# 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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### 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 $n \times 1$ ...
235 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?!! ...
32 views

### Getting a wrong plot after NIntegration

I am trying to plot this function numerically. R2T = ...
1 vote
27 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 <...
59 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?!! ...
1 vote
62 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 ...
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: $$\int_{\mathbb{R}} \mathrm{e}^{\mathrm{i}kx}\mathrm{d}x=2\pi\delta(x)$$
99 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 ...
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 <...
67 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 ...
66 views

### Incorrect result of AsymptoticSum

Trying in version 13 on Windows 10 ...
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 ...
57 views

### DSolve doesn't solve a second order differential equation

I am trying to solve an ordinary differential equation: ...
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 ...
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： ...
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 ...
108 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 ...
1 vote
284 views

### Integration not working

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

### Composite function derivatives

I would like to calculate the numerical partial derivatives (numerical gradient) of this function: ...
72 views

### Sort a List a Delete case [closed]

I try to sort a list in this way I have a polynomial DeleteCases[Table[Cos[(2 π)/3 k] z^k, {k, 0, 8}], 0, {-1}] gives ...
42 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 ...
68 views

### The inverse Laplace transform alters parameter constraints

I have this Laplace transform: $$\left( w \frac{L}{L+s}+(1-w) \frac{Q}{Q+s}\right)^n \ for \ L>0, Q>0,0<w<1.\ (1)$$ ...
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 ...
49 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 ...
45 views

1 vote
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, ...
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 ...
Through taking the derivative of $\binom{n}{k}$ w.r.t $n$ repeatedly, I found the recursive formula: $$\frac{\partial^a}{\partial n^a}\binom{n}{k}=\sum_{j=0}^{a-1}\binom{a-1}{i}\frac{\partial^j}{\... 0 votes 1 answer 109 views ### Second order differential operator in Mathematica I am trying to write the code for the following expression in Mathematica:$$\partial_{x} e^{-g x}=-g e^{-g x}+e^{-g x} \partial_{x}\,. I was able to do so with the help of the following links with ...
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 $\lambda \ge 0$...