Questions tagged [calculus-and-analysis]

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

Filter by
Sorted by
Tagged with
1 vote
1 answer
18 views

Plotting, Integrating two variable function with cross-restricted domain

Hello, I have two problems. the first is plotting 3D function, the domain is "0<x<y<1". (I could find examples like integrating function with domain 0<x<1, 0<y<1, but I ...
user avatar
  • 125
1 vote
1 answer
102 views

Integral of orthogonal Bessel functions

This is the basic form of the problem i am solving. The main difference with the integral on the photo and my example is that i have my integral defined from b to c instead of 0 to a, and Bessel ...
user avatar
0 votes
0 answers
44 views

Integral with triangular functions in exponential and numerator

I am trying to find the solution of an integral with a triangular function in the numerator and in an exponential, but after an hour Mathematica has not given me an answer. I wondered if there is a ...
user avatar
  • 131
0 votes
0 answers
50 views

Useless and incorrect result of AsymptoticIntegrate

In version 13 on Windows 10 I try to find asymptotic of the integral used in potential theory ...
user avatar
  • 16.7k
0 votes
0 answers
41 views

Output of expressions unable to have operations be performed on the expression

I am currently trying to use the code linked in the catalog of spacetimes pdf to calculate chirstoffel symbols for a metric which follows as n := 4 ...
user avatar
  • 119
0 votes
1 answer
44 views

Plot for DSolve in mathematica [closed]

I don't Plot it's not working!!, can you help me? ...
user avatar
2 votes
1 answer
49 views

Integration over an implicit region

A question asks me to calculate the following integral using NIntegrate: Calculate the double integral ... where D is the area bounded by the four lines ... With ...
user avatar
7 votes
3 answers
1k views

Mathematica 13.0 simplifies trigonometric integral wrong

I calculate the following general expression: ...
user avatar
0 votes
0 answers
59 views

Getting a wrong plot after NIntegration

I am trying to plot this function numerically. R2T = ...
user avatar
1 vote
1 answer
29 views

Getting the same result from Integrate as Probability

I'm trying to solve a Baysian inference problem (although the details are not all that important for this question) I define two probability distributions P and <...
user avatar
0 votes
1 answer
61 views

Numerical Plot for an example

I would like to compare the numerical and analytical solution with plot for this example but something is wrong I don't know how to fix it?!! ...
user avatar
1 vote
0 answers
65 views

What's the meaning of Global?

I'm calculating an integral, Integrate[(t e^(-z t) e^(-q t))/(1-e^(-t)), t], and the result is ...
user avatar
  • 121
0 votes
0 answers
54 views

Settings that integrate gives also distributions as solutions

How can I tell Mathematica that I also want distributions as solutions for Integrate? Example: $$\int_{\mathbb{R}} \mathrm{e}^{\mathrm{i}kx}\mathrm{d}x=2\pi\delta(x)$$
user avatar
  • 101
0 votes
0 answers
39 views

Replace Derivative[ i ][ f ][ t ] with f[ i, t]

Assume the PadeApproximant is carried over f[t0] * g[t0] with the order {1, 1}, that is <...
user avatar
0 votes
2 answers
101 views

Integrate: slow and wrong results

Very often I struggle to understand what is happening when I try to integrate stuff in Mathematica. Generally, it deals very well with ugly symbolic integrals. But I have an example in which it deals ...
user avatar
  • 169
0 votes
2 answers
68 views

Incorrect result of AsymptoticSum

Trying in version 13 on Windows 10 ...
user avatar
  • 16.7k
0 votes
0 answers
57 views

DSolve doesn't solve a second order differential equation

I am trying to solve an ordinary differential equation: ...
user avatar
10 votes
3 answers
2k views

Can Mathematica calculate this elliptic, triple integral?

Integrate[(4 a b/Pi) (a^2 + b^2 - 2 a b Cos[c])^(1/2), {a, 0, 1}, {b, 0, 1}, {c, 0, Pi}] I'm using basic plan, it gives me the result like that. The ...
user avatar
  • 125
-3 votes
1 answer
68 views

Taking sentences with a spatial factor [closed]

To ask my question precisely, I should say that I have got many terms, among them some have coefficients $M^n$. Some things like : $$f = f_1(M) + f_2(M) + M f_3(M)+ M^2 f_4(M)+f_5(M)+...$$. I need to ...
user avatar
  • 57
0 votes
1 answer
74 views

How come I can't get $\int f(t)$ from performing derivative/anti-derivative operation on $\int f(t)$?

I know the the area under the curve of some function between the coordinates $t_0$ and $t_1$, is: $$\int_{t_0}^{t_1} f(t) \space dt=\frac{\left(t_0^2+t_1^2\right)^2}{4t_1^2}$$ How do I find $f(t)$? I ...
user avatar
  • 1,481
2 votes
1 answer
69 views

Selecting a solution range that is independent of a variable value

This symbolic computational question derives from this mathematical one on math.SE: Find all values of $a \in \mathbb{R}$ for which $f(x;a) = x^3 - 3 a x^2 + 3 a x - 2$ is non-decreasing. My ...
user avatar
2 votes
1 answer
118 views

How to integrate this product of Exp[] and Cos[] using Mathematica

I would like to integrate the following product of Exp and Cos: ...
user avatar
  • 699
5 votes
1 answer
109 views

Evaluating PlusMinus to 2 decimal answers

How do I evaluate and expand an expression containing PlusMinus such that: N[PlusMinus[1, 1]] returns 2, 0 I'm stuck at ...
user avatar
2 votes
0 answers
43 views

Why does Mathematica not know some integrals diverge?

I want to analyse the convergence of some complicated 1d integrals that may have divergences at $x=0$, similarly to the harmonic integral $\int_0^a 1/x \ \mathbb{d} x$, which I know is divergent. When ...
user avatar
0 votes
2 answers
36 views

`Assuming` combined with mathematical notation of `Integrate`

I am trying to write down the following expression Integrate[Exp[-a/2/x]/x/(x + 1), {x, 0, b}, Assumptions -> a > 0 && b > 0] using mathematical ...
user avatar
0 votes
1 answer
68 views

The inverse Laplace transform alters parameter constraints

I have this Laplace transform: $$\left( w \frac{L}{L+s}+(1-w) \frac{Q}{Q+s}\right)^n \ for \ L>0, Q>0,0<w<1.\ (1)$$ ...
user avatar
0 votes
0 answers
50 views

splitting integrand based on variable dependence

For multiple integration, I would like to automatically check whether the integrand can be split up to a product of terms, each dependent on as small a subset of the variables as possible. E.g., given ...
user avatar
0 votes
0 answers
33 views

Integer parameter assumption gives incorrect result when integrating

There are some dangerous pitfalls that can happen when evaluating some integrals, assuming that some parameters are integers. For example, consider the following: ...
user avatar
  • 951
0 votes
0 answers
45 views

Algorithm: Permutations & Signature

Theoretical side Simple example: If I have two sets $A_1=\{1,3\} ,A_2=\{2,3\}$ and Permutations[{1, 2, 3}]= $\left( \begin{array}{ccc} 1 & 2 & 3 \\ 1 &...
user avatar
1 vote
1 answer
61 views

How to perform the first and second derivatives of Nth polynomials?

Suppose  $P(x,y)=\displaystyle\sum^{N}_{i+j=0}\alpha_{ij}x^{i}y^{i} \equiv \alpha_{00}+\alpha_{10}x+\alpha_{01}y+a_{11}xy+\ldots+a_{0N}y^{N}$ is a multivariable polynomial of $N$th degree. I want to ...
user avatar
3 votes
1 answer
102 views

Inconsistent results between NIntegrate and Integrate

I get these inconsistent results What is going wrong? Fast oscillating terms? Small exponential factors? But then, why the result seems to toggle between values 1 and 2, rather than being a real ...
user avatar
  • 315
0 votes
2 answers
44 views

Limit is not actually evaluated, but wolframalpha does [closed]

I'm trying to evaluate the limit $\lim_{x \to a} f(x)$ of the function $f(x)=\dfrac{1}{1+\tfrac{a^2}{4x(a-x)}\sin^2 \left(b\sqrt{a-x} \right)}$ using mathematica, and it should yield $\dfrac{1}{1+ab^...
user avatar
1 vote
1 answer
69 views

How do we just have $\log$ solution?

Mathematica solves this but I want the solution just as Ln[..]?!! DSolve[y'[t] == 3/2 a*y[t] ((y[t] + b)^2 - f), y[t], t] thanks
user avatar
0 votes
0 answers
107 views

Dictate Mathematica to use the contour integration method

I want to evaluate an integral, which can be in principle computed exactly. For $a>0$ and $k_1, k_2 >0$, define $G(x) = (x+ia)^3$. The integral that I have is $$I = \int_{\mathbb R^4} dy_1dy_2 ...
user avatar
0 votes
0 answers
39 views

How to analytically solve for an intersection of two functions on an interval?

I would like to analytically solve for the intersection of two functions on a given interval and store the solution as a function (of parameters) for later use. How can I tell Mathematica to look for ...
user avatar
1 vote
0 answers
23 views

Commutation of the partial derivatives on scalar in xAct

I do not know how to automatically commute partial derivatives on a scalar and simplify it. For example, if I have: $$\partial_a \partial_b \partial_c f- \partial_c \partial_a \partial_b f $$ where $f$...
user avatar
  • 57
4 votes
2 answers
149 views

The jumping problem when rolling reuleaux triangle

I'm making an animation of a Reuleaux triangle rolling on a straight line like this The animation generated by my code is not continuous, is there a simple way to eliminate jumping? ...
user avatar
  • 4,910
0 votes
1 answer
74 views

How to get the derivative from this implicit equation with differentials? [duplicate]

The idea is here to have a implicit equation and take from both sides of the equation the differential and solve out of this the derivative The derivative is the ratio of two differentials and can be ...
user avatar
  • 649
0 votes
2 answers
77 views

How to set integral starting from 0 in the symbolic solution to ODE

I have the following ODE Bfull'[t] == - (p0/( p0 + (1 - p0) E^Integrate[α[s], {s, 0, t}])) * α[ t] (S[t] - Bfull[t]) + α[t]*c + δ * Bfull[t] where α and S ...
user avatar
  • 53
2 votes
2 answers
108 views

Plot the general and a particular solution for this differential equation

In a previous question, I had obtained a differential equation from: Starts with this implicit equation: (x - a)^2 + y^2 == 1(1) ( circles on x -axis ) $(x-a)^2+y^2=...
user avatar
  • 649
2 votes
1 answer
93 views

How Implicit differentiate in order to get a differential equation [closed]

Starts with this implicit equation: (x - a)^2 + y^2 == 1(1) ( circles on x -axis ) $(x-a)^2+y^2=1$ Is the set of equations of the given circles. This set contains ...
user avatar
  • 649
5 votes
1 answer
245 views

Poincare section for a perturbed string

I am trying to find the Poincare section of a perturbed string in a gravitational background with a magnetic field. The plots that I am trying to reproduce are from this paper (page 11). The code that ...
user avatar
  • 181
1 vote
1 answer
103 views

Integrals on symbolic regions

Let's define a region as r=Polygon[{{-a,0},{a,0},{a,h}}]. I want to integrate some function over that area. Say x^2. So, ...
user avatar
1 vote
1 answer
61 views

Solve functional integral equations

I encountered one problem which is to find $F(\lambda)$ which satisfies $1 = \int_{-\pi}^\pi e^{i k \lambda} dF(\lambda), \forall k \in \mathbb{Z}$ and the answer is $F(\lambda) = 1$ if $\lambda \ge 0$...
user avatar
1 vote
2 answers
81 views

Using Loop to find a specific Energy

I am given a Hamiltonian: ...
user avatar
  • 181
6 votes
3 answers
314 views

Neglecting higher order terms in a Lagrangian

I have a lagrangian which is modified by variable change. I want to neglect all the 4th order and higher terms in the new lagrangian. The code being used is given below: ...
user avatar
  • 181
0 votes
2 answers
77 views

Assumptions in Integration for positive real values [closed]

I want to evaluate the following integral in Mathematica. $$ \int_0^\infty \frac{a^{-t}-b^{-t}}{t} dt = \ln \left(\frac{\ln b}{\ln a} \right)$$ I try to enter this, but Mathematica can't figure it out....
user avatar
0 votes
1 answer
66 views

Power Series and Interval of Convergence [closed]

How could I find the power series and interval of convergence for x/(3+x^2)?
user avatar
  • 1
0 votes
3 answers
243 views

Computing the elliptic integral $\int \frac{1}{x \sqrt{f+\frac{a}{x^3}-\frac{k}{x^2}}} \, dx$

I don't know how to solve this with or without Rubi?!! ...
user avatar
0 votes
1 answer
28 views

Evaluating partial derivative at a point

I have a function in 5 variables, lkl, and I want to evaluate its second derivative wrt tau at a point. (I will also later want ...
user avatar
  • 103

1
2 3 4 5
84