# 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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### Interrupted plot lines when multiple branches of an ODE solution are plotted

I am plotting the following: ...
• 3,466
52 views

### How can I get KroneckerDelta to contract an index?

I have a sum like f = Sum[x[i]^2, {i,1,Infinity}] and I want to take a derivative of this with respect to one of the variables, e.g. ...
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### Use Mathematica to solve equation derive the probability distributions using the Principle of Maximum Entropy

I am reading the article Deriving probability distributions using the Principle of Maximum Entropy and trying to derive some of the equations in it automatically using Mathematica. I want to solve the ...
55 views

### How to increase the precision of numerical derivatives?

I need to make sure about precision of numerical derivatives in my calculations. I use finite element method to obtain a wave function, then I take derivatives of this numerical wave function to get ...
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### Stop Mathematica from expanding Dirichlet beta and eta functions

It seems that Mathematica treats DirichletBeta[s] and DirichletEta[s] merely as symbols for ...
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1 vote
59 views

### How to understand the output of following integration?

If one tries to evaluate the following integral, Integrate[(u Cos[k])/( 4 \[Pi] (u^2/16 + (-\[CapitalLambda] + Sin[k])^2)), {k, -\[Pi], \[Pi]}] one gets following ...
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### A Simple Integrate

I'm facing the integral ...
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### Solve an equation for different values

I was trying to solve this equation for different value of a constant (a) but the solution is not different for those values?!! b and m are positive values. ...
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### Caputo-Hadamard fractional derivatine nonlinear equation system

I tried it make it solved and plot but im confused, NDsolve, DSolve, ParametricNDSolve didnt work. Please help me, and please write anything.Thank you. ...
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### How to fix accuracy error?

When I run the code this type of error appears: ...
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### Integral of non-singular cosine apparently doesn't converge

After running the following code I get an error that simple integrals are not converging. I make a false assumption that e>0, and proceed to evaluate the integral over e. Mathematica doesn't ...
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### Integrating an expression, that Mathematica cannot solve, via hints or substitutions?

Integrating the following expression, if possible, requires some hints or substitutions which I cannot find. ...
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### Finding the mean and variance of a distribution

I have tried unsuccessfully to use Mathematica to derive both the expected value (mean) and variance of a particular statistical distribution of interest to me. The distribution is a discretized ...
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### Why Doesn't Mathematica Evaluate This Integral? [closed]

I am using Mathematica (the online version, but not WolframAlpha) and I'm trying to estimate the integral $\int_{-1}^1 e^{\frac{i}{1+x^2}}\,dx$. To do so, I've entered: ...
• 143
1 vote
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### NIntegrate with big error estimates

I'm trying to calculate a 4-dimensional integral using standard wolfram mathematica methods, but I can't get rid of a big calculation error. My integral ...
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### Evaluate the following simple continued fractions

A continued fraction is a fraction whose numerator is an integer and whose denominator is an integer added to a fraction whose numerator is an integer and whose denominator is an integer added to a ...
74 views

### How to use rhs of a given list in a code? [closed]

I have the following Mathematica code: ...
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1 vote
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### Convergence with Maximize - Iterations, Precision

I have problems with some applications for finding convergence - below is one example of failure for {x=0.35,y=0.35,z=0.3}, but it works fine for {x=0.3,y=0.3,z=0.4}. How can I increase the iterations ...
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1 vote
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### Why is there an error in one case and not in the other?

Why does the error occur for P[34, 14] whereas for P[33, 14] has no error? How to get rid of this error? ...
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1 vote
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### Integral of (Elementary) Volume Form over Orientable Surface of Genus 2?

Per this post on math.stackexchange.com, I am told it is impossible to find an elementary formula for a coordinate patch covering of the orientable surface of genus 2 (or higher genus) (or the non-...
348 views

Consider following expression: $\int_0^1 \sqrt{4194 x^4-6804 x^3+3960 x^2-972 x+90} \, dx$ If i use N[] to calculate it, i get following result: $N\left[\int_0^1 \sqrt{4194 x^4-6804 x^3+3960 x^2-972 x+... 3 votes 1 answer 40 views ### How to troubleshoot NIntegrate non-numerical error? I am trying to evaluate a 2d integral (denoted as x and y here) with a function that involves a numerical integral at each point.... • 33 1 vote 1 answer 218 views ### Why Wolfram 12.1 not calculated? [closed] Why doesn't scientific software count, ... • 21 0 votes 0 answers 41 views ### Encountered a singular Jacobian while solving nonlinear equations I am solving the nonlinear questions in equation 4.1a-4.1c given in the paper. (https://arxiv.org/pdf/cond-mat/0008249.pdf) but no success.I posted similar questions in the link Encountered a singular ... • 51 9 votes 1 answer 650 views ###$\int \frac{\tan^2 x}{1+x^2} dx\$

Motivated by this integral, which does not evaluate in Mathematica, I'm wondering if there is some trick or substitution that will solve the indefinite integral. My motivation is to find integrals ...
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1 vote
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### How to remove/ (avoid) the # sign in "Solve" output [duplicate]

I am trying to find an equation of A with variable B using the Solve function. I have the first derivative of firm A's profit with respect to location a, which is equal to zero. I have the first ...
87 views

### Encountered a singular Jacobian while solving nonlinear equations

I am solving the nonlinear questions in equation 4.1a-4.1c given in the paper. (https://arxiv.org/pdf/cond-mat/0008249.pdf) but no success. ...
• 51
Consider the following non-linear equation: $$k x = \frac{\frac{9}{4}-y^{22/25}}{2\ 2^{19/25} y^{22/25}-\frac{9}{4} \left(10 y+e^{-y}\right)^{22/25}-1}$$ where k ...