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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4
votes
1answer
91 views

Writing a function that finds the difference between two maxima

Suppose i have two functions: $\qquad -2x^2 +5x+3$ and $\qquad -5x^2 +2x+3$ To solve the point where the functions are at maximum i use the command NMaximize ...
4
votes
1answer
127 views

Jackson Integral

Following an old post, I have tried to make a function that calculates the Jackson integral of $q$-calculus: ...
3
votes
2answers
153 views

Computing a binomial series

How can I compute the following series: Module[{n = 10^6}, Sqrt[n] * (4^-n) * NSum[Binomial[2*n - 1, n - k]/((2 k - 1)^2 + Pi^2), {k, 1, n}]] including ...
1
vote
1answer
59 views

Total and partial derivatives [closed]

The following piece of Mathematica code calculates the total derivative of a function $f(x,y(x))$ and compares it with what it should be. However, the result is not zero: ...
0
votes
0answers
57 views

Integrate an expression and simplify the result

I have to find the indefinite integral of the following: $$\int\sqrt{ax^4 + bx^3 + cx^2 + dx + e} dx$$ where a, b, c, d, e are constant of the order 0.0001 or less but always greater than 0. I ...
0
votes
0answers
65 views

Switching from Integrate to NIntegrate

I'm trying to decrease the amount of time that it takes to run the following code: ...
1
vote
3answers
60 views

A function calculating a multiple integral and taking multiplicity as a parameter

I have a function of the following form: $$ \varphi_n(x)= \underbrace{\int\limits_\mathbb{R}\ldots\int\limits_\mathbb{R}}_{n}\exp\left[-\sum\limits_{j=2}^{n}\left(x_{j}-x_{j-1}\right)^2-(x-x_{n})^2\...
10
votes
3answers
472 views

Maximize violating constraints

I have Maximize[{(h*10)/(300*(100 - (l^.5 + d^.4 + H^.6))), (l + d + H + h) == 669, l > 0, d > 0, H > 0, h > 0}, {h, l, d, H}] I believe ...
0
votes
0answers
77 views

Setting up and solving an equation

I would like to solve the equations: $$ F(\xi;x,t)=\int_0^\xi u_{0}(\xi)\:d\xi+\frac{(x-\xi)^{2}}{2t} $$ to use in evaluating: $$ u(x,t)=\dfrac{\int_{-\infty}^\infty \dfrac{x-\xi}{t} e^{-1/2ReF}d\xi}...
3
votes
1answer
57 views

Integrating a gradient and matching terms automatically

I am trying to integrate a function $\nabla w(x,y)$ indefinitely knowing both components of $\nabla w(x,y)$. I have a function dw[x_,y_] that I have defined. I then ...
1
vote
2answers
137 views

How to do this integral? [closed]

Is there any workaround to do this integral? Integrate[(x^2+2 x+1+(3 x+1) Sqrt[x+Log[x]])/(x Sqrt[x+Log[x]] (x+Sqrt[x+Log[x]])),x]
0
votes
0answers
33 views

How can I get left-sided-sequence with InverseZTransform

InverseZTransform[z^2/((4 - z)*(z - 1/4)), z, n, Assumptions -> {1/4 < Abs[z] < 4}] (* -(1/15) 4^-n (-1 + 16^(1 + n)) *) the result is not true.It only ...
1
vote
1answer
119 views

Summing infinite series that converge only for some parameter values

The input Sum[d^t,{t,0,Infinity}] produces output 1/(1-d) which is correct for $|d|<1$. But for $|d|\geq1$ the sum does ...
1
vote
1answer
32 views

Mathematica Integral[] return [closed]

I am new to mathematica and while trying to find the double integral of 8-xy over -2 ...
0
votes
2answers
89 views

Expression of an integral

I am doing the following integral in Mathematica with $a>0$: $$\iint e^{-\frac{(x_{1}+x_{2}-2b)^2}{4a}}dx_{1}dx_{2}$$ My code is ...
0
votes
0answers
187 views

Implicit hidden assumptions of Mathematica with Limit

I've stumbled upon the following symbolic limit (a tricky one): Limit[(Sqrt[2] v)/Sqrt[v^2 - c^2 (1 - 1/c Sqrt[c^2 - v^2])], v -> 0] Mathematica gives 0 as ...
23
votes
5answers
6k views

How can I differentiate numerically?

Mathematica has two ways to integrate: Integrate and NIntegrate. But what about D? ...
2
votes
1answer
88 views

Getting wrong result when Integrating under an assumption [duplicate]

The simple integral $$\int_0^b \cos\left(\frac{2\pi m(y-\eta)}{b}\right) \cos\left(\frac{2\pi \eta}{b}\right)\mathrm{d}\eta$$ can be easily evaluated by Mathematica as, ...
0
votes
0answers
53 views

Using DeleteCases to ignore term of Product

I'd like to calculate $\int_{-\infty}^{\infty}\mathrm{d}x/(1+x^6)$ through a variation of the residue formula, which is $\int_{-\infty}^{\infty}f(x)\mathrm{d}x=2\pi i\sum \text{Res }f$ for Residues in ...
3
votes
1answer
103 views

Indefinite integral of nested trig functions [closed]

I tried vainly to integrate nested trig functions like Integrate[Sin[Cos[x]], x] Mathematica does not find a solution. At first I thought there was no solution, ...
19
votes
3answers
2k views

How to deal with complicated Gaussian integrals in Mathematica?

As we know, for most Gaussian integrals, we can get the analytical result. Now I have many Gaussian integrals to treat, which have the following general form, ...
0
votes
0answers
48 views

Problem with indefinite integral [closed]

How do I calculate this integral with mathmatica? integrate[(Exp[-x/a]Exp[-p x/a])/(x^2 (1-(a/t)^2 Exp[-2 x/a])^(1/2)),x] a, p, t are constants
0
votes
2answers
175 views

How can I solve this integral analytically?

I want to solve the following integral: Integrate[( E^(-ω/Λ) Sin[((ω + Ω) t)/2] Sin[(ω t)/ 2])/((ω + Ω)/4) , {ω, 0, ∞}] But unfortunately Mathematica cannot ...
-2
votes
1answer
55 views

Finding unit vectors which makes an angle 60 degrees with both {1, -1, 0} and {1, 0, -1} [closed]

Find unit vectors which makes an angle 60 degrees with both vectors {1, -1, 0} and {1, 0, -1}.
40
votes
2answers
761 views

Why does Mathematica report that $\int_1^\infty\frac{\sin(\sqrt{x})}{\sqrt{x}}dx$ = $2\cos(1)$?

Bug introduced in 7.0 or earlier and persisting through 10.4 or later Mathematica 10 gives the following very odd result, ...
6
votes
1answer
98 views

How correctly use WhenEvent to detect when gradient is over a certain value?

So I wish to stop integrating my PDE when the spatial gradient is larger than some value, let's say 10. That is to say, my WhenEvent condition wants to be stop when the the maximum gradient over all x ...
0
votes
1answer
56 views

Evaluate as much of an integral as possible [closed]

Consider the integrand $\qquad \cos(x+\sin^{-1}(x)) = \sqrt{1-x^2} \cos(x) - x \sin(x)$ If I ask Mathematica to integrate $\cos(x+\sin^{-1}(x))$, Mathematica is unable to do so analytically (due to ...
4
votes
3answers
260 views

How can I plot a paraboloid?

How do I plot a function for a paraboloid? Im putting together surfaces to model lipstick. I need the paraboloid for the top part and then I'll be cutting the paraboloid at angle with another surface. ...
3
votes
2answers
106 views

Correct behavior of Integrate involving logarithmic cut, or possible bug?

I just discovered that Integrate with simple poles in its integrand sometimes gives different results depending on number type of its limit (Exact vs Inexact). <...
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 ...
16
votes
1answer
278 views

Integrate returns imaginary answer for smooth, real function

Bug introduced in 7 or earlier and persisting through 10.4 I'm trying to evaluate the integral: $$\int_0^{\infty} \frac{1}{4 b \sqrt{\pi} r} e^{-(b-r)^2}(e^{4 b r} - 1) \mathrm{d}r$$ with $b>0$...
5
votes
2answers
231 views

RegionPlot of ImplicitRegion is incorrect

Bug fixed in 10.4. Why does RegionPlot of the ImplicitRegion give an incorrect plot? Also, will how does this affect ...
7
votes
3answers
366 views

Where did I go wrong with my implementation of the trapezoidal rule?

One method for doing quadrature, called the trapezoidal rule, improves accuracy by connecting the points on the curve corresponding to the points of subdivision with line segments, forming trapezoidal ...
2
votes
0answers
96 views

How to Mellin transform a complicated Log integrand?

I got a question concerning an integral. I need to know the analytical expression. I have to Mellin transforn a function and the integral is then sth. like this: $$ \int x^{N-1} \frac{Ln(a -x)}{1-x} ...
3
votes
1answer
65 views

Evaluating function

I'm trying to evaluate this function, which is gradient of integral with variable limit of integration: $$ u(x,y,t)=\nabla(\int_{v(x,y)}^\infty \frac{e^{-b(t-\tau-c)^2}}{\sqrt{\tau^2-{v(x,y)}^2}} d\...
1
vote
1answer
106 views

Asymptotics of sum of binomials

I would like to find the asymptotics of Sum[Binomial[n,i]*1/i^((n+1)/2),{i,1,n}] I saw Find asymptotics of Sum[2^i*Binomial[n-i-1,2*n/3-1],{i,0,n/3}] but I can'...
23
votes
2answers
557 views

Symbolic derivatives are being calculated numerically

Just found the following while debugging a problem. Mathematica is calculating the derivative of IntegerPart[x] in some odd way: ...
0
votes
1answer
43 views

Limits at infinity not neglecting added constants [closed]

This is such a simple question that I'm sure it must be answered somewhere, but I haven't had any luck finding an answer. I am trying to simplify expressions of the form: $$f(x) = A\left(\frac{1+e^{x}}...
1
vote
1answer
77 views

How to calculate the derivative at a point of a non-integrable multivariable function?

I want to integrate this function with respect to θ1 and then take the derivative of that function with respect to n. Since the ...
3
votes
2answers
218 views

Use Meijer-G function to represent elementary functions

I want to represent these elementary functions: $x^{2}\sqrt{x}$, $\sin{4x}$, and $x\ln{x}$ as cases of MeijerG. What arguments should I give to ...
1
vote
1answer
72 views

The assumption in integration does not work?

I am new to mathematica. Here is the question. I try to do the following integration with the assumption that k1<0, k2<0 and k1,k2 are real number. However, the result includes \sqrt{k1}? ...
1
vote
1answer
230 views

Derivative of a symbolic matrix

I need to write an elasticity equations as: {{a*∂/∂x,b*∂/∂y},{c*∂/∂x,d*∂/∂y},{e*∂/∂y,f*∂/∂x}}.{{u},{v}} where a,b,...,f are ...
0
votes
1answer
59 views

Same integral gives different results with assumption

b = 1 k = 12560 r = 500 res = Integrate[Exp[I*k*x*Sin[o]]/(r + x*Sin[o]), {x, -b/2, b/2}] resab = Abs[res]^2 Plot[resab, {o, -Pi/20, Pi/20}, PlotRange -> Full] ...
0
votes
0answers
79 views

How to evaluate this integral

I am trying to evaluate the following integral in Mathematica: ...
2
votes
1answer
83 views

How to plot linear term of a function expanded by Taylor seires in Mathematica?

I am quite new in Mathematica and I am trying to plot a linear term of a particular function in Mathematica. I have tried something like this: ...
1
vote
2answers
74 views

Problems in animating graphs and its extrema

I tested to animate 2D graph and its extrema for simple case using Mathematica. ...
7
votes
2answers
430 views

Need help with the Lagrange multiplier method

Well I am new to Mathematica and got really stuck solving this problem. In class, I was ask to use the Lagrange multiplier method to find the maximum and minimum value of $f(x,y) = x^2+y^2$ which ...
0
votes
2answers
105 views

Using Mathematica to find the areas described by polar curves

I am working on a project and I need to find the area of the surface inside the polar-curve $r=2\cos(\theta)$ and outside the polar-curve $r=1$. The graph is pretty straightforward: just two ...
4
votes
2answers
351 views