Questions related to the calculus and analysis branches of Mathematica, including, but not limited to, limits, derivatives, integrals, series, and residues.

learn more… | top users | synonyms (3)

0
votes
1answer
221 views

Why the result by hand is different from the built-in DSolve?

Yesterday, I used the Mathematica to solve a differential equation by the built-in command DSolve: ...
2
votes
1answer
100 views

How to solve this definite integral in mathematica?

I am a beginner in mathematica. I tried to solve this integration but not able to solve it. Can any body help me how to solve this integral in mathematica? Here is my integral, $$\int_{a}^{b} ...
4
votes
2answers
213 views

A suspicious result of an integral

I integrated this term in Mathematica: $$\int_{-\infty}^{\infty} d\omega*\sin(s*\omega)*\frac{1}{e^{\beta*\hbar*\omega}-1}*\frac{\omega}{\omega^{2}+\gamma^{2}}$$ The code in Mathematica: ...
0
votes
0answers
64 views

To calculate the differential of a function

I need to calculate the differential of a function WaveNumber. However, when I compile the code, it generates followig error: Infinite expression 1/0. ...
0
votes
1answer
75 views

is this a possible integration bug? [closed]

I am find a discrepancy in evaluating an integral which has given me trouble all day. I have finally isolated where the problem is which I now frame: I define the integral in terms of a delayed ...
2
votes
1answer
240 views

step by step interactive indefinite integral

WolframAlpha can give step by step solution for indefinite integral. There seems to be similar question but for derivatives. Is there a way that I can generate my own step by step solution for ...
10
votes
1answer
318 views

Limit of sequence of functions behaving strange

I'm trying to determine the limit of the sequence of functions $$f_n(x)=\left(\frac{1}{\pi}\arctan(n x) + 1/2\right)^n. $$ I define ...
14
votes
1answer
212 views

Is it a bug in Limit?

Bug introduced in 9.0 and fixed in 10.0.0 Mathematica 9 on Windows and WolframAlpha says Limit[Sin[Sqrt[x+1]]-Sin[Sqrt[x]],x->Infinity] is ...
6
votes
3answers
295 views

Using Grad, Div, etc in polar coordinates

I'm trying to use the newish functions Grad and Div to work with a PDE with circular or spherical symmetry and getting what looks to me like a wrong result. However, I'm not sure of this--perhaps I ...
2
votes
3answers
5k views

Step-by-step definite integration

I am interested in obtaining the intermediate steps for rather straightforward symbolic definite integrations (e.g., from an elementary calculus text). As an example, for $\int_0^1 x\,dx$ I'd like ...
0
votes
1answer
118 views

Why is my expression not a quantified system of equations? [closed]

Who can help me to understand why my code is wrong? It is giving me a message saying "is not a quantified system of equations and inequalities"?
0
votes
1answer
118 views

How to integrate a function of a direction, over the hemisphere

The Mathematica documentation Integrate over Regions gives an example of how to simply integrate over a sphere (surface): ...
1
vote
1answer
86 views

Help with singular integral

I'm new in Mathematica. I need solve a singular integral like $$\int_a^b \frac{A_0 + A_1 s + A_2 s^2 + A_3 s^3}{(B_0 + B_2 s^2 + B_4 s^4)(t-s)}ds$$ where $A's$ and $B's$ are reals and ...
1
vote
1answer
89 views

How can I avoid a scoping problem when differentiating?

I simplify my real problem as follows: I define a rule function as Clear[rule]; rule[i_] := tt -> i; the real rule function is not this simple. I define a ...
1
vote
0answers
38 views

Combining Manipulate and NDEigenvalues [closed]

I think there may be a quick solution to this problem which I can't seem to fix at the moment. The question is how do we eliminate the error in the following ...
33
votes
1answer
709 views

How to augment the realm of functions Mathematica thinks it knows how to integrate symbolically

My question involves extending the functionality of Integrate over specific integrals in the most generic manner. Specifically, is it possible to "hack into" ...
2
votes
3answers
145 views

Calculate and plot the tangent hyperplane to a function of three variables

If f:= x^3 + y*x*z - z^2 + x*z and if {{1,2,1},{2,7,8},{6,0,2},{9,1,1}} are points, how can I find the tangent plane to ...
28
votes
2answers
1k views

Bug in mathematica analytic integration?

I found Mathematica provides me a wrong answer for a relatively simple analytically solvable integral: ...
9
votes
1answer
567 views

Symbolic scalar-by-matrix derivative

Let's say I want to calculate the following scalar-by-matrix derivative $$\frac{\partial}{\partial A} \text{tr} \left[(\vec X^T A)^T (\vec X^T A)\right],$$ with $\vec X$ and $A$ being a $n \times 1$ ...
28
votes
1answer
437 views

many indefinite integrals do not evaluate in 10.1, looking for the cause

Bug introduced in 10.1 and fixed in 10.2 Many integrals no longer evaluate in V 10.1 when they did in 10.0.2 Here are some 23 integrals as an example, that all produced results in V 10.0.2, but ...
10
votes
1answer
144 views

How to predict the degree of the first series coefficient?

Given an expression f that is a function of x and a number x0, what is the least integer ...
6
votes
3answers
346 views

How to do algebra on unevaluated integrals?

I am working with functions calculated from a set of general basis functions. ...
13
votes
1answer
461 views

Why is this infinite series wrongly computed by Mathematica?

Bug introduced in 7.0 and fixed in 10.0 Could you let me know if Mathematica (newer versions) is able to correctly compute this one? ...
1
vote
1answer
114 views

Strange behavior of `FourierSinCoefficient`

FourierSinCoefficient works normally like this and the result is checked with Integrate. ...
2
votes
1answer
139 views

Function to calculate finite difference

I wrote a function to calculate multivariate finite difference of different orders ...
4
votes
1answer
84 views

How to collect terms with z-derivative?

my equations are very long (several pages). Here I will provide simple example: ...
5
votes
1answer
110 views

How to do matrix calculus in Mathematica?

I would like to differentiate Ax with respect to A where A is a matrix. Now, obviously, I know the derivative is x but for more nasty expressions, is there a way to differentiate expressions with ...
1
vote
1answer
48 views

Evaluate list of determinant of Hessian at list of points

If f:= x^2y + z^3 + xz; and if {{1,2,9},{2,4,6},{9,5,9},{3,3,1},{6,5,3}} is a list of points. I need to evaluate the hessian at ...
6
votes
1answer
116 views

Unexpected Behavior from Integrate with PrincipalValue -> True

Bug introduced in 9.0 or earlier and persisting through 10.3 or later The following code, taken from my answer to 97024, ...
3
votes
1answer
151 views

Multivariable Calculus Chain Rule

I am getting ready to write a notebook for the chain rule in Multivariable Calculus for my students. I do know: ...
7
votes
0answers
86 views

Strange kernel segmentation fault in Integrate

Bug introduced in 8.0 or earlier and persisting through 10.3 Define tointegrate = D[V[y1[t], y2[t]], y2[t]] D[V[y1[t], y2[t]], {y1[t], 2}] and try to find its ...
0
votes
1answer
48 views

if-conditional tracing a half-sphere [closed]

I have a 2D discrete plane (x,y) and I would like to assign an amplitude to each point in the plane. Each dimension runs from -1 to 1. Say I want to assign an ...
4
votes
2answers
268 views

Convergence and value of a complex power series

I've done a little math and I got the following power series expansion of $\log z$ about $z_0=-2+i$. $$\log z=\log(-2+i)+\sum_{n=1}^{\infty}\frac{(-1)^{n+1}}{n(-2+i)^n}[z-(-2+i)]^n$$ I've shown that ...
4
votes
1answer
146 views

Bad performance of Integrate (and WolframAlpha) for an Integral of Bessel function of the first kind

The following returns unevaluated in WolframAlpha. Also in my machine Mathematica needs quite a lot of time to compute it. ...
4
votes
0answers
114 views

Puzzled by Assumptions [duplicate]

I don't know if this has already been discussed. Integrate[BesselJ[2 m + 1, x], {x, 0, ∞}, Assumptions -> m ϵ Integers] ...
19
votes
2answers
2k views

Usage of Assuming for Integration

For some reason, when I enter the following integration in Mathematica Assuming[{k ∈ Integers}, Integrate[ Exp[ I k t], {t, -π, π}]] the result turns out to be ...
12
votes
6answers
480 views

Correct way to integrate a certain function

I want to integrate $$\int_{0}^{2\pi} dt_1 \frac{a + b\cos(t_1 - t_2)}{c + d\cos(t_1 - t_2)}$$ where $a, b, c, d, t_2$ are real numbers and $c + d > 0$ & $0 \leq t_2 \leq 2\pi$. I used a ...
1
vote
2answers
150 views

Find the explicit solution of the integral

I want to calculate the integral: assuming that we are familiar with the relation: The answer should be: The code that I've used is the following: ...
0
votes
2answers
117 views

Why does Integrate[] return an expression with 'True' in it?

I am running Mathematica 10 on Windows 10. I'm trying to analytically evaluate a definite, principal value integral: ...
7
votes
2answers
406 views

Check homework integration in Mathematica

Given in my homework I have to compute (by hand) $$\iint\limits_{x^2+y^2\leq 1}(x^2+y^2)\,\mathrm dx\,\,\mathrm dy.$$ My solution so far: Let $f(x,y)=x^2+y^2$ and $K=\{(x,y)\in\mathbb{R}^2:x^2+y^2\leq ...
1
vote
1answer
80 views

Find Values of a and b for a Limit

I am having trouble finding the values of a and b for which $\lim \limits_{x \to 0}$ $(\frac{\sin (ax) + bx)} {(x^3)}) = -32/3 $. In Mathematica I have entered: ...
7
votes
1answer
600 views

Integrating over Bessel Function erroreous? (Hankel Transform)

Bug introduced in 8.0.4 or earlier and persists through 10.2. The Hankel Transform is given by Integrate[f[x] x BesselJ[0, x t], {x, 0, Infinity}] It is ...
2
votes
1answer
148 views

Derivatives of vectors

I have an issue with derivatives of vectors ...
0
votes
1answer
41 views

How can evaluate this function [duplicate]

Suppose this function F[c_, n_, s_] := Module[{}, Abs[s - 1 + (-1 + c)^n]] I calculate its second derivative on c ...
1
vote
1answer
67 views
2
votes
2answers
85 views

Strange failure of Series and Derivative

I just spend three hours and posted two Questions trying to figure something out, and it turned out all the confusion was caused by this mysterious quirk. I want to expand g[x,v] in v at v=0, using ...
0
votes
1answer
97 views

Hessian of function at many points

If f:= x^3 + 2yz + 5 x^2z is a function and if {2,0,1},{3,9,2},{8,5,6},{1,1,7} are points. I would like a Hessian of ...
0
votes
1answer
45 views