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
63 views

Functions in functions

I have three functions f(x,y) , g(t) , and h(t) and somehow I have to find (d/dt)f(g(t),h(t)) where t = 0. How would I go about writing this in Mathematica? In this equation g(t) is taking place of x ...
1
vote
1answer
67 views

Derivative of an expression containing a symbolic sum [duplicate]

Is there a general pattern for working with symbolic sums in Mathematica? For example here's a derivative I want to compute: ...
0
votes
0answers
27 views

a complicated Sum [migrated]

I don't know how i can calculate this complicated multivariate sum : $$ S(l,k)=\sum_{|m|=k} s_{l,m}=\sum_{|m|=k} l(l-1)(l-2)\dots(l-m+1) $$ Where $m=(m_1,\dots,m_n)$, $l=(l_1,\dots,l_n)$, and $k$ a ...
-1
votes
0answers
33 views

Approach to integration? [on hold]

I write one code such: ...
-1
votes
0answers
41 views

Inverse Laplace with Logaritms [on hold]

I need to find the inverse laplace to this function, I tried to use this fact: But I end in 2 integrals of e^(-kt)/t that aren't convergent. How can I solve this Problem?? Thanks for your help
7
votes
3answers
246 views

Mathematica complaints that convergent integral diverges

Bug introduced in 10.0.0 Trying to do the integral ...
5
votes
0answers
127 views

Integrate wrong for absolute value of trig function

I was trying to get $\int_0^1 \lvert \cos(2 \pi k x) \rvert \,\mathrm{d}x$ for $k \in \mathbb{Z}$, and was surprised by the result (using Mathematica 10.0.1.0): ...
2
votes
2answers
65 views

Providing wrong answer on integral $\int_{-\frac{2}{3}}^{\frac{2}{3}} \left(\text{Ln}\left(\cos ^4(x)\right)+1\right) \, dx$ [closed]

I tried to evaluate the following in mathematica $\int_{-\frac{2}{3}}^{\frac{2}{3}}{1+\ln \left( \cos ^{4}\left( x \right) \right)}dx$ and got the answer as $0.91905 - 3.94746*10^{-16} I$. However, ...
3
votes
0answers
50 views

Integrate yields complex value, while after variable transformation the result is real. Bug?

I have the follwoing integral: Integrate[1/Sqrt[0.7 + 0.3*(1 + z)^3], {z, 0, Infinity}, Assumptions -> z \[Element] Reals] >> -3.36354 - 3.85013 I the ...
0
votes
0answers
22 views

Plot3D and NIntegrate issues

f[x_, y_] := 2*x - y Plot3D[f[x, y], {x, -1*Sqrt[4 - y^2], Sqrt[4 - y^2]}, {y, -2, 2}] NIntegrate[f[x, y], {x, -1*Sqrt[4 - y^2], Sqrt[4 - y^2]}, {y, -2, 2}] I ...
0
votes
2answers
54 views

Taking derivatives

This is my code: X := g[P] P = a*t R = t*X FOC = Dt[R, t] This is what I get for the last line: ...
0
votes
1answer
44 views

How to differentiate an integral on Mathematica?

I am so new on Mathematica. I try to find the first variation of this function according to $t$ on mathematica but I could not achieve. Here is the function ; ...
3
votes
1answer
95 views

Working with abstract vectors

I often need to compute derivatives or integrals involving N-dimensional vectors (where the dimension could be equal to 2 or 3 but is not particularly relevant for the sake of the derivation). The ...
3
votes
1answer
111 views

Contour integration *directly* [duplicate]

The archetype (Just serving the question by being the simplest example): $$\oint_{|z|=1}\frac{dz}{z}=2 \pi i$$ Well known, fundamentally important, easy to prove, famous, wonderful. Yes, I can ask ...
-2
votes
1answer
149 views

Mathematica Giving Me Trouble [closed]

I'm new to mathematica and am just learning the basics. I've run into a few things that I can't figure out. The first is this: "Number 11" ...
3
votes
3answers
128 views

Factoring a scalar function out of a vector

I've taken a first and second derivative: ...
8
votes
1answer
164 views

Mathematica integration failure - new or old?

Bug introduced in 7.0.1 or earlier Consider the following integral: Integrate[Log[a Cos[x]^2 + b Sin[x]^2], {x, 0, 2Pi}] This takes a LONG time (this is ...
0
votes
1answer
90 views

Integration of linked PDFs over probability simplex

I'm trying to integrate the following expression: f[a1,p1+p2+p3+p4]*f[a2,p2+p3+p4]*f[a3,p3+p4]*f[a4,p4] Where ...
0
votes
0answers
86 views

How do I select terms by derivative order for integration by parts?

I am trying to calculate derivatives of an integral wrt parameters of the integrand. ...
6
votes
5answers
369 views

Find function inverse

I'm trying to find the inverse of a function: (30*x^2 (1 - x)^2) (* where 0<x<1 *) I tried all the following options: 1. ...
0
votes
1answer
168 views

Is this function convex?

How can I determine convexity of the function f = Log[ x, 1 + (x^a - 1) (x^b - 1)/(x - 1)] with the parameters $a,\,b$ belonging to the interval $(0,1)$ in ...
2
votes
2answers
718 views

About generating power series

For an arbitrary function $f(x,y)$ I am defining functions LogMT1 and LogMT2 as follows, ...
0
votes
3answers
279 views

Solving an Integral Numerically

I have been trying to solve the integral equation below, but cant seem to find a way out of this. Can someone please help me out with suggestion? $f(t)=\int_0^{\infty}\frac{K_1a(t)}{a(t)+K_2}\,dt$ ...
2
votes
2answers
77 views

Integration of piecewise function

I'm trying to understand why Mathematica is not evaluating a piecewise function, while it's able to evaluate each of the regions separately. This fails: ...
2
votes
1answer
116 views

How to solve time dependent Optical Bloch Equations for a three level system?

I am trying to solve the optical block equations for three level system which are time dependent, which i generated using the "Atomic Density Matrix" package. When i use the command to solve this 9 ...
0
votes
0answers
9 views

Cauchy sequences, not converging to zero [migrated]

True or False? If {x_n} and {y_n} are Cauchy and x_n + y_n > 0, for all natural n, then {1/(x_n + y_n)} cannot converge to zero. attempt:False: If both sequences are Cauchy, then they are convergent ...
27
votes
6answers
1k views

Finding length of intersection of two surfaces

I would like to know how we find the length of the intersection of two surfaces. For instance, in the following example,a surface intersects with a plane: How do we find the length of intersection ...
1
vote
1answer
36 views

NMaximize not substutiting parameters of objective function [duplicate]

NMaximize is not substituting parameters of its objective function. Is there a way to fix that? I have a three line program that exhibits the problem. ...
2
votes
1answer
116 views

Double integral changing the limits

This integral does not evaluate: Integrate[ Integrate[1/(E^((a - c)^2 + (b - c)^2) ), {c, 0, 1}], {b, -Infinity, Infinity}] However, reversing the integrals ...
0
votes
3answers
61 views

Is there a way to rewrite integrals in Mathematica using u substitution?

In Mathematica, can I give it an integral and a few substitution rules and have it rewrite the integral in terms of those variables?
1
vote
2answers
59 views
4
votes
0answers
156 views

Strange behaviour of MMA in derivatives of some standard functions

There are some peculiar things to be discovered in derivatives of some standard functions in MMA: Strange behaviour Example 1: Abs We have ...
8
votes
3answers
314 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 ...
5
votes
2answers
172 views

Is there a built-in function which detects singularities in a function?

Given a function f[x] and a region M in the complex x-plane, how can I find singularities of f in this region, i.e., issue a ...
0
votes
0answers
35 views

Custom simplification of symbolic definite integral with regards to bounds

I would like to rewrite symbolic definite integrals such that the bounds are always positive. For example : $\int_{-\infty}^\infty f(x) \mathrm{d} x \rightarrow \int_0^\infty \left[ f(x) + f(-x) ...
3
votes
1answer
136 views

How to plot the result of this singular integral?

Please I open a new post here after this one : http://mathematica.stackexchange.com/a/59203/10158 Now I want to plot the function $f(a,b)$ as a function of $b$ for different values of $a$ : $a=0.5$ , ...
1
vote
2answers
122 views

How to calculate the analytical result of this singular integral? [duplicate]

I'm trying to solve this integral: $I(a,b)=\displaystyle{\int_1^{\infty }\dfrac{e^{-ax}}{\sqrt{x^2-1} (1+x\sqrt{1-b^2}) (x-1/\sqrt{1-b^2})} \, dx} \,\, \,\,(a \;\textrm{real>0} \, , 0<b<1)$ ...
1
vote
3answers
122 views

When NSolve fails due to a differential situation?

c = 1.1111; y[x_] = x - c Sin[x] NSolve[y[x] == 0, x] The method has procured no result. Successive derivatives were plotted in an attempt to fix the problem. ...
0
votes
1answer
94 views

Solving Coulomb Integral [closed]

I am trying to solve so-called Coulomb Integral of two Gaussians: ...
1
vote
0answers
95 views
4
votes
1answer
92 views

Efficient Dyson series implementation

I'm trying to implement a Dyson series \begin{array}{lcl} U(x,x_0) & = & 1 + \int_{x_0}^{x}{dy_1V(y_1)}+\int_{x_0}^x{dy_1\int_{x_0}^{y_1}{dy_2V(y_1)V(y_2)}}+\cdots \\ & &{} + ...
7
votes
6answers
810 views

Trying to prove that $x\sin(\frac{\pi}{x})\ge\pi \cos(\frac{\pi}{x})$ for $x\ge 1$

Consider the function f[x_] := x Sin[Pi/x] I want to prove that this function is increasing for $x\ge 1$. This can be done with the first derivative. We have to ...
1
vote
1answer
38 views

Specifying independence of a variable in a function

I am dealing with a function of a finite number of variables and among the operations I wish to do is to differentiate it repeatedly with respect with any of the variables. Now this function happens ...
5
votes
1answer
183 views

How to find this limit correctly?

How to find the limit Limit[n*Sin[2*Pi*Exp[1]*n!], n -> Infinity] ? Mathematica 10 outputs ...
6
votes
1answer
207 views

Integral of x^p

Can anyone explain why Mathematica does not return a conditional expression that handles the case of p=-1 for Integrate[x^p,x]? ...
0
votes
1answer
82 views

Sum rule in integration not working [duplicate]

I am new to Mathematica and I just tried to play around with some integrals. But the sum rule in integration doesn't work. Here a simple example: Mathematica doesn't recognize that $\int_0^h (1-f(x)) ...
7
votes
2answers
274 views

How to simplify the integration result of the following program?

In the following program, the fec[x] is a function depending on $x$ while q3[t] and q5[t] ...
8
votes
3answers
1k views

how to simplify symbolic integration

The following is the code: ...
2
votes
1answer
88 views

Finding a root of a parameterized integral

I have a function given as a parameterized definite integral: f[a_] := Integrate[BesselJ[0, x - a] BesselJ[0, x + a], {x, -∞, ∞}] I suspect it has a root near ...