# 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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### Are the conditions in ConditionalExpression necessary or sufficient?

I computed a limit and obtained it in the form of a ConditionalExpression (see below). Substituting the variables with numerical values in the resulting formula ...
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### Step by step solution of a limit of a sequence - Calling Wolfram|Alpha in Mathematica

I'd like to visualiza the step-by-step solution of the following limit by calling Wolfram|Alpha in Mathematica, but I don't know how to specify that n is a positive integer variable: ...
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### Plotting a complex function under transformation

I am trying to plot the unit circle $\vert z\vert=1$ under the transformation $z\to z+\frac1z$ using mathematica. In general I want to plot a complex function $f(z)$ under the transformation $\phi(z)$....
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### Primitive of a continuous function over $\Bbb R$

A continuous function over $\Bbb R$ has a primitive that is also continuous over $\Bbb R$. However, it often happens with Mathematica and other CAS that the result is not continuous, especially with ...
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### Finding sequence limits from matrix determinants

I have a problem whereby I want to calculate the limit of a sequence of determinants of matrices of increasing dimensions using the DiscreteLimit command. To illustrate this, I use an example with a ...
151 views

### How does MMA use $\varepsilon-\delta$ language to find the limit?

In the help document of Reduce function, I can find an example of using the definition of limit to find the asymptote: ...
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### Find vectors describing two interconnected pyramids in Euclidean space

I need the help of competent linear algebra specialists in Mathematica. In the Euclidean space, two tetrahedrons are turned at different angles. Their vertices coincide with the beginning of the base ...
34 views

### How to discritize a function domain (break xy-plane to a grid/mesh of squares with vertex values for evaluation)? [closed]

I wrote a code using MATLAB to discritize a function's 2D domain into squares/rectangles, whose vertex data (x,y) I can use to evaluate the function at. Then I sum these values over all vertices to ...
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### How can I get this integral to Compute

I'm trying to compute the following expression and get an analytical answer but Mathematica ends up spitting back the input expression. Hoping someone can shine some light on this. ...
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### Integrate 2D Gaussian over a segment

I have the following 2D Gaussian: ...
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### Constructing and plotting a special periodic function

I need to program and plot the following special function in Mathematica 12.0: $$a_{1}(t)= \sum_{n\geq 1} \beta_{n}(t),$$ such that, for every $n \geq 1$  \beta_{n}(t)= \displaystyle \sum_{...
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### define function as a result of gradient returns unexpected result

This is probably very simple problem, but what am i doing wrong? c[x_, y_] := x*y; Grad[c[x, y], {x, y}] d[x_, y_] := Grad[c[x, y], {x, y}]; d[1, 1] Returns: <...
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### Area of circle segment

Why does it take so much time computing a simple area of segment of a circle radius $a,$ width $h<a?$ Integrate[Sqrt[x ( 2 a - x)], {x, 0, h}] Would it ...
157 views

### How to calculate volume under $f(x, y)$?

I have the following function: σ = 0.3; μ = 5; cy =0; cx=0; f[x_,y_]=Exp[-(1/2)((Sqrt[(x-cx)^2+(y-cy)^2]-μ)/σ)^2]/(σ*Sqrt[2*π]) Plotting this with: ...
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### WolframAlpha does not give stepwise solution for a simple twodimensional integral

Why does the behave this particular way: ...
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### How to simplify an expression with implicit vector functions and cross product operation?

1.The pattern is set in order to calculate the integral of a derivate of a function (to return original function, first fundamental theorem of calculus) ...
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### Radial Mathieu functions, divergence problem

I am working on a project that requires the utilization of even Mathieu functions. This is the definition of my functions: Even Mathieu function: ...
370 views

### Integration of probability density function

I would like to integrate the function so that I know the probability between values between 0 and 90000 ...
I am trying to numerically verify that, over a closed circular path, the line integral of a physics-inspired complex quantity $z_Q = P \cdot \frac{\partial}{\partial Q} S$ is the same regardless of ...