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.
4,456
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Finding curl of a scalar function?
I am having some trouble with a problem on my calc 3 homework that asks me to compute curl(∇f). I'm confused because we are given a scalar function and my professor only taught how to compute curl ...
- 1
3
votes
6
answers
495
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How to ask Mathematica to compute the given sum of the differences of the numbers of the given two sets?
I have two sets of real numbers, say,
set1= {b1, b2, b3, b4, b5, b6, b7, b8, b9, b10, b11}
...
- 41
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1
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91
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On the Dirichlet integral
Continuing this topic, once the Dini-Neumann problem is solved:
$$
\begin{cases}
\Delta f = 0 & \text{on} \; \Omega \\
\frac{\text{d}}{\text{d} n} f = y\,n_x - x\,n_y & \text{on} \; \partial\...
- 4,385
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Does the computation time for the determinant of a symbolic matrix depend only on the size of matrix? or, the form of the entries also plays a role?
I have a large ($50\times 50$) sparse matrix $M$ whose entries are symbolic, and most of them are of these exponential form: E^(-((I x)/2)) (3 + x) and ...
- 21
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34
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Proving that the Second Derivative of a Function is Less than 0 Over an Interval of Time (i.e. Convex) [closed]
So, I have a very gross function that I want to prove is convex over an interval. I have next no knowledge of Mathematica besides what I have read about it today, and I am unsure if I am going about ...
4
votes
1
answer
156
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Sum Converges or Diverges?
I am running MMA 13.1.0.0 on Windows 10 - x86.
Is there any way to get Mathematica to conclude that this sum converges (maybe it needs some additional input)?
...
- 2,266
3
votes
1
answer
207
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How to find (p,q)-derivative in Mathematica?
In the study https://link.springer.com/article/10.1007/s00025-018-0783-z, in Eq. (5), the author defines the $(p,q)-$derivative as
$$
D_{p, q} f(x)=\frac{f(p x)-f(q x)}{(p-q) x}, \quad x \neq 0.
$$
In ...
- 422
4
votes
1
answer
121
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How to know the minimal mesh size of NIntegrate?
Sometimes it is necessary to know the discretization mesh size in numerical integration. But since NIntegrate is a complicated composition of various algorithms, it ...
- 4,432
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145
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How evaluate a mixed derivative at a point? [closed]
f[x_, y_] := x*Exp[x + y]
df[x_, y_] := D[f[x, y], x]*Sin[q] + D[f[x, y], y]*Cos[q]
df[x, y]
df[1, 2]
The later doesn't evaluate the mixed derivative at the ...
- 199
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votes
2
answers
61
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Calculating the equilibria of a system of two coupled oscillators?
Equations:
I have the following system of ODEs:
Phi1'[t]=omega1-a*Sin[Phi1[t]-Phi2[t]];
Phi2'[t]=-omega1-a*Sin[Phi2[t]-Phi1[t]];
Question:
Is there a ...
- 515
0
votes
0
answers
34
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Partial derivative unexpectedly returning 0 [closed]
Please do excuse me if this is a daft question, in either Mathematic context or just Math context.
I have defined functions as follows:
...
- 1
1
vote
1
answer
63
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Differential operator not working
Could someone help me understand why this code does not work?
I paste the code here but I am unable to format it:
...
- 255
1
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0
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21
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Taking the derivative of a product
EDIT: see here
I am new to Mathematica and I am trying to work though deriving the maximum likelihood estimator for the Poisson distribution as an exercise to familiarize myself with how Mathematica ...
- 111
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0
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27
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Question for NSolve
When I am writing the following code
NSolve[x Cosh[x]==0,x]
I received as an answer
...
1
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1
answer
39
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1
vote
0
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64
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What's the difference between f[a_,b_][x_,y_] and f[a_,b_x_,y_]? [duplicate]
I tried to find information in reference guide. Didn't find.
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1
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Finite result under "Integrate" while infinite under "NIntegrate" of a complicated integral with "NSum"
I have been trying to compute the following complicated integral along with summation, details codes/function of which is given below:
...
4
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2
answers
123
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1
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2
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62
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Newton Method with a Parameter in the equation
I know the Raphson Newton method for the equation $f(x)=e^{-x}-x$, it is written with the following code
...
0
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0
answers
24
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Mixed system of PDE and integral equations is solved manually, but not solved automatically
I continue to study the issue raised here. There is one technical difficulty that requires a separate topic.
I have a system of equations:
...
- 2,112
0
votes
1
answer
50
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Solving an integral
Given the dimensionless Hubble function:
$$E^2(z) = \biggl ( \frac{H(z)}{H_0} \biggr)^2 = \Omega_m(1+z)^3+ (1-\Omega_m)e^{\int_0^z\frac{1+w0+w1*z}{1+z} dz} $$
I would like to calculate the ...
- 2,521
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40
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How can I make Mathematica catch one-off cases where the answer is different? [duplicate]
I wanted to compute
$$\frac{2}{L}\int_0^L\left(1+2\cos\frac{3 \pi x}{L}\right)\cos\frac{n \pi x}{L}\,dx,$$
so my input was
...
1
vote
0
answers
46
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Replace original function inside its derivative
I'm trying to simplify a derivative calculation. I have the Zhs in function of x :
...
6
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1
answer
561
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Wrong result of Laplace Transformation [closed]
I am trying to calculate the Laplace Transformation of the following function:
$$f(x) = \theta(t+1)-\theta(t-1)$$
where $\theta(t)$ is the Heaviside step function defined as:
$${\displaystyle \theta(x)...
-5
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0
answers
48
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Why isn't Mathematica giving me the answer? [closed]
When I try to write my code, it just repeats the question instead of answering it. Does anyone know why? It seems to do this with almost everything.
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2
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3
answers
148
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Question in Derivatives and TableForm
Using the TableForm command, I want to find the derivatives up to the fourth order of the function $f(x)=\cos{x^2}/x$ and give the results in Matrix form.
0
votes
2
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39
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How do I change the display of the RevolutionPlot3D of the Z direction?
Im using Revoultion Plot 3d and I'm looking for a way to change the Z bound.(like for exsample only graphing from the height of 1000-5000) These are my commands. So far I have only been able to figure ...
- 3
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2
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163
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Simplifying and interpreting a RootSum output
I am trying to compute this integral with a parameter s. How I can simplify the output expression containing Rootsum, ...
- 11
2
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2
answers
215
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I need to find the obtuse angle between the following two lines
I need to find the obtuse angle between two lines but I am not sure how to code it.
my two angles are 𝑥+√3𝑦=1 and (1−√3)𝑥+(1+√3)𝑦=8
I already did the calculations but im just not sure how ...
- 21
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56
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Integral behaviour?
I'm trying to find a standard integral, which shows itself up in general relativity (proper distance in Schwarzschild metric). For example in this video. The integral is shown as
where $r_s< r$ ...
- 386
4
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0
answers
89
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Differentiating with D vs. Derivative
I was tinkering with something and needed a high-order derivative of a function that, when differentiated, needs the product rule (and so, subsequent derivatives - without simplification - become ...
- 2,626
2
votes
4
answers
218
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Space enclosed between a list of numbers and the X-axis
I have lists of numbers, consisting of 8 different numbers in each list.
I will get a line if I display the list as ListLinePlot, the first number will be 1 on the X axis, and the last 8.
Is there a ...
- 297
9
votes
2
answers
963
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"Simple" integral with very long, complicated value
Part of the value of symbol-manipulation programs such as Mathematica is that even extremely complicated problems—ones beyond computation "by hand"—can be addressed.
I'm seeking some ...
- 37.2k
2
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1
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160
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Integrals that cannot be solved with a direct approach
I'm collecting problems for which the basic or direct approach in Mathematica (v. 13 or later) does not work, but requires some trick or mathematical insight. I'd like to start with integration.
For ...
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60
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2
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1
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88
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How can I make sure that the two given numbers are exactly the same?
I have the given numbers $n1$ and $n2$. How can I make sure that these two numbers are exactly the same? Numerically, using {N[n1,40], N[n2,40]}, by increasing the ...
- 369
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32
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Defining parameter as function without losing properties of the derivative
I have built a code that is later on solved dynamically depending on values I set using Manipulate while plotting. However, I came across a problem I cannot resolve. So, I defined ...
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0
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28
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Differentiating matrix function in `Table` from
I am trying to get an analytical expression for derivaives of an algorithm explained here.
I usually use automatic diff. a lot, but since this part of function will not change, I thought to implement ...
- 111
2
votes
2
answers
168
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The derivative anomaly in Mathematica 13, showing in the Plot[] function
Edit:
Still inexplicably, it was found that in the Plot[] functions, showing a correct curve plot for the expression computing the derivative incorrectly, when '...
- 181
1
vote
1
answer
62
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Calculating the spectrum of the Fredholm coefficient in the Fredholm equation [closed]
I am solving the Fredholm problem of the second kind, using the given code:
...
- 769
1
vote
2
answers
68
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How to ask Mathematica to rewrite the larger arguments of sine function as a smaller number which is multiple of $\frac{2\pi a}{11}$
I have a trigonometric function $Exp$ where $\{f,g,h,k\}$ are some parametric functions, and $a\in\mathbb{N}$ and $x>0$.
$$ Exp=f \cdot \sin \left(\frac{58 \pi a}{11}+x\right)+g\cdot \sin \left(\...
- 1,159
1
vote
0
answers
52
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Definite Integration involving Error function from 0 to infinity
I am trying to integrate the following:
$y=\int_0^\infty x\left(Erf[\frac{x-a}{c}]-Erf[\frac{x-b}{c}]\right)dx$
Here a,b, c can take only positive real numbers.
However, in Mathematica, I don't get ...
3
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1
answer
94
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8
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1
answer
272
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Still bug in Integrate. 3
Let us consider in version 13.1 on Windows 10
r = Integrate[1/(x - a)/Sqrt[1 - x^2], {x, -1, 1},
Assumptions -> a \[Element] Reals]
...
- 19.6k
2
votes
1
answer
145
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Why "Integrate[Abs[x1 - x2], {x1, 0, t}, {x2, 0, t}]" get wrong output?
To verify the following double integral
$$
\int_0^t{\int_0^t{\left| x_1-x_2 \right|\mathrm{d}x_1\mathrm{d}x_2}}=\frac{t^3}{3}
$$
The MATHEMATICA (12.0.0 on Win10-64) got the following wrong output
<...
- 31
1
vote
3
answers
117
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How to calculate the range of $a$ that satisfies $a^x>x$ for any real number $x$?
I'm trying to calculate the range of $a$ that satisfies $a^x>x$ for any real number $x$. Reduce[a^x > x, a] fails. If it's not possible to get a symbolic ...
- 113
4
votes
1
answer
77
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Bug in Integrate involving hypergeometric functions?
I am working with v. 13.0.0.0 for Mac. I am attempting to compute the following integral with Mathematica for integer values of L>=2 and with ...
- 587
-1
votes
1
answer
67
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Finding solution of differential equation using DSolve
On solving this differential equation mathematica "shows system allocation memory" error. I want to find solution of f but not able to find that.
DSolve[{f[0] == 1., Derivative[1][f][0] == 0....
3
votes
0
answers
76
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IntegrateChangeVariables give a wrong result?
Bug introduced in 13.1.
RegionPlot[x^(1/(x + 1/x)) + y^(1/(y + 1/y)) >= E, {x, 0, 7}, {y, 0, 7}]
We can calculate the area by integral:
...
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