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
1answer
91 views

How should i correct this error?

Sn = Sum[1/((k + 1)^2), {k, 1, n}] SSn = Sum[Sn*Fibonacci[n], {n, 0, m}] Limit[(1/(Fibonacci[m + 2] - 1))*SSn, m -> Infinity] Limit::ztest1: Unable to ...
7
votes
1answer
329 views

How to code around known MMa special-case failures?

Fourier Analysis and Signal Processing often require these integrals on functions f[x] that won't be known in advance. ...
1
vote
1answer
104 views

How to rotate vectors in vector plot?

I'm writing an exam for my calculus students and am seeking help with using Mathematica on a particular problem. Here's my idea: I want to give a multiple choice problem that has four choices of ...
0
votes
0answers
106 views

Boundary value problem: complicated functionals

I am trying to solve a non-linear boundary value problem where the differential equation is a convoluted function of the variable I am trying to solve for. I have attached the code defining the ...
4
votes
1answer
271 views

How to solve this Integral equation

D[x[t] - x[t - 1]/(2 E), {t, 3}] + Integrate[E^(-δ)*x[t - δ]/5^t, {δ, 2, 2.5}] == 0 I found solve this problem is hard with Mathematica. I also find a article ...
-4
votes
1answer
49 views

How to Integrate [duplicate]

I have the following Table ...
-2
votes
1answer
126 views

How to integrate a table? [closed]

I have the following Table (dy/dx)={24,24.5,25,25.4} How do I proceed to interpolate the table and compute Integrate[Sqrt[1+(dy/dx)^2],{x,65,68}] ?
1
vote
2answers
85 views

Integrate full derivative

I want mathematica to do Integrate[D[f[x],x], {x,0,t}] and achieve the answer f[t]-f[0]. But Mathematica doesn't intergrate ...
5
votes
2answers
179 views

Multidimensional integral to compute the end-to-end distribution of a FENE ideal chain

How do I evaluate the mean end-to-end squared distance of a FENE ideal chain at fixed inverse temperature $\beta$ in the canonical ensemble? This quantity is defined as the mean value ...
2
votes
1answer
79 views

How to define the symbolic expression $V = \frac{1}{N} \sum_{i=1}^N ( y_i(g) - z_i)^2$ in Mathematica?

I want to define this expression symbolically: $V = \frac{1}{N} \sum_{i=1}^N ( y_i(g) - z_i)^2$ in which $\{y_i(g)\}_{i=1}^N$ is to be understood as a symbolic sequence that depends on a vector $g$. ...
1
vote
0answers
81 views

Derivative with respect to a tensor

I am trying to differentiate a tensor with respect to another one in Mathematica, but I can't do it. Down below is the code I am using: ...
2
votes
2answers
155 views

Calculating a Volume Integral limited by two z planes and a given conical surface [closed]

I have been given this question to integrate a function over a region, and I have been at it for 6 days now and I can not for the life of me come up with a solution because the integral is way too ...
1
vote
0answers
109 views

Where can I learn to use mathematica comprehensively? [duplicate]

I've heard great things about all the wonders and capabilities of mathematica. I've had the software for sometime now, but all I know how to do are simple calculations and stuff shown in the hands on ...
4
votes
2answers
227 views

How to force correct answers for Integrals of Cos[mx]*Cos[nx]? [duplicate]

This is a big problem if you do anything with a Fourier Series. This statement: Assuming[Element[{m, n}, Integers], Integrate[Cos[m*x]*Cos[n*x], {x, 0, 2 Pi}]] ...
7
votes
3answers
330 views

Negative integral of a positive function

fixed in 10.1 (windows) For a parameter $t\in (0,1)$ $Assumptions = t ∈ Reals && t > 0 && t < 1 I define an obviously positive function ...
2
votes
1answer
114 views

How to get a more compact form of this probability calculation?

Inspired by the probability calculation here, I am trying to solve a little general one: $$\mathbb{P} (\sum_{i=1}^{m-1} A_i + \sum_{i=1}^{m} S_i < L < \sum_{i=1}^{m} A_i + \sum_{i=1}^{m+1} ...
0
votes
0answers
45 views

Find the maximum/ minimum of the function f(x,y,z) = x+2y+3z on the curve of intersection of the plane x-y+z = 1 and the cylinder x^2+y^2 = 1 [duplicate]

How to write the program for: Find the maximum/ minimum of the function f(x,y,z) = x+2y+3z on the curve of intersection of the plane ...
0
votes
2answers
59 views

How to calculate improper integral [closed]

Hello, How to calculate the "r" (limit) of this improper integral ?
5
votes
1answer
263 views

How can I Integrate large trigonometric expressions more efficiently?

I have a requirement to integrate some large symbolic expressions containing products of trigonometric functions. A single integration is averaging 7 minutes, and I have 2628 expressions to integrate, ...
3
votes
1answer
77 views

Integrate[] does not work when the function has an antiderivative function

This function (1 + (1 + 1/(2*Sqrt[x]))/(2*Sqrt[Sqrt[x] + x]))/(2*Sqrt[x + Sqrt[Sqrt[x] + x]]) has the antiderivative function, since ...
0
votes
1answer
68 views

Computing a binomial series

I have a simple question: how to compute the following series? Sqrt[1000000]/4^1000000 NSum[Binomial[2*1000000 - 1, 1000000 - k]/((2 k - 1)^2 + Pi^2), {k, 1, ...
1
vote
0answers
60 views

MacDonald formula for Modified Bessel Functions

Mathematica seems to not know these two integrals: $$\int_0^{\infty} e^{-x \cosh{\xi}} d\xi = K_0(x)$$ $$\int_0^{\infty} e^{-\frac{1}{2} \Big( \frac{x y}{u} + u \frac{x^2+y^2}{x y} \Big) } K_{i t}(u) ...
6
votes
1answer
331 views

How to solve this probability symbolically or numerically?

I am trying to calculate the following probability $$\mathbb{P} \big(\sum_{i=1}^{m} (A_i + S_i) \le L < \sum_{i=1}^{m+1} (A_i + S_i) \big)$$ where, $$A_i \sim \exp(\lambda), \quad S_i \sim ...
4
votes
4answers
686 views

Visualizing Line Integrals

I have a plane curve $C$ described by parametric equations $x(t)$ and $y(t)$ and a function $f: \mathbb{R}^2 \rightarrow \mathbb{R}$. The line integral of $f$ along $C$ is the area of the "fence" ...
1
vote
0answers
70 views

integral with Re[] function, need help [closed]

I tried to compute with Wolfram Mathematica the following integral The code is ...
0
votes
2answers
134 views

How to help MMA to simplify integrands?

MMA sometimes has to grind for LONG time on easy integrals: ...
0
votes
0answers
66 views

Can Mathematica do this integral over $\mathbb{R}^n$?

I have the following function: $$\phi_{k,n,r}: \mathbb{R}^n \rightarrow \mathbb{R}, (x_1,…,x_n)\mapsto (1-r^{n-k}e^{\sum_{i<k}x_i})e^{\sum_{i<j}x_i-x_j}e^{(2-n)\sum_i x_i}$$. Is there any way ...
5
votes
2answers
709 views

Mathematica 10 cannot solve definite integral

Bug introduced in 10.0.0, solved in 10.0.2 Mathematica 10 fails to solve the following integral, saying that it does not converge. ...
4
votes
1answer
397 views

Integrate over piecewise function defined using /;

f[x_] := x /; x<0 f[x_] := x^2 /; x>=0 Integrate[f[x],{x,-1,1}] The above does not work (Mathematica returns it unevaluated), but the below does. ...
3
votes
2answers
337 views

How to numerically integrate this integral

I am unable to do this definite integral in Mathematica 9. Is there any command so that I can get the numerical value of the above integration? Code: ...
0
votes
2answers
80 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
115 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 ...
0
votes
1answer
114 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
83 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
93 views

Negative Infinity limit [closed]

As a beginner I am trying various functions of mathematica to practice. I am at the limit function. I am trying this ...
0
votes
1answer
196 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
284 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
105 views

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

Element[Abs[Infinity], Complexes] returns False, that's right. But ...
2
votes
2answers
252 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 ...
2
votes
1answer
102 views

Hilbert transform of density of states [closed]

I am trying to evaluate analytical integration over density of states, for example G(Z)=int[f(x)/z-x,{x,x1,x2}] , where ...
4
votes
1answer
302 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
259 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
67 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
141 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 ...
1
vote
1answer
100 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
190 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 ...
3
votes
1answer
169 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 ...
0
votes
0answers
107 views

Mathematica Integrate implicit assumptions returns a function not defined in some points while NIntegrate performs integration safely

Hi guys i'm performing a standard integration with mathematica routine Integrate, the function i'm integrating is the following: ...
2
votes
4answers
203 views

Problem in finding the numerical maximum

I need to find the numerical maxima of the function $$i(s)=\bigg[ \frac{\sin{50\pi (\cos s+1)}}{\sin{10\pi (\cos s+1)}} \bigg] ^2$$ Or in the mathematica input form: ...
5
votes
2answers
235 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 ...