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

Divergent integral error

I'm integrating a product of two functions which is bounded on the interval from -Inf to 0, and diverges from 0 to +Inf. The error that I get says that the integral diverges on {0,+Inf}... How did ...
6
votes
1answer
105 views

Why is RegionMeasure so slow when calculating intersection area of a 2D and a 3D object?

If you think this description is too long, you can read the problem directly I know normally when one wants to calculate an region, this guide is useful. However, when it comes to calculating an ...
1
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0answers
47 views

Partial Derivative of f with respect to x1 [duplicate]

How can I calculate the partial derivative of a series like e.g. $$ a = \sum _{i=1}^n \left(2 x_i^2+z\right) $$ with respect to $x_{1}, x_{2},... x_{n}$ using Wolfram Mathematica? I tried it with: ...
2
votes
1answer
85 views

Implicit derivatives in one line. How do I do it?

I have this little script to derive implicitly $PrePrint = # /. {D[y_, x_, NonConstants -> {y_}] :> y'[x]} &; Example: ...
10
votes
6answers
738 views

Integrate gives wrong results

Integrate[a/(Sin[t]^2 + a^2), {t, 0, 2 Pi}] $$\int_0^{2 \pi } \frac{a}{a^2+\sin ^2(t)} \, dt$$ gives $0$ This cannot be true. What is going on? If I insert a ...
4
votes
2answers
116 views

Imaginary terms in the derivative of Jacobi theta function (2) on the real line

I am trying to calculate/plot the derivative of the second Jacobi theta function $d\theta_2(0, e^{-\pi t} )/dt$. Calculating or plotting the function itself works fine: ...
3
votes
1answer
75 views

How do I color Riemann integral rectangles using conditionals?

I'm builind a function to visualize the Riemann Integration process to any function using rectangles. Everything is fine, except that I need the color of the rectangles to change if they're under the ...
26
votes
1answer
452 views

Are greek symbols causing different evaluation?

I've updated today to Mathematica 9.0.1.0 from version 8 and found something that absolutely confuses me. Let us define a piecewise function: ...
6
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2answers
212 views

Curvature Application

I found these amazing animations at https://courses.engr.illinois.edu/tam212/avt.xhtml#avt which I think will be wonderfully useful when teaching multivariable calculus next semester. I've started to ...
3
votes
2answers
350 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: ...
6
votes
3answers
195 views

Limit of Nested Radical $\sqrt{1+\sqrt[2!]{2^2+\sqrt[3!]{3^3+…}}}$

I want to find limit of infinite nested radical $\quad \quad \sqrt{1+\sqrt[2!]{2^2+\sqrt[3!]{3^3+...}}}$ but I don't know how to define this expression in Mathematica. How can I define it and ...
5
votes
1answer
261 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 ...
15
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5answers
773 views

How to make a Line[] with no end?

I'm trying to do this: In this graph, the secant points are aproximated in order to become the tangent, it seems I need some kind of function which plots a line based on two points and it's points ...
11
votes
2answers
4k views

Equation of a line that is tangent to a curve at point

A common problem in the derivative section of calculus texts is "find the equation of the line that is tangent to the curve $y = \ldots$ at the point $P$." To find the line that is tangent to $y = 2 ...
1
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2answers
83 views

Ask about the variable and constants in partial derivative in a loop

EDITED I have a function in a list like : func={2(x^2)+x*y+3(y^2)}; I want to have a UI that ask me which parameter (x or y) is a variable in a ...
2
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2answers
127 views

MaxValue of a periodic function

I want to find the maximum of a periodic function on the interval [-Pi,Pi]. What I tried is the following: ...
10
votes
2answers
249 views

Asymptotics of $\frac{\sum _{i=0}^{\lfloor n/2 \rfloor} {2(n-2i) \choose n-2i} {n \choose 2i} {4i \choose 2i}}{2^{3n - 1}}$

I am fairly sure that asymptotically $$\frac{\sum _{i=0}^{\lfloor n/2 \rfloor} {2(n-2i) \choose n-2i} {n \choose 2i} {4i \choose 2i}}{2^{3n - 1}} \sim \frac{2}{\pi n}.$$ I tried ...
4
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3answers
134 views

How to get multiplication of the elements of a specific list/Matrix

Assume there is a list: List1={a,b,c,d}; Then I want to get these calculation: ...
1
vote
2answers
62 views

How to tell Mathematica that a limit converges to a product of two variables

I have looked through the manual and Im simply just stuck trying to make Mathematica solve this: ...
5
votes
1answer
166 views

Confirming conservation laws for complex valued functions

Consider the nonlinear Schrödinger equation (I would like to do this for a more complicated set of equations, but to gain understanding I'll consider this simplified case) $$A_t+iA_{xx}+i|A|^2A =0,$$ ...
2
votes
0answers
87 views

Converting integral equations to differential equations

I am trying to use Mathematica to convert integrals to differential equations, of any order. An example of an integral equation is given below, in Mathematica code. Could you please advise as to the ...
6
votes
1answer
158 views

Defining a function implicitly and calculating its derivatives

I'm interested in using Mathematica's symbolic manipulation to obtain, for a particular function $f$, derivatives of arbitrary order evaluated at zero. Normally I'd use the ...
0
votes
1answer
85 views

FullSimplify not giving me a physically useful answer for Mott scattering

I am using Mathematica to find the cross-section for Mott scattering over an extended target. I evaluated ...
3
votes
3answers
135 views

Calculating $\lim_{x\to 1} \, \int -\frac{i \text{Li}_2\left(x-x^2\right)}{\sqrt{3} \left(x-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)} \, dx$

How can we force Mathematica to compute this limit? $$\lim_{x\to 1} \, \int -\frac{i \text{Li}_2\left(x-x^2\right)}{\sqrt{3} \left(x-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)} \, dx$$ It seems it ...
5
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1answer
207 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
1answer
157 views

Definite Integral over Bessel Function

Hello I am interested in evaluating the following integral. ...
3
votes
1answer
126 views

Why does Mathematica list the variables in a double integral backwards?

I am an advanced novice Mathematica user and have done a fair amount of single-variable calculus things with it. This semester I am using Mathematica for multi-variate calculus and when I tried to ...
0
votes
0answers
47 views

Bounds of a closed curve

how to find the rectangular bounds of a curve which is of the form f(x,y) and forms a closed loop. The sides of the rectangle are parallel to the axes and are tangents to the curve. The time taken for ...
6
votes
1answer
534 views

Integrating over Bessel Function erroreous? (Hankel Transform)

Bug introduced in 8.0.4 or earlier and persists through 10.0.2. The Hankel Transform is given by Integrate[f[x] x BesselJ[0,x t],{x,0,Infinity}] It is ...
0
votes
0answers
89 views

Symbolic representation of bessel series derivative

I want to get symbolic expression for BesselJ derivative, where BesselJ is represented as series: ...
1
vote
2answers
87 views

Integrating a compound expression

I have an integral of the form I[r]=∫(arExp[-r]-brSin[k(r-d)]Exp[-r])BesselJ[0,kr]dr where Besse1J[0,kr] is the modified ...
11
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3answers
377 views
4
votes
1answer
76 views

Formal Differentiation

I'm trying to formally differentiate an expression. (I am aware of how to differentiate formally?, but am unable to generalize the idea) For example: ...
2
votes
1answer
118 views

Integration doesn't work

I'm trying to obtain the following integral: ...
0
votes
0answers
60 views

PolyLog does not simplify

How come mathematica can not simplify a simple expression involving the PolyLog function? An example is: You know that ...
17
votes
5answers
1k views

Mathematica gives wrong result while Wolfram|Alpha is correct

Why does Mathematica and Wolfram|Alpha give different results based upon the same code? I know Wolfram|Alpha's 7.85 is correct.
2
votes
1answer
117 views

Double integral over normal pdf gives inconsistent answer

I am using Integrate function to do the following double integral ...
1
vote
1answer
85 views

Absolute uncertainty and error propagation with lists [closed]

I am trying to do some error propagation using mathematica. This is my second day using the program. I am trying to take the derivative of a numerical function that is made up of the following lists. ...
6
votes
1answer
213 views

Solving $\frac{dx}{dt} = A \frac{ (1-x)}{(t-t^2)} - \frac{(B*x -C*x^2)}{(t-t^2 )*(t-x)}$

I would like to solve the following equation: $\frac{dx}{dt} = A \frac{ (1-x)}{(t-t^2)} - \frac{(B*x -C*x^2)}{(t-t^2 )*(t-x)}$ I have already posted it here, but still it doesn't work for me (I ...
0
votes
0answers
48 views

Sharp Ratio Maximization, Closed Forms

I am trying to get a closed form for the following first order conditions (n=4): Here's the nb-File. The code is as follows: ...
2
votes
2answers
159 views

Two ways to speed up slow Integrate[]s? (Can't do either)

I run into problems like this all the time on the complicated integrands I pass to Integrate. The following code works but takes a veeery looong time: ...
15
votes
6answers
497 views

No response to an infinite limit

Trying to compute this limit, things seem to get frozen, even for hours. What would you recommend to fastly compute it? ...
0
votes
2answers
137 views

How to help MMA to simplify integrands?

MMA sometimes has to grind for LONG time on easy integrals: ...