# 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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### How to express the function $a(t)$ knowing a parametrization $a(\eta)$ and $t(\eta)$?

I have this function : $$\tag{1} a(\eta) = \sqrt{\sin{2 \eta}},$$ and this time variable : \tag{2} t(\eta) = \int_0^\eta a(\eta') \, d\eta'. \end{...
106 views

### How can I find the domain of $x$ for which the function $g(x)\geq0\;$?

I have this function ($x>0$) $$f (x)=\frac{\sqrt{g (x)}+4 x \left(x^2+1\right) \sin (\pi x) \cos ((3+\pi ) x)}{x^4+2 x^2+1+\left(4 x^2+\left(x^2-1\right)^2 \cos (2 \pi x)\right)}$$ ...
1k views

### How to determine if a function is continuous?

I wish to write code for Riemann-Stieltjes integrals in Mathematica. A necessary condition for the theorem to hold is that the function must be continuous. The domain of the function is a closed real ...
63 views

### How to do a fast numerical computation of an oscillatory integral including HeunC function using Mathematica?

I am trying to numerically compute the following integral in Mathematica ...
51 views

### How to make derivative as a function

g[z_] := z^2 l[z_] := D[g[z], z] How to make the derivative of a function as a new function. Here I am showing the simple case.
102 views

### Get curve values at a given altitude

If I have the following data: ...
76 views

### Numerical integration of a function with singularity

I am trying to find the following integral numerically, ...
80 views

### Superimposed data on top of each other in a Do Loop

If I have 4 different types of data such (that I get from an Excel file) as: https://pastebin.com/j3Bgfxqm I am trying to implement a ...
258 views

### Bug: Wrong limit in Mathematica 11.1.1 and current WolframAlpha

Bug introduced around 11.1.1 and fixed in 11.2 ...
335 views

### Getting wrong limit with Bessel

Bug introduced in 7.0 or earlier and fixed in 11.3 I computed a following limit (related to the asymptotic expansion of the sequence A000009 - number of partitions ...
62 views

### Calculating the integral

The question is asked in the mathstackexchange. There is no answer. I can't solve it by hand, also. Maybe we can solve it with Mathematica. Appreciate all your help, effort. Best regards. ...
148 views

### Integration not working

Can't seem to get this integration to work. s, n, b, b, l are all constants. ...
74 views

### I'm getting 0 when I evalute an integral I know is non-zero [closed]

Here is my code: ClearAll[n, y]; Integrate[(1 - y^n)/(1 - y^2), {y, 0, 1}, Assumptions -> Re[n] > -1] When I evaluate it, Mathematica 12.0 is giving me $0$, ...
104 views

### Solving an equation with Reduce

In the equation shown in the code that follows, I must find or eliminate rb, but Mathematica is reluctant to work with my Reduce ...
347 views

### Solving Integral Equation -numerical solution

I am trying to find a (numerical) solution to the following integral equation: where $\epsilon$ is a real valued function and $\beta$ and $c_0$ are constants. MMA code: ...
166 views

### How do I draw a conformal mapping from the z-plane to the w-plane

I am total beginner in Mathematica. Don't know a thing. I need to draw some diagrams for showing the conformal nature of map $w=e^z$. I need to draw some contours in $z$-plane; e.g., horizontal line, ...
66 views

### Laplace Transform - Differentiation in Time property demonstration

I have a signal x[t_]=t/3 Exp[-3t] UnitStep[t] and the laplace transform as ...
53 views

### Solve method in Mathematica, symbolically solving method

I am looking for a way to solve this equation symbolically with Mathematica. ...
161 views

378 views

### Calculating a double integral

I want to calculate the following integral: \int^{10}_{0}\int^{\pi}_{0}\sqrt{(37-\frac{45\cdot37\cdot x^2}{74\cdot 150})^2\cdot \sin(t)^2-(40-\frac{27\cdot37\cdot x^2}{16\cdot 150})^2\cdot \cos(t)^2}...
80 views

### How reliable is AsymptoticIntegrate?

In new mathematica 12 there is a new function AsymptoticIntegrate. However, it seems that it gives me incorrect results in some cases. To be completely honest, it ...
22 views

### Can't plot derivative of Hankel function [duplicate]

I am trying to plot the first derivative of $H^{(1)}_3 (ix)$ with respect to its argument $ix$, where $H^{(1)}_3 (ix)$ is the Hankel function of the first kind with order $3$, $x \in \mathbb{R}$ is a ...