# Tagged Questions

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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### Define a function that is an integral that takes a function as argument [closed]

How can I define a function $F$ in Mathematica that does the following: $$F(a,b,P) = \int_a^b P(1-t) \, dt,$$ where $P(t)$ is some function, say, a polynomial? More specifically, I would like to be ...
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### Constant Heat Flux Boundary Condition for the Differential Heat Equation

I am attempting to solve the transient heat equation for a very simple geometry and I am getting a junk solution. I have identified two distinct regions (wall and super-heated fluid layer) with their ...
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### How to collect terms with z-derivative?

my equations are very long (several pages). Here I will provide simple example: ...
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### Evaluate list of determinant of Hessian at list of points

If f:= x^2y + z^3 + xz; and if {{1,2,9},{2,4,6},{9,5,9},{3,3,1},{6,5,3}} is a list of points. I need to evaluate the hessian at ...
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### How to predict the degree of the first series coefficient?

Given an expression f that is a function of x and a number x0, what is the least integer <...
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### Combining Manipulate and NDEigenvalues [closed]

I think there may be a quick solution to this problem which I can't seem to fix at the moment. The question is how do we eliminate the error in the following ...
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### if-conditional tracing a half-sphere [closed]

I have a 2D discrete plane (x,y) and I would like to assign an amplitude to each point in the plane. Each dimension runs from -1 to 1. Say I want to assign an <...
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### Puzzled by Assumptions [duplicate]

I don't know if this has already been discussed. Integrate[BesselJ[2 m + 1, x], {x, 0, ∞}, Assumptions -> m ϵ Integers] ...
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### Unexpected Behavior from Integrate with PrincipalValue -> True

Bug introduced in 9.0 or earlier and persisting through 10.3 or later The following code, taken from my answer to 97024, ...
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### Find Values of a and b for a Limit

I am having trouble finding the values of a and b for which $\lim \limits_{x \to 0}$ $(\frac{\sin (ax) + bx)} {(x^3)}) = -32/3$. In Mathematica I have entered: ...
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### How to do matrix calculus in Mathematica?

I would like to differentiate Ax with respect to A where A is a matrix. Now, obviously, I know the derivative is x but for more nasty expressions, is there a way to differentiate expressions with ...
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### Bad performance of Integrate (and WolframAlpha) for an Integral of Bessel function of the first kind

The following returns unevaluated in WolframAlpha. Also in my machine Mathematica needs quite a lot of time to compute it. ...
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### Derivatives of vectors

I have an issue with derivatives of vectors ...
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### Why does Integrate[] return an expression with 'True' in it?

I am running Mathematica 10 on Windows 10. I'm trying to analytically evaluate a definite, principal value integral: ...
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### How can evaluate this function [duplicate]

Suppose this function F[c_, n_, s_] := Module[{}, Abs[s - 1 + (-1 + c)^n]] I calculate its second derivative on c ...
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### Find the explicit solution of the integral

I want to calculate the integral: assuming that we are familiar with the relation: The answer should be: The code that I've used is the following: ...
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### Strange failure of Series and Derivative

I just spend three hours and posted two Questions trying to figure something out, and it turned out all the confusion was caused by this mysterious quirk. I want to expand g[x,v] in v at v=0, using ...
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### About taking limit of an integral on Wolfram Alpha/Mathematica [closed]

I tried computing this quantity on Wolfram Alpha, but I couldn't get any answer: ...
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### How can I solve this limit? [closed]

How can I solve this limit? thanks you!!!
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### Hessian of function at many points

If f:= x^3 + 2yz + 5 x^2z is a function and if {2,0,1},{3,9,2},{8,5,6},{1,1,7} are points. I would like a Hessian of ...
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### How would you calculate a contour integral? [duplicate]

How would you be able to calculate a contour integral of 1/(((z-1)^2)*(z-i)) over the contour |z-1| = 1? Not sure how to type ...
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### Integral of DiracDelta giving an unusual answer

I have been getting a number of seemingly inconsistent solutions to integrals of Dirac delta functions in which the integrand evaluates to DiracDelta[0] at one of ...
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### A 1D numerical integral Mathematica cannot compute, from physics

A well know result in theoretical physics is that a sum over Matsubara fermionic frequencies, i.e.: $$S = \sum_{n=-\infty}^{\infty} h(\omega_n) \hspace{32pt} \omega_n=(2n+1)\frac{\pi}{\beta}$$ can ...
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### Solving a functional equation

Suppose I have two functions f[x,y,z] and g[x,y,z], both analytically defined. I want to solve for a function ...