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
104 views

Derivative in function form

I have a function in mathematica defined as b[n_, x_] := x^n/n!/\!\(\*UnderoverscriptBox[\(\[Sum]\), \(k = n\), \(\[Infinity]\)]\*FractionBox[\(x^k\), \(k!\)]\) ...
2
votes
1answer
492 views

Using Integrate to define a function

I'd like to define a function by way of the output of a definite integral with symbolic bounds. For instance, F[m_,k_] := Integrate[x,{x,m,k}] would define ...
1
vote
1answer
122 views

Tough Calculation, novice mathematica user

I have an equation, that I've been calling $b_N(x)$ that satisfies the following identity: $$-Nb_N(x)^2=(x-N)b_N(x)+xb_N'(x)$$ where $b_N'(x)$ is the first derivative. I take the derivative then of ...
0
votes
1answer
103 views

Multidimensional NIntegrate problem of the function decaying as 1/x^2

The function I am trying to integrate is more complicated but I can simply write the function as (I had made a typo error, sorry. The '+' sign in front of the r should be '-'): $f(\omega ) = \int ...
0
votes
1answer
363 views

Integrating elements from matrix

oI'm kinda new at using Mathematica. What I'm trying to do is create a matrix with elements inside. ...
21
votes
2answers
322 views

Backslide of Limit

A friend of mine showed me this example: Limit[Sum[Sin[Pi*k/n]/(n + 1/k), {k, 1, n}], n -> Infinity] This sample calculates well in v8.0.4: but not in ...
1
vote
1answer
149 views

Why Abs[Infinity] is an element of the real numbers

Element[Abs[Infinity], Complexes] returns False, that's right. But ...
2
votes
2answers
532 views

Using RegionPlot3D to make a cone under restrictions

I have to plot a cone that satisfies this statement: Use the RegionPlot3D command to draw a picture of a cone with its point at the origin. The other end of the cone is a circle with radius 5 ...
6
votes
3answers
354 views

How to do algebra on unevaluated integrals?

I am working with functions calculated from a set of general basis functions. ...
4
votes
1answer
432 views

Problem on limit involving complex numbers

I have $${\frac{(6 k+1)^{k}}{(2 k+5)^{k}}}*(z-2 i)^k$$ and I need to find it's limit for $k$ approaching infinity. ...
14
votes
1answer
273 views

Why do big-O terms disappear in definite integrals since Mathematica 9?

In Mathematica 8, when I computed the following input: Integrate[Series[Cos[x], {x, 0, 2}], {x, 0, a}] Mathematica returned an expression that had a O[a^4] in ...
2
votes
0answers
77 views

Order of integration resolves “Indeterminate expression encountered.”

Bug introduced in 10.0.0 and fixed in 10.0.1 Today I came across the following integral: ...
1
vote
2answers
188 views

Integration over a (non-parametric) curve defined by indicator function

I want to integrate the real function myFun defined on a 2D plane over the line locus, defined as the solution of a set of ...
2
votes
1answer
149 views

How can I simplify this implicit equation to an explicit equation

How can I simplify this implicit equation to an explicit equation: Tan[5 y/12] - (7 y/((x)^2 + (y)^2 - (3.5)^2)) == 0 i.e: $y=f(x)$ where $y$ is a explicit ...
5
votes
2answers
208 views

Unexpected Integration Constant [closed]

Why does this integration Integrate[15-30x+6x^2-1/(x+5),x] return 700 as integration constant? If we make a slight modification ...
4
votes
1answer
296 views

Derivatives of functions with arbitrary number of variables?

I am trying to define a function f[x1,x2,...,xn] with n integer but not specified. And then I would like this funktion to behave ...
5
votes
2answers
254 views

Limit not giving expected result

I am taking the limit Limit[Sin[π Sqrt[4 n^2 + n]], n -> ∞] the returned answer is Interval[{-1, 1}] I think the right ...
3
votes
1answer
196 views

Problem with series expansion and integrate

I have the following very simple code. A power series in a-parameter, function f[x], is integrated with respect to x, and the ...
3
votes
1answer
120 views

Strange integration

Bug introduced in 9.0 or earlier and fixed in 10.1 Note: Beginning with V10.1, this integral returns unevaluated but without error messages. I tried to evaluate this line ...
1
vote
0answers
91 views

Can NIntegrate be used with the Levin method in several dimensions?

I've got some data in the form of an interpolating function. It's a function of three variables, $\rho(x,y,z)$. I'd basically like to integrate this with some phase over a cube of known size, like $$ ...
0
votes
1answer
97 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
609 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: ...
5
votes
1answer
306 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): ...
4
votes
0answers
87 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 ...
1
vote
2answers
137 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
60 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: ...
1
vote
1answer
223 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 ; ...
10
votes
4answers
437 views

Mathematica complaints that convergent integral diverges

Bug introduced in 10.0 and fixed in 10.0.2 Trying to do the integral ...
2
votes
0answers
190 views

Mathematica not evaluating q derivative of Jacobi theta function

Jacobi theta functions, $\theta_a(u,q)$ for $a=1,2,3,4$ are defined in the unit disk $|q|<1$. For some reason that I would like to understand, Mathematica does not evaluate numerically the $q$ ...
3
votes
3answers
202 views

Factoring a scalar function out of a vector

I've taken a first and second derivative: ...
2
votes
1answer
235 views

Definite Integral over Bessel Function

Hello I am interested in evaluating the following integral. ...
10
votes
2answers
260 views

Mathematica integration failure - new or old?

Bug introduced in 7.0.1 or earlier, persists through 10.1 Consider the following integral: Integrate[Log[a Cos[x]^2 + b Sin[x]^2], {x, 0, 2Pi}] This takes a ...
2
votes
2answers
513 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: ...
8
votes
3answers
622 views

Biot-Savart Law/Magnetostatics Solution

I am working on solving the Biot-Savart Law equation for the magnetic field around a charged ring of uniform current density. The expression that Mathematica gives is rather nasty, as expected. Notice ...
7
votes
5answers
2k 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. ...
3
votes
1answer
1k 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 ...
1
vote
1answer
63 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. ...
10
votes
2answers
501 views

Interpolating an Antiderivative

I'd like to be able to make InterpolatingFunctions for antiderivatives of functions that can't be integrated symbolically. However, the following code returns ...
1
vote
2answers
64 views

Convergence problem when I try to integrate a function of one variable and one symbolic parameter

I have an integral with a parameter a and a > 0 ...
2
votes
1answer
193 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
618 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?
10
votes
3answers
460 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 ...
1
vote
2answers
270 views

Integrating Squared of Interpolating Function with respect to one variable

I am interested in evaluating a two dimensional interpolating function produced by solving the wave equation. Here is the code that includes the resulting interpolating function. ...
4
votes
0answers
238 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 ...
6
votes
2answers
396 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
54 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) ...
5
votes
1answer
253 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 $a$ : $a=0.5$ , ...
2
votes
2answers
193 views

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

I'm trying to solve this integral: $I(a,b)=\displaystyle{\int_1^{\infty }\dfrac{e^{-ax}}{\sqrt{x^2-1} (1+x\sqrt{1-b^2}) (x-1/\sqrt{1-b^2})} \, dx} \,\, \,\,(a \;\textrm{real>0} \, , 0<b<1)$ ...
3
votes
3answers
185 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. ...
26
votes
3answers
855 views

Symbolic integration error

fixed in 10.1 (windows) I'm running Mathematica 10.0.0 and encountered a disturbing error in the symbolic integration of a rather simple function ...