# 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.

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### Function asymptotics showing different result after inter integration [closed]

I have a function fg[r_, t_, t2_, \[Phi]_, DR_]. I want to do the following Integrate it for t2 from 0 to t Then take the asymptotic limit r-> 0 The result of ...
47 views

### Plotting an integral with solving for a specific constant [closed]

Given an Integral I(t) which is a function of a constant tc, this constant is determined with the condition I(tc)=0, how can I add this condition?
47 views

### Numerical Integration without giving all values

Is there a way to solve expressions numerically, while keeping other variables. For example, I want to Integrate the expression below for $\theta p,\theta q$ while keeping other things as it is. The ...
43 views

### How to linearize these terms in many different variables?

How to linearize these terms in q[t] and p[t,y] ...
41 views

### Seeking Wolfram Mathematica Techniques for Detailed Step-by-Step Solution of Integral Equation Transformation

Hello Mathematica Community, I am working on a mathematical problem where I need to transform an integral equation into a simpler form using Euler's Formula and the Error Function. My current ...
42 views

### Derivative of a function in euclidean distance [closed]

differentiate W in (Z=XW, D1=distance(Z[, 1]), D2=distance(Z[, 2]), D3=distance(Z[, 3]) exp[-D1/theta _1 -D2/theta _2 -D3 /theta _3]) where W is 5 by 3 matrix, Z is 100 by 3 matrix and X is 100 by ...
44 views

### How do I find roots of a third degree polynomial? [closed]

expr = G^2 X^3 - 2 Δ G X^2 + Δ^2 X + ((ℏ *G*η* k*Subscript[E, l]^2)/(m*Subscript[Ω, m]^2)) == 0
75 views

### Integrate with Max and Min under assumptions runs forever

I'm trying to solve an integral under certain conditions on the parameters. The following is my code. ...
1 vote
52 views

Given that the initial area in a Sierpinski triangle is A_0 and the subsequent areas $$(A_n) =A_0 (3/4)^n$$ , what is the formula to calculate the leading ...
73 views

### What does "{True,True}" mean in the result of IntegrateChangeVariables?

I want to change variables in the following integral: Integrate[q*D[z[x, y],x]^2, {x, -∞, ∞}, {y, -∞, ∞}] as follows: ...
98 views

### Integral of complex exponential with assumptions

I feel confident this problem has been posed before but alas I cannot find it. ...
39 views

### Time derivatives not working [closed]

I have the following code: ...
141 views

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### How to linearize this equation in two different variables?

How to linearize this equation in two different variables p[t] and q[t,y]: ...
1 vote
53 views

### First order differential equation with two conditions

I want to produce all possible solutions for this equation: ...
46 views

### Limit giving indeterminate result

I have a function $r_h(v)$ given by, $$r_h (v) = \left(\frac{m_0}{2 g} e^{-g v_f} \left(-1+e^{-g(v - v_f)} \right) \right)^{1/5}$$ where $m_0$ and $g$ are just numbers. I want to take the limits of ...
106 views

### Integrate function differing from RUBI's Int function in version 13.3.0

I had Mathematica Version 12.3.1 Student Edition and Integrate and RUBI's Int functions produced the same answers for my purposes with good results. I updated my version to 13.3.0 Student Edition and ...
1 vote
100 views

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### How to chose appropriate finite limits for NIntegrate?

I want to NIntegrate a function using finite limits so it gives a result as close as possible to a result which I would get making the limit ...
1 vote
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### How to speed up this integration?

I try to evaluate this integral: ...
59 views

### Plotting list of points to a special graph

Given Mathematica code of eigenvalues in different variable-paths , I want to add experimental data in the path Gamma-X ; X-Gamma ; and M-Gamma . Here is the code : ...
271 views

### Symbolic integral with UnitStep functions

I want to symbolically evaluate the following integral (with real positive parameters L1, L2, ...
68 views

### How to make NIntegrate with large integration limit?

I try to double integrate this equation with respect to $b$ and $f$ ...
1 vote
78 views

### Minimization of an implicitly specified function

exp - an experimental data, where expT - temperature, expChi - magnetic susceptibility I ...
58 views

### Syntax error trying to rewrite expression using rules

I want to use Mathematica to calculate derivatives of some long, complicated expressions. I have an integral with integrand $I_*$ which is a functional that depends on $h(x,t)$ and $\phi(x,t)$. The ...
70 views

### Divergent series $\sum _{k=0}^{\infty } (2 k+1)^{3 k+1} z^k$ and LambertW function [closed]

I can get values from the following function, $$\sum _{k=0}^{\infty } (2 k+1)^{3 k+1} z^k$$ could you tell me how you could check those values using the Lambert function in integral form or if you ...
1 vote
151 views

### Why does Mathematica fail to compute $\int_{0}^{\infty} \sin(ax^2) dx$ whereas Wolfram Alpha seems to be able to do it? [closed]

I was symbolically computing $$\int_{0}^{\infty} \sin(ax^2) dx$$ Via the command: Integrate[Sin[a*x^2], {x, 0, Infinity}] But it seems to fail with mathematica, ...
50 views

### Different integral values for analytically same integrals

Consider a function $L$ with parameters $h=0.1,\ D=1.5$ $L(m,x):=e^{-\frac{2\ (\frac{x}{h}-m)^{2}}{D}}$. While the integrals $\int_{-\infty}^{+\infty}L(0,x)dx$ and $\int_{-\infty}^{+\infty}L(40,x)dx$ ...
137 views

### Finding the area enclosed by two curves

I am trying to find the area enclosed between two curves (i.e., two datasets). The challenge is to estimate the cross-sectional area. as indicated in blue. The first dataset represents the bathymetry ...
447 views

### Galactic rotation speed

Rotation speed vc[R] in reduced units for M33 looks like 0.342331 Sqrt[R^2/(0.728117 + R^2)^0.87955] Knowing ...
142 views

### Finite sum of complex exponentials giving wrong result [closed]

I was playing with the following sum: $$\sum_{k=0}^{2} e^{\frac{2\pi i k^2}{3}} = e^{0} + e^{\frac{2\pi i}{3}} + e^{\frac{8\pi i}{3}} \ne 0,$$ which is non-zero, at least according to Wolfram|Alpha. ...
88 views

### How can I find maximums of a function without Table and FindPeaks?

I have the following equation \pi_{xx} = \exp(-2 k_x^2 \sin^2(\frac{t}{2})) k_x^2 \theta(t) \times \bigg[ -\frac{\sin(2t)}{2} - \cos(t) \sin(t) (1 - k_x^2 \sin^2(\frac{t}{2})) + 2 ...
1 vote
84 views

### How can Mathematica merge $(1/t)^{1/3} t^{17/3}$ in an expression?

(1/t)^(1/3) t^(17/3) How to let Mathematica simplify it?
1 vote
206 views

### Integration giving unknown messages

I am trying to integrate the following Integrate[(Log[1 - t] t^(-(1/2) + eps))/(1 + t),{t,0,1}] To simplify this I am doing a further transformation ...
79 views

### How to find the maximum of an equation based on a variable? [duplicate]

I have the following periodic function, as a function of K and t. I need to know what is the maximum of each recurrence as accurate as possible for k={10,20,40,60,80} The equation is as follows, \$pixx ...
106 views

### Why does Area produce finite values for this area? [closed]

Let us consider in 13.3.1 on Windows 10 the region reg = ImplicitRegion[{x*y >= 8, y >= 8 x^3, y <= 27}, {x, y}]; and its area ...