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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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
87 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: ...
3
votes
2answers
156 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
118 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 ...
-2
votes
1answer
123 views

Power series graphs?

I would like to graph this function and its first 6 Taylor polynomials on the same axis, but I'm not sure how to start: f[x_] = Exp[x]; Plot[f[x], {x, 0, 1}]
4
votes
2answers
233 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
333 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
272 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
78 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 ...
1
vote
1answer
84 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 ...
3
votes
0answers
80 views

MacDonald formula for Modified Bessel Functions

How can I make Mathematica understand 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) } ...
6
votes
1answer
335 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
695 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
137 views

How to help MMA to simplify integrands?

MMA sometimes has to grind for LONG time on easy integrals: ...
-1
votes
3answers
249 views

Defining an alternative derivative function?

I want to calculate the derivative at a point, but I do not want to use the built-in derivative function D. I began with this definition of the derivative , ...
0
votes
0answers
73 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 ...
7
votes
2answers
774 views

Mathematica 10 cannot solve definite integral [duplicate]

Bug introduced in 10.0 and fixed in 10.0.2 Mathematica 10 fails to solve the following integral, saying that it does not converge. ...
4
votes
1answer
410 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
354 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
81 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
133 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
115 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
84 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
101 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
207 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
287 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
107 views

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

Element[Abs[Infinity], Complexes] returns False, that's right. But ...
2
votes
2answers
270 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
104 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
3answers
278 views

How to do algebra on unevaluated integrals?

I am working with functions calculated from a set of general basis functions. ...
4
votes
1answer
319 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
262 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
70 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
148 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
104 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
194 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
197 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
111 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
210 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
237 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
140 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
109 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
61 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
93 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
269 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
0answers
228 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): ...