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
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
154 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
46 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
143 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
104 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
122 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
159 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
240 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
223 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
96 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
362 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
179 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
207 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
142 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
226 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
271 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
119 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
99 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
128 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
176 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
126 views

Differentiation help [closed]

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

Integrate does not work on my expression

I am trying to integrate a simple equation. The code is as follows ...
0
votes
1answer
84 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
213 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
350 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
191 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
140 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
311 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
161 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
158 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
59 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
907 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
243 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
86 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
59 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
24 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
113 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 up....
2
votes
1answer
171 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
130 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 ...
7
votes
1answer
211 views

Why should the spatial derivative order of the ODE *not* exceed two?

Following this question I came across this strange behaviour. Let me define a 1 D interval implicitely ...
1
vote
1answer
137 views

How does one verify the derivative of $ f(x) = \sum^{K_2}_{k_2=1} c_{k_2} \exp\left(- \big(a^{(2)} - t^{(2)}_{k_2}\big)^2\right)$

I wanted to verify the derivative of the following equation: $$ f(x) = \sum^{K_2}_{k_2=1} c_{k_2} \exp\left(- \big(a^{(2)} - t^{(2)}_{k_2}\big)^2\right)$$ for that I wanted to write a symbolic ...
1
vote
1answer
72 views

ND and D yielding strange results

Both of the following codes, using ND and D, differentiates my function Flux[] incorrectly. If the derivatives are plotted, it can be seen that both are the original function multiplied by some ...
0
votes
0answers
23 views

Plotting a dispersion curve with complex wavevectors [duplicate]

I want to reproduce a dispersion curve from P. Zou's thesis found here: http://www.ipd.anl.gov/anlpubs/2001/06/39620.pdf on Pg. 31, Eq. 2.13. The problem is, the code below only gives values for the ...
5
votes
3answers
299 views

Extrema of a function of three variables

To identify and classify the critical points of the function $f(x,y,z)=x^3+xz^2-3x^2+y^2+2z^2$, I used the Hessian matrix method. ...