# Tag Info

## New answers tagged calculus-and-analysis

### Symbolic scalar-by-matrix derivative

Outline Discussion Using Differentials Using the NonCommutativeMultiply package NCAlgebra Using MatrixD Using xAct Discussion (code sections below) There is an ambiguity that has not been mentioned. ...
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### Modify derivative expressions with substitutions

OK...I think I got it, but maybe not the most efficient way. Need to add a conditional /; dy-1 >= 0 before the rule ...
Accepted

### Derivative of piecewise function returns one more case

Clear["Global*"] Instead of using g != 1 use g < 1 || g > 1, then ...
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### Derivative of piecewise function returns one more case

It looks like Mathematica insists on having a default condition (with value zero, unless otherwise specifed). With ass=D[U[c,n,g,p],c] You can construct something ...
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### Symbolic integration and numerical integration yield very different results

The problem is not Integrate, but the numerical evaluation following Integrate. Consider for example ...
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### Mathematica doesn't evaluate an expression

I think your expression E[t] inside Solve should be Exp[t]. Try this instead, where I ...
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### Definite Integration by parts

There's a resource function, based on the the internal utility ResourceFunctionHelpersIntegrateByParts: ...
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### Evaluate Tricky Multivariable Integral

I solved the issue and thought it instructive to post the solution: A contributor in the comments mentioned using NumericQ with ...
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### How to calculate this integral with highly oscillating integrand?

Here's a fast way: ...
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### How to calculate this integral with highly oscillating integrand?

Stripping "GlobalAdaptive" of the "extras" produces correct results quickly: ...
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### How to calculate this integral with highly oscillating integrand?

The issue with this integrand seems to be the highly oscillatory nature which makes it difficult to find the right step spacing. In the following I will give two methods to deal with the small step ...
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### How to calculate this integral with highly oscillating integrand?

With patience, Monte Carlo methods can be effective ...
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### How to calculate this integral with highly oscillating integrand?

It's kind of a pain, but you can break up the integral yourself. integrand = (Cos[2022*t]*Sin[10050*t]*Sin[10251*t])/(Sin[50*t]*Sin[51*t]) To determine where one ...
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### Can this type of function be plotted faster using NDSolve instead of NIntegrate?

Note: This is an extended comment. This integral can be expressed in terms of the MeijerG special function: ...
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### Can this type of function be plotted faster using NDSolve instead of NIntegrate?

How can I apply NDSolve to this function? Do you want to apply NDSolve or do you want to plot the integral faster? The plot can ...
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### How to calculate this integral with highly oscillating integrand?

Note: As OP has pointed out in a comment, a similar calculation is available here on Math SE. OPs integral can be written as $$\int_0^{2\pi} f(50t) f(51t) \cos(2022 t) dt$$ with the auxiliary ...
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Accepted

### Consecutive neighbours of Hypergeometric ${}_1 F_1(a,b,z)$

For $c\approx0$ we can use a series-expansion for the second term on the right-hand side: $$_1F_1(a,c;z) = \frac{a z}{c}{_1}F_1(a+1,2;z)+O(1)$$ which turns the OP's expression into an approximation ...
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### General limit of a function with Pochhammer for any natural number

The function can also be written as f1[z]*f2 where ...
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1 vote

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### Plot eigenvalues of fractional Laplacian in 1D

We can compute eigenvalues with using Haar wavelets collocation method as follows (see also our code here) ...
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1 vote

### How could I deal with and mark point of singularity or non-existance?

Dibbo: Best if you break it up into small parts and test them separately. First just need to get the DE working. You have three bugs: You define b=2 but specify it as a parameter in ...
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1 vote

### I'm trying to solve the indefinite integral of a real function (with a bunch of real parameters inside) but the result is a complex function

the result is a complex function and I cannot accept this solution. Maple 2022.1 gives anti-derivative with no explicit I in it. Here it is. It is in terms of cos/...
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### How to plot several lists for different values of independent variable in a same graph?

We can use Do loop as follows ...
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### Possibly incorrect result of DiscreteLimit

In version 13.1 on Windows 10 ...
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### Integrate[Sqrt[(1 - Cos[t])/(Cos[a] - Cos[t])], {t, a, Pi}, Assumptions -> 0 < a < Pi] gives a Complex Expression rather than Pi

Assumptions are not always applied as constraints. (Took a bit extra massaging to get the result of Integrate into its fully simplified form under the assumptions.) ...
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### Integrate[Sqrt[(1 - Cos[t])/(Cos[a] - Cos[t])], {t, a, Pi}, Assumptions -> 0 < a < Pi] gives a Complex Expression rather than Pi

$a$ needs to be between 0 and Pi/2 so that Cos[a] remain positive in order to simplify the sqrt which comes into play using the ...
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1 vote

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Accepted

### Bug in FullSimplify

I'm not sure this is truly a workaround, since your original Sum will not yield a function of x, but for this particular case we can notice that ...
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1 vote

### Plot of massless particles on unstable null circular geodesic : Finding an alternative for GraphicsMeshFindIntersections and reducing code length

This is a more functional way to do step 1: ...
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Accepted

### Plot The Magnetization

Function g[k_] := Tr[Eigenvalues[h[k]]] is periodic with a period of 4 Pi, therefore we suppose that integral should be defined ...
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### This trigonometric integral "has exceeded the time limit for your plan"

TrigFactor and TrigReduce the integrand to see a systematic, FourierCos like expansion depending on n. ...
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### This trigonometric integral "has exceeded the time limit for your plan"

Somehow trig integrals, especially those with parameters and removable discontinuities, often have tricky antiderivatives. One can apply a standard identity: ...
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### This trigonometric integral "has exceeded the time limit for your plan"

In 13.1 on Windows 10 Integrate[Sin[(2 n + 1) x]/Sin[x],{x, 0, Pi/2},Assumptions -> n \[Element] PositiveIntegers] Pi/2 ...
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Accepted

### This trigonometric integral "has exceeded the time limit for your plan"

One alternative: Table[Integrate[Sin[(2 n + 1) x]/Sin[x], {x, 0, Pi/2}], {n, 0, 10}]
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1 vote
Accepted

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