# 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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### To calculate the differential of a function

I need to calculate the differential of a function WaveNumber. However, when I compile the code, it generates followig error: Infinite expression 1/0. ...
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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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### Please, help to find the area enclosed by the curves: ContourPlot[{x + y^2 == 0, x + 3 y^2 - 2 == 0}, {x, -2, 2}, {y, -2, 2}]

Please, Help to find the area between two curves. ContourPlot[{x + y^2 == 0, x + 3 y^2 - 2 == 0}, {x, -2, 2}, {y, -2, 2}]
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Consider: ...
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### Computing the first derivative in x, y ,and z

I have the following function: f:=x^3+yz+z^2x; I need to compute the first derivative in x, ...
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### Determining the order of continuity (smoothness) of a function

Is there any method to determine the order of continuity of a function (just like an interpolant) over a given domain, or at least determine the continuity on a given order? For example, according to ...
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### Computation (or estimation) of an trigonometric Integral with a parameter

I am trying to calculate the following integral which contains a parameter. I have used the Integrate and FullSimplify using assumptions but Mathematica fails to produce an analytical solution. ...
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### Integration result with incomplete beta function

I'm doing some calculations (double integration) which results in the incomplete beta function occurring as an end result. My input is: ...
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### Plotting the exponential of 1/(y-x)

What is the best way to handle this situation? ...
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### is this a possible integration bug? [closed]

I am find a discrepancy in evaluating an integral which has given me trouble all day. I have finally isolated where the problem is which I now frame: I define the integral in terms of a delayed ...
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### How to calculate the volume of a solid enclosed by surfaces? [closed]

I am asked to calculate the volume of the solid enclosed by the following equations: (in polar coordinates) r = Cos(θ) z = 2 + x² + y² z = 0 I know the second equation can be changed to its polar ...
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### Derivative of $e^{-1/x^2}$ [closed]

I'm trying to get derivative of $$e^{-1/x^2}$$ (also in other points than 0, e.g. 1) with D[E[-1/x^2], x] or ...
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### How could I check if a differential equation crosses a specific value? [closed]

I'm designing a magnetic field to simulate relativistic speeds in a small cyclotron. I need to see if the ratio -R/B * dB/dR crosses 0.2 in a certain range, and right now I'm trying to do that by ...
I am attempting to perform a convolution involving the Dirac Delta function: $\int_{-\infty}^{\infty} \frac{1}{t+1} \cdot \delta(t+1)\ dt$ I would expect that the result of this integral is ...