# 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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### 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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### 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 ...
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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### 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 ...
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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### 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 ...
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 ...
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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### 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 ...
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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### 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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I have code ...
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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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### SystemException[“MemoryAllocationFailure”] in Integrate

Integrating products and ratios of piecewise linear functions throws the error ...
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### Derivative of predictor function

Given some data dat, we would like to generate a predictor function. Therefore we use ...
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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 ...
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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### 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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### 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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### 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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### 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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### 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 ...
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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### 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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### 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*) and ...
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### 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: ...
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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### 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 ...
Consider $\qquad \underset{h\to 0}{\text{lim}}\dfrac{\sqrt{h+x}-\sqrt{x}}{\sqrt{h+x}-\sqrt{x}}$ Here is what I get when I evaluate it Mathematica: When I calculate it by hand and in other ...