# 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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### Coupled heat transfer equations using collocation method

Using the collocation method proposed here, recently this problem has been solved. I am trying to solve a similar problem described by the equations given below. My attempt in Mathematica is ...
• 143
1 vote
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### How to get this expression in a wanted form

This is the endresult of integration calculation (I*Log[(b - I*z)/(b + I*z)])/(2*b) See the question integral calculation post This endresult must transformed to a ...
• 649
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### Evaluation of this definite complex integral

I want to obtain the symbolic expression for this definite complex integral: $\int_0^z \frac{1}{b^2+z^2} \, dz$ Then doing a subtition z in the Integral's upper boundary ...
• 649
1 vote
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### Integration shows different result after manual u-substitution

I'm working with sine and cosine integral functions, and stumbled on this weird issue when performing integration in Mathematica. I worked out the following integral by hand and found: ...
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### Is this a bug in Integrate?

I try to find with Mathematica 13.0.0 on Windows 10 the following integral (This is not art for art's sake, see McCrea W. H., Whipple F. J. W.Random paths in two and three dimensions, Proc. Roy. Soc. ...
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### Finding Coefficients in a Perturbation Problem related to Chaotic Dynamics

I am trying to reproduce the results from this paper: Chaotic dynamics of a suspended string in a gravitational background with magnetic field I am currently stuck with finding the coefficients. First ...
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### Roots, multivariable functions and Mathematica [closed]

Let $f(x,y)=(10 x^2 + 4 x y - 2 x + 4 y^2 - 4 y + 1)^2 (32 x^2 - 64 x y + 24 x + 40 y^2 - 28 y + 5)^2$ ...
292 views

### why these integrals fail to evaluate in V 13 compared to V 12.3?

This was also reported to WRI. [CASE:4903465] I'd like to know why these integrals no longer evaluate in V 13 and timeout after 3 minutes while using the same PC and OS they all evaluate quickly in ...
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### Equating the coefficients to get following relation

I have a system of differential equations as follows: ...
• 405
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### I'm beginner and do not how to plot the Basins of attraction by the methods

For a complex polynomial $P(z)$, define $T$ by $T(z)=z-\frac{P(z)}{P^{\prime}(z)}$, where $P^{\prime}(z)$ is the first derivative of $P(z)$. We consider Newton method for finding the roots of ...
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1 vote
170 views

### How to get the implicit function solution of ODE?

For example, ODE: $$(2x - 5y + 3)dx - (2x + 4y - 6)dy = 0$$ The implicit function solution: $$(2x+y-3)^2 (4y-x-3) = C$$ However, if it is solved directly with DSolve, the solution is very complex: <...
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### How can I perform this calculation in another program done, also in Mathematica? [closed]

This is done in Maple in steps (see picture) , and i want to do this on the same manner with steps in Mathematica.
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### How do I get the n-th derivative of the function f(s) [closed]

How do I get the n-th derivative of the function f(s) The result of the n-th derivative is also shown in the picture and the n-th derative
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For example: ...
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### How to improve the resolution of Region image boundary or the density of boundary sampling points?

I want to draw the region between two function curves （Sqrt[x], x^2）： ...
• 1,365
168 views

### How to get the expression of a special function?

How to get the expression of a special function? Like gamma function: Gamma[z]=Integrate[t^(z-1)/e^t, {t, 0, Infinity}]
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### How to find then-th derative for function f(s) [closed]

How to calculate the n-th derative for f(s)
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### Convergence of a complete elliptic integral

How to prove that the following integral assuming $k^2 < 1$ $$\int_{0}^{1} \frac{d x}{\sqrt{1-x^2}\sqrt{1-k^2 x^2}}$$ is convergent? ...
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### Weird Infinite Limit results when dividing functions

I am getting 0 or 1 for the limit when dividing the two functions but Log of the same constant when taking the limit individually. ...
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1 vote
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### Numerical integral in complex polar coordinates

point = {m -> -3, \[Nu] -> -0.2} ...
1 vote
54 views

### How to prove the inequality of undefined function?

For example, how to prove the following inequality? ...
• 1,365
1 vote
95 views

### Non- linear ODE

I was working on this equation but I can't get out something for this: ...
• 381
549 views

### Infinite sum bug

Why: Limit[Sum[Sqrt[-i^2 + n^2]/n^2, {i, 1, n}], n -> Infinity] (* 0 *) but: Integrate[Sqrt[1 - x^2], {x, 0, 1}] (* Pi/4 *) ...
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51 views

### Adding Assumptions in double integral written in "math input" mode

I've the following double integral and I'd like to write Assumptions->Re[c]>0, but if I try to do it, I get a syntax error. How can I add the above condition but without changing the ...
90 views

### The prime superscript didn't work as derivative

I am really new to Mathematica. I tried a lot of ways but I failed I am using the Adomian polynomial to decompose a function. The polynomial is generated by: Then in my case I need to decompose ...