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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0
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1answer
46 views

How can evaluate this function [duplicate]

Suppose this function F[c_, n_, s_] := Module[{}, Abs[s - 1 + (-1 + c)^n]] I calculate its second derivative on c ...
1
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2answers
171 views

Find the explicit solution of the integral

I want to calculate the integral: assuming that we are familiar with the relation: The answer should be: The code that I've used is the following: ...
2
votes
2answers
90 views

Strange failure of Series and Derivative

I just spend three hours and posted two Questions trying to figure something out, and it turned out all the confusion was caused by this mysterious quirk. I want to expand g[x,v] in v at v=0, using ...
1
vote
1answer
75 views

About taking limit of an integral on Wolfram Alpha/Mathematica [closed]

I tried computing this quantity on Wolfram Alpha, but I couldn't get any answer: ...
0
votes
1answer
46 views

How can I solve this limit? [closed]

How can I solve this limit? thanks you!!!
0
votes
1answer
102 views

Hessian of function at many points

If f:= x^3 + 2yz + 5 x^2z is a function and if {2,0,1},{3,9,2},{8,5,6},{1,1,7} are points. I would like a Hessian of ...
1
vote
2answers
201 views

How would you calculate a contour integral? [duplicate]

How would you be able to calculate a contour integral of 1/(((z-1)^2)*(z-i)) over the contour |z-1| = 1? Not sure how to type ...
4
votes
0answers
112 views

Integral of DiracDelta giving an unusual answer

I have been getting a number of seemingly inconsistent solutions to integrals of Dirac delta functions in which the integrand evaluates to DiracDelta[0] at one of ...
5
votes
1answer
129 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
133 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
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1answer
78 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 \chi_{N}=\frac{[(2\cosh(J))^{N+1}(\lambda_{0}+\lambda_{1})^{N}((\mu_{0}+\mu_{1}...
0
votes
2answers
92 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
72 views
0
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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
84 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
89 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
102 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
74 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
59 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
61 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
149 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
45 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
142 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
103 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
110 views

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

I have a fairly complicated function: ...
1
vote
1answer
121 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
155 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
237 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
221 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 Interval[{-2,2}]....
1
vote
1answer
94 views

Symbolic Integration gives wrong answer [closed]

I have tried to integrate the following expression in Mathematica 10.1 ...
4
votes
3answers
149 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
190 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
360 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
73 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
171 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] I'...
1
vote
0answers
60 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
136 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
219 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
259 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
117 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
94 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
98 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 $u(x)\in\mathcal{S}(\mathbb{R}^...
0
votes
1answer
127 views

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

I'm trying to integrate this function by Mathematica ...