# 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 can I do partial derivation for F(y,y') with respect to y'? [closed]

This is a part of a question on the master/doctor degree graduate school entrance test for Tokyo Univ. in 2016. The conditions are below ( ) Here is the question. I have to make a differential ...
1answer
97 views

### Why are the results of integrations of a DiracDelta related integrand and its approximations strikingly different?

Let us consider a double integral, treating it as a functional which corresponds a number to a function, ...
2answers
305 views

### center of mass of a 2D square

Using Mathematica, find the center of mass of a 2D square not centered at the origin. center: (x0, y0) ...
1answer
54 views

### Principal value of a double integral numerically

I have several integrals of the form : where and . where a,b,wc and T are constants and PV denotes the Cauchy principal value I tried to integrate one of this form using NIntegrate however when ...
0answers
30 views

### Assume some expression is false

I need to Reduce a complicated function and I want to exclude some conditions A and B. How do I assume that the expression A is ...
1answer
64 views

### Simplify not working

I am trying to simplify the following expression code: ...
3answers
114 views

### How to get out coefficient of term in series?

Suppose I have a function $f(s,t) = [(1-t^2)(1-s^2t^2)]^{-1/2}$. Is there a way to get the general coefficient in this power series of the form $s^{2k} t^{2n}$?
0answers
34 views

### Four dimensional symbolic integration using HalfSpace

Consider the regions $r1 and$r2 defined as follows, ...
2answers
57 views

### Error in Integration of special functions using mathematica 12.0

When I try to integrate the following, Integrate[-GegenbauerC[22,-1/2,x]/(1+k*x),{x,-1,1}] where -1<k<1 and k!=0, Mathematica gives different results if I ...
0answers
97 views

### How to perform integration with Dirac Delta in Mathematica?

I am trying to calculate the integral $$y(x)=\int^b_a dz\delta(x-w_z)$$ were $\delta$ is the dirac delta function, $a=-3$, $b=3$ and $w$ is a one-dimensional matrix such that for some values of $z$ ...
0answers
31 views

0answers
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### First derivative of curve and onset and endset points

If I have the following data: ...
0answers
39 views

### Is there a function to quickly find the Cauchy main value of a function at a pole?

Suppose, f[x] has a pole at a. How do I quickly find Limit[(f[a+h]+f[a-h])/2,h->0] ? I ...
3answers
43 views

### ND gives expression instead of number

I have a function sol defined as a solution to an equation (computed numerically). Specifically ...
1answer
29 views

### Plot of derivative does not show

I have following function 4/((1 + v1[h])*(1 + v2[h])): ...
0answers
59 views

### About what does FunctionSurjective think so long time?

Having tried a new in 12.2 command FunctionSerjective, I executed FunctionSurjective[z^(5/2), z, Complexes] // AbsoluteTiming ...