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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1
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1answer
55 views

How could I check if a differential equation crosses a specific value? [closed]

I'm designing a magnetic field to simulate relativistic speeds in a small cyclotron. I need to see if the ratio -R/B * dB/dR crosses 0.2 in a certain range, and right now I'm trying to do that by ...
0
votes
1answer
67 views

Only real numbers (Fullsimplify) [duplicate]

I've to do some complex calculation with Mathematica and if I put in my code it gives me something big back, so is it possible to say that my variables are strictly real numbers, by sing the ...
12
votes
1answer
163 views

Why do singularities disappear when performing convolutions with the Dirac Delta function?

I am attempting to perform a convolution involving the Dirac Delta function: $\int_{-\infty}^{\infty} \frac{1}{t+1} \cdot \delta(t+1)\ dt$ I would expect that the result of this integral is ...
2
votes
0answers
57 views

How do I let Fourier Transform know that it is a linear operator? [duplicate]

I have the following issue with FourierTransform, Fourier transform doesn't seem to know it is a linear operator. ...
0
votes
2answers
58 views

Functional in Integration [closed]

I have evaluated the following code: k[θ_] := Sin[θ/2]^2; Do[Print[Integrate[1/Sqrt[1 - k[θ]*(Sin^2)[ϕ]], {ϕ, 0, π/2}]], {θ, 0, π/3, π/12}] But I don't know why ...
0
votes
1answer
119 views

How to integrate a function of a direction, over the hemisphere

The Mathematica documentation Integrate over Regions gives an example of how to simply integrate over a sphere (surface): ...
0
votes
0answers
40 views

Solving Integral -syntax or interpretation problems

WA interpreter achievement not well this entry from Mathematica, steps need to see the full resolution input WA ...
1
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3answers
135 views

Evaluating two equivalent integrals apparently gives two different results

I have a integral and I use two different symbols in an interchangeable way, but I do not get same expressions when I swap them. Can some one explain why? ...
7
votes
0answers
86 views

Strange kernel segmentation fault in Integrate

Bug introduced in 8.0 or earlier and persisting through 10.3 Define tointegrate = D[V[y1[t], y2[t]], y2[t]] D[V[y1[t], y2[t]], {y1[t], 2}] and try to find its ...
1
vote
1answer
106 views

Is it possible to double integrate my function over real numbers?

I have a fairly complicated function: ...
1
vote
1answer
100 views

Calculate an integration limit to obtain a certain area under a curve

I have a function that looks like a sigmoid curve. I would like to calculate the right integration limit so that the area under the sigmoid curve has a given value. my curve: ...
1
vote
2answers
115 views

Piecewise Integration

I am trying to integrate a piecewise defined function twice. It represents the acceleration of a projectile. I am obtaining it's position as a function of time if it starts from rest at the ground, ...
5
votes
4answers
207 views

Limit of partial sums involving inverse squares

Consider the finite sum rs[x_, n_] := x/n Sum[n^2/(i + (n - i) x)^2, {i, 1, n}] Is there a way to bring Mathematica to calculate the limit for ...
14
votes
1answer
213 views

Is it a bug in Limit?

Bug introduced in 9.0 and fixed in 10.0.0 Mathematica 9 on Windows and WolframAlpha says Limit[Sin[Sqrt[x+1]]-Sin[Sqrt[x]],x->Infinity] is ...
1
vote
1answer
90 views

Symbolic Integration gives wrong answer [closed]

I have tried to integrate the following expression in Mathematica 10.1 ...
4
votes
3answers
119 views

Express function derivative in terms of the function itself

I'm working on a minimization problem that involves the standard logistic function $f(x) = \frac{1}{1+e^{-x}}$ along with its simple derivative $f'(x) = f(x) \cdot (1 - f(x))$ The correctness of ...
2
votes
2answers
178 views

Finding extremums of Abs[complex function]

We have a function same as f[x_]=Cos[x] Cos[2 x] + I Sin[x] Sin[2 x] The final objective is to find all extremums of Abs[f[x]] in [0,2 pi]. But in the first ...
7
votes
3answers
341 views

Limit of a real function

Evaluating Limit[2^x Log[x], x -> 0, Direction -> -1] (right limit) gives correctly the answer -∞ but the ...
1
vote
1answer
68 views

Differentiate functions

I have two functions: F1[t_, g_] := a1*t + a2*g F2[t_, g_] := b1*t + b2*g I want to evaluate $(dt/dF1)_{F2}$; i.e., differentiate $t$ over $F1$ when $F2$ is ...
4
votes
4answers
147 views

Implicit function theorem to higher order

Consider f[x_, y_] := Csc[0.482` y] Sin[0.963` x - 0.482` y] + 3.247` Csc[0.333` y] Sin[0.667` x - 0.333` y] + 5.049` Csc[0.119 y] Sin[0.238 x - 0.119 y] ...
1
vote
0answers
55 views

Continuous integration of a tensor function using discrete density values

Hei, I am wondering is it possible to implement continuous integration using Integrate() of a fourth order tensor with discrete density values. ...
3
votes
2answers
202 views

Slightly increasing complexity of function increases calculation time by magnitudes

I am trying to calculate an impedance value from voltage and current functions. The calculation method is based on how an actual measurement device performs it. I have two different current function, ...
5
votes
3answers
109 views

Differentiate a numerically defined function

My function is f[a_, b_] := NIntegrate[Sqrt[(Cos[t] - a)^2 + b^2], {t, 0, Pi}] I want to calculate g[1,1] where ...
4
votes
1answer
163 views

How to make Mathematica express an equation in terms of previously defined functions

I was given a problem for my physics class, and perhaps I have taken it too far, but I wish to finish what I started. I have a function (i warn you that this does not look pretty) ...
0
votes
3answers
200 views

Residue theorem and multiple poles in contour integral

I had a query on multiples poles in [Contour Integral][1] using the [Residue Theorem][2]. I had an integral which I wanted to solve using the Residue Theorem. By the help of mathematica experts i ...
3
votes
3answers
102 views

How to express and take symbolic derivative of expression with finite sum

I have the expression: $$ p_i = \frac{e^{x_i}}{\sum_{j=1}^{n} e^{x_j}} $$ which I defined with the following Mathematica code: ...
2
votes
2answers
90 views

Integration procedure with real parameters

The output of the following integration appear to produce imaginary terms, even though the parameters {a,b} have been specified to be real. My question: Is there a way to perform this integration ...
3
votes
0answers
91 views

Using NIntegrate and DiscretePlot to visualize pseudodifferential operators

In harmonic analysis, pseudodifferential operators are a way to generalize the notions of derivatives, through the use of Fourier transforms. The basic idea being, Let ...
0
votes
1answer
114 views

Integrating 2d exponential function symbolically with polynomials of 2nd order running for days

I'm trying to integrate this function by Mathematica ...
1
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2answers
164 views

How to solve this two algebraic equation simultaneously for u and H ?(all real number)

I want to find the non-zero value of H when beta is changing(especially what value of beta when increasing will there be a non-zero H value). H is between [0,100]. This is actually the calculation ...
1
vote
3answers
123 views

Differentiation help [closed]

I am new in Mathematica. I want to differentiate ...
0
votes
1answer
128 views

Integrate does not work on my expression

I am trying to integrate a simple equation. The code is as follows ...
3
votes
1answer
59 views

In NMinimize, how can I efficiently handle NIntegrate errors for non-integrable functions?

I am using NMinimize to find parameters that minimise the integral of a function in the least squares sense: ...
0
votes
1answer
82 views

Integrate works but NIntegrate doesn't

I have a complicated integral function that I'm trying to evaluate, which will have to be done numerically. I wanted to try a simpler one first, one that has an analytic form, because I could check ...
0
votes
2answers
202 views

Singular integral mathematica

A = Integrate[Sin[2 x] / (A1 - B1 Sin[2 x] + C1 Cos[x] - D1 Sin[x]), {x, 0, 2 Pi}] The calculation is taking too much time; not returning any results. Any help?
17
votes
1answer
267 views

How to determine if a function is continuous?

I wish to write code for Riemann Stieltjes integrals in Mathematica. A necessary condition for the theorem to hold is that the function must be continuous. The domain of the function is a closed ...
3
votes
3answers
178 views

Plotting the region bounded by parallel lines

I am working on the integral $$\int\int_D (2x+y)^2 e^{x-y}dA,$$ where $D$ is the region bounded by $2x+y=1$, $2x+y=4$, $x-y=-1$, and $x-y=1$. I need to shade the region bounded by these lines, so I ...
4
votes
2answers
127 views

Symmetrise a complicated expression

I am calculating the derivatives of a symmetric function $F(a_1, a_2)$ and got very complicated expressions, which I'd like to write in a symmetric form with respect to $1 \leftrightarrow 2$ (clearly ...
2
votes
1answer
297 views

How to evaluate this integral?

Why can it not evaluate this integral? Please help. Integrate[Exp[-r^2]* r^2*Log[Exp[-r^2]* r^2*(2.5 - r^2)*(2.5 - r^2)], {r, 0, 10}]
5
votes
1answer
155 views

Visualize transformation used in multiple integration

In class, we will sketch the region $D$ in $R^2$ bounded by the curves $xy=1$, $xy=4$, $y=x$, and $y=x+2$. Then we will use the change of variables given by $u=xy$ and $v=y-x$. We need to show that ...
7
votes
1answer
156 views

Old fashioned region method?

Just stumbled across this idea in http://users.rowan.edu/~hassen/Mathematica/Volume%20III/Chapter%2015.pdf. ...
0
votes
0answers
58 views

The system can not be solved

I'm trying to solve this equation: f[a_][r_]=((a*r/12)*(1+(r/12))^n)/(((1+(r/12))^n) - 1) When I type Solve[f[a][r]==p, a] ...
12
votes
1answer
882 views

1/x integration giving 0 instead of infinity [duplicate]

I stumbled across the fact this integral: Integrate[1/y, {y, 0, 1}, GenerateConditions -> False] returns 0 Anybody ...
3
votes
1answer
126 views

Derivative of conjugate multivariate function

I have a problem with Mathematica, taking the derivative of the conjugate of some function. I know that a similar question has been posed before here, but the solution did not work for multivariate ...
-1
votes
1answer
74 views

Wrong condition for the convergence of the integral $\int_0^\infty t^a \exp(-i t^b) dt$

The integral $\int_0^\infty t^a \exp(-i t^b) dt$ converges for $-1 < a < b - 1$ or $b - 1 < a < -1$. However, ...
4
votes
0answers
54 views

How to take the second derivative of a complicated function using limits [closed]

I have a very complicated function of one variable consisting of exponential and error functions combined in various ways. Mathematica can't take the derivative of this function in the usual way ...
0
votes
0answers
23 views

Show[cp1,cp2, …] but PlotLabel in cp2 does not show up [duplicate]

I am visualizing the extrema of $f(x,y)=x^3+3y^2$ constrained to the level curve $g(x,y)=xy=-4$, found by using the Lagrange Multiplier Method. ...
2
votes
1answer
105 views

Why can't Mathematica do this limit?

(Glancing past the fact that one can do this by hand in a second...) Are there any extra conditions I can give Mathematica to make it evaluate limits like this? I'm not sure why it's getting choked ...
2
votes
1answer
164 views

Calculate the limit of an integral

How can I use Mathematica to find the limit:$$\lim_{x\rightarrow 0^{+}}\frac{\int_{1}^{+\infty}\frac{e^{-xy}\quad-1}{y^3}dy}{\ln(1+x)}=?$$ I tried this ...
0
votes
2answers
110 views

How does one define a function that takes vectors as arguments but also derivatives?

Summary: tldr; I just want to implement a version of the following mathematics function: $$ f(a) = c_1 e^{-(a - t_1)^2} + c_2 e^{-(a - t_2)^2} + c_3 e^{-(a - t_3)^2}$$ in mathematica, and be able ...