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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5
votes
1answer
128 views

A 1D numerical integral Mathematica cannot compute, from physics

A well know result in theoretical physics is that a sum over Matsubara fermionic frequencies, i.e.: $$ S = \sum_{n=-\infty}^{\infty} h(\omega_n) \hspace{32pt} \omega_n=(2n+1)\frac{\pi}{\beta} $$ can ...
1
vote
0answers
123 views

Solving a functional equation

Suppose I have two functions f[x,y,z] and g[x,y,z], both analytically defined. I want to solve for a function ...
0
votes
1answer
77 views

Finding the limit of a complicated expression [closed]

I've never used Mathematica before, so I'm really struggling to use it right now. I have a complicated function $\qquad ...
0
votes
2answers
91 views

Please, help to find the area enclosed by the curves: ContourPlot[{x + y^2 == 0, x + 3 y^2 - 2 == 0}, {x, -2, 2}, {y, -2, 2}]

Please, Help to find the area between two curves. ContourPlot[{x + y^2 == 0, x + 3 y^2 - 2 == 0}, {x, -2, 2}, {y, -2, 2}]
2
votes
1answer
67 views
0
votes
4answers
287 views

Computing the first derivative in x, y ,and z

I have the following function: f:=x^3+yz+z^2x; I need to compute the first derivative in x, ...
1
vote
0answers
88 views

Determining the order of continuity (smoothness) of a function

Is there any method to determine the order of continuity of a function (just like an interpolant) over a given domain, or at least determine the continuity on a given order? For example, according to ...
1
vote
2answers
48 views

Computation (or estimation) of an trigonometric Integral with a parameter

I am trying to calculate the following integral which contains a parameter. I have used the Integrate and FullSimplify using assumptions but Mathematica fails to produce an analytical solution. ...
2
votes
2answers
79 views

Integration result with incomplete beta function

I'm doing some calculations (double integration) which results in the incomplete beta function occurring as an end result. My input is: ...
1
vote
1answer
120 views

Plotting the exponential of 1/(y-x)

What is the best way to handle this situation? ...
0
votes
1answer
78 views

is this a possible integration bug? [closed]

I am find a discrepancy in evaluating an integral which has given me trouble all day. I have finally isolated where the problem is which I now frame: I define the integral in terms of a delayed ...
-1
votes
1answer
86 views

How to calculate the volume of a solid enclosed by surfaces? [closed]

I am asked to calculate the volume of the solid enclosed by the following equations: (in polar coordinates) r = Cos(θ) z = 2 + x² + y² z = 0 I know the second equation can be changed to its polar ...
0
votes
1answer
98 views

Derivative of $e^{-1/x^2}$ [closed]

I'm trying to get derivative of $$ e^{-1/x^2} $$ (also in other points than 0, e.g. 1) with D[E[-1/x^2], x] or ...
1
vote
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
71 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
171 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
60 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
143 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
44 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
vote
3answers
139 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? ...
8
votes
0answers
100 views

Strange kernel segmentation fault in Integrate

Bug introduced in 8.0 or earlier and persisting through 10.4 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
109 views

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

I have a fairly complicated function: ...
1
vote
1answer
113 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: ...
2
votes
2answers
139 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, ...
6
votes
4answers
229 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
218 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
91 views

Symbolic Integration gives wrong answer [closed]

I have tried to integrate the following expression in Mathematica 10.1 ...
4
votes
3answers
141 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
186 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
356 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
70 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
159 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
58 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
205 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
119 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
201 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
232 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 ...
4
votes
3answers
114 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
93 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
94 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
125 views

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

I'm trying to integrate this function by Mathematica ...
1
vote
2answers
174 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
124 views

Differentiation help [closed]

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

Integrate does not work on my expression

I am trying to integrate a simple equation. The code is as follows ...
3
votes
1answer
68 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
206 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
315 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
188 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 ...