive substance is present. What is the half-life of the radioactive substance? What code would I use to solve this problem? I don't know how to start it.
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1answer
45 views

Issue with Erf function and comparaison with Maple [closed]

I warn you that I am completely new to Mathematica and I apologize in advance if my question is very stupid. I define the function $f(x)$ in the following way (it is very close to the function ${\rm ...
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3answers
31 views

I want to maximise my function over a particular domain

I have tried NMaximise. But I am getting an error always. Even if my command is correct. My function is Cos[π E^x] and I want to maximise it over the range (-3,3)
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2answers
240 views

Limit if the limit is a function

Can MMA find limits if the limit can be expressed as a function? Example: $$\lim_{x \to \infty}\frac{\Gamma\left(\frac{x+1}{2}\right)}{\Gamma\left(\frac{x}{2}\right)} =\sqrt\frac{x}{2}=\infty$$ $\\\\$ ...
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Write some expressions of the integral

I am trying to apply the Hamilton principle and the final part is the integration. then I should pick some parts only in sperate equation. for example. The full equation is ...
4
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3answers
229 views

Question about plotting a curve and tangent lines

This is a Mathematica question. I have a function $y=x^3$. “Fun1” is any point on the curve. At the point Fun1, draw a tangent line at that point to the curve. At another point where the curve and the ...
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1answer
46 views

How to convert a Piecewise function in a HeavisideTheta function?

I want to convert a Piecewise function in a HeavisideTheta function in order to correctly evaluate its derivatives at the point of abrupt change and then integrate the result along the axis. How can I ...
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1answer
46 views

Assuming two integers are odd

Is there a way to assume both n and k are odd in Mathematica? Assuming[{n > 0, k > 0}, Exp[-I*(\[Pi]/2)*(n^k)] // FullSimplify] n=1,3,5,7,... k=1,3,5,7,... ...
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0answers
54 views

All double integrals produce error [closed]

I am a beginner to the Mathematica community; however, for my Multivariable Calculus class I have made a number of double integrals that have worked successfully. Today, while working every single ...
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1answer
46 views

Find n-th derivative of the function, display it and then evaluate it at a point of choice

What would be the correct syntax to find the order derivative "$n$" in MMA, and to be able to evaluate it in a certain point. We ask for an example ; Find the order derivative 2 and evaluate ...
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2answers
87 views

Can't compute the Integral

I tried to calculate an integral with the function Integrate, but it runs for a long long time without any answer. I have been checking the integrand and it seems ...
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3answers
130 views

How to interpret these integrations with DiracDelta?

Let us consider the double integral of DiracDelta[y-x^2] over the triangle with vertices at $(-1,0),\,(-1,2),\,(1,0)$. Mathematica calculates it as an iterated ...
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1answer
48 views

Integral involving orthogonal functions (quantum harmonic oscillator eigenstates)

I have a question about the capabilities of the Integrate command for general parameters. We know that there is a system of functions: ...
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1answer
91 views

How to understand these integrals with DiracDelta?

Namely, Integrate[DiracDelta[y - x^2, z], {x, -2, 2}, {y, -2, 2}, {z, -2, 2}] (*2 Sqrt[2]*) and ...
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2answers
113 views

Exporting a FEM mesh from a parametric surface

How is it possible to export a mesh for suitable finite element analysis (such as Abaqus) from a parametric surface expressions? I'm working on this kind of surface: ...
3
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3answers
637 views

Why doesn't Mathematica integrate this?

I am trying to do this integral in Mathematica: f[x_] := A*Exp[-x^2*M/(2*kb*T)]*DiracDelta[v - Abs[x]] Integrate[f[x], {x, -Infinity, Infinity}] It just writes out ...
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3answers
50 views

How to calculate the derivative of the solution of DSolve?

It should be a particularly straightforward problem to solve. However I cannot manage to do it. I get a solution from a differential equation via DSolve. I just want to calculate now the derivative of ...
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1answer
81 views

Find the probability (relative volume) of a certain 4-ball with respect to Hilbert-Schmidt measure

Let us consider the set of points {x,y,z,1-x-y-z} and impose the strict ordering constraint ...
2
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2answers
157 views

Unexpected Indeterminate result from evaluating a limit [closed]

Consider $\qquad \underset{h\to 0}{\text{lim}}\dfrac{\sqrt[4]{h+x}-\sqrt[4]{x}}{\sqrt{h+x}-\sqrt{x}}$ Here is what I get when I evaluate it Mathematica: When I calculate it by hand and in other ...

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