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# 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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590 views

### Integrate of Heaviside Function returns an error answer

I try to evaluate an Integral of a Heaviside function, but it turns out with an erroneous output(zero). Here is my integral: ...
1k views

### Symbolic integration in real domain only ( assumptions and ComplexExpand don't work)

Integrate[m^2/((x - m^2)^2 + y^2), m] mathematica gives me a complex-valued reuslt, but maple 17 gives me what I want. I tried using assumptions, but it doesn't ...
529 views

### finding an argument of a complex number

What is the simplest way to find the argument of the following function? ((1 - E^((I π (1 - α))/(β - α)) z)/(1 - E^(-((I π (1 - α))/(β - α))) z)) as I tried the ...
136 views

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### How to calculate this integral? Integrate[BesselJ[0, x - BesselJZero[0, 1]]/x, {x, -Infinity, Infinity}]

I tried to calculate the following integral, but it returned unevaluated. ...
440 views

### How do I get a general form for n-th derivative of a function? [duplicate]

I tried the following but it basically returns unevaluated: ...
164 views

### Strange behavior of Integrate

I'm trying to calculate the following integral using Mathematica 9.0.1.0 a11=Integrate[Abs[Sin[b+x]],{x,0,2*\[Pi]}] This should be a simple problem; however, it ...
640 views

### how to reduce the time to calculate triple integral

i want to evaluate the following integral, but it takes 15 min to do it. i must reduce the time to calculate it, i have to do a table and create a graph, but takes too long. anyone have an idea ? ...
104 views

### Is there a more idiomatic way to solve this implicit differentiation problem?

Here's an exercise from a calculus text by Larson and Edwards: Find the rate of change of the distance between the origin and a moving point on the graph of $y = x^2 + 1$ if $dx/dt = 2$ ...
624 views

### Plotting derivatives of B-splines

I am trying to solve an electrodynamics problem numerically by using B-splines a basis function. Please don't ask me why, but if you really wanna know, here is the assignment. Using the following ...
552 views

### Derivatives of list elements

Bug introduced in 8.0.0 and fixed in 9.0.0 Could someone explain the odd behavior of the Derivative function when drawing arguments from lists? We have, ...
39 views

### Plot derivative of integral with changing limits [duplicate]

My code is: Plot[D[Integrate[E^(t*(-x^2)),{x,t+2,t^2}],t],{t,-2,3}]. The errors/warnings are: ...
533 views

### Why does Mathematica give an incorrect answer to this multiple integral?

This is not a new problem but I would like to understand why Mathematica gives the result that it does. (Volume of a hypersphere) ...
5k views

### How to make traditional output for derivatives

Hello again after some pause. i have a problem how to present partial derivatives in traditional form, not as Mathematica gave it to me in its notation. So I want to present this ...
155 views

### Simple Question: Derivative of a path

I have a path V[t_]:={3t^2,2,6t}, and I define F[t_]:=V[t]/Norm[V[t]]. I simply want the derivative of ...
4k views

### Laurent series expansion

Can someone share how to find the Laurent series expansion of $$f(z)=\frac{1}{(z^2-1)(z^2-4)}$$ centered at $0$ on the annulus $1<|z|<2$?
6k views

### How do I evaluate a double or triple integral over a region?

Say I need to evaluate the integral $\iiint_W f(x,y,z) dx dy dz$ and $W$ is a region given to me like $W = \{ (x,y,z) : 1 \leq x^2 + y^2 \leq 4, 1 \leq z \leq 5\}$. I don't how to do this with a ...
207 views

### Why does Integrate return a solution that is not defined at a particular point when it actually is well defined at that point?

I am trying to compute Integrate[Sqrt[x^4 + (y - y^2)^2], {x, 0, y}] Mathematica 8 gives ...
354 views

### integrating slightly complicated expression which includes Abs

I have been waiting for Mathematica to give me something for the following integral, errors welcome, but it has been "running" for almost 30 minutes now. ...
628 views

### Mathematica cannot calculate a limit

When I evaluate Limit[E^(-n)*Sum[n^k/(k!),{k,0,n}], n -> ∞] Mathematica gives me the result ...
144 views

### Getting poles of a Gamma functions [duplicate]

Why do the following 2 sequences give different answers? n = 1.5 Series[Gamma[0.5 - n - x], {x, 0, 2}] Series[Gamma[-1 - x], {x, 0, 2}] (..clearly the output from the second expression is correct ...
240 views

### Strange result from evaluating a Limit expression

Bug introduced in 9.0 and fixed in 10.0 When I evaluate the limit of (1-Cos[x]) Sin[1/x] at x = 0 in Mathematica 9, I obtained <...
1k views

### Why does Integrate declare a convergent integral divergent?

When I try this command Integrate[1/Sqrt[(s^2 - u)^2 - 1], {s, m, Infinity}, Assumptions -> u > 2 && m > 10] Mathematica declares that the ...
1k views

### Implicit differentiation to find the slope of the tangent line to the graph at the indicated point [duplicate]

I used ContourPlot to plot the graph of x Sin[Pi y] - y Cos[Pi x] == 1 with the following input: ...
204 views

### Limit of a subsequence

I am trying to calculate limit for a subsequence <${ a }_{ {n }^{ 2} }$> because I was trying to see that limits of sequences and subsequences are both same. I was able to generate the sum for ...
805 views

### How do I represent a system dynamics feedback loop?

In System Dynamics, if I want represent the relationship between Speed and Distances, I create a Flow (Speed) and a Stock (Distance) as you can see in this Insight Maker Sample . Heres an Image of how ...
3k views

### Is it possible to impose “Assumptions” in DSolve or equivalent? (differential equation solving)

When DSolve tries to solve differential equations, it is sometimes not smart enough to generate conditions according to different possible value of parameters. ...
129 views

### How to evaluate an integral

I am trying to evaluate this integral Integrate[(kx^2/2)*Sin[λx], x] from -pi/2(lamda) to pi/2(lamda) Everything there is a constant, and the only variable is x....
292 views

### Computing the minimum distance in a contour plot

I have the following Mathematica code ...
374 views

### Convergence and value of a complex power series

I've done a little math and I got the following power series expansion of $\log z$ about $z_0=-2+i$. $$\log z=\log(-2+i)+\sum_{n=1}^{\infty}\frac{(-1)^{n+1}}{n(-2+i)^n}[z-(-2+i)]^n$$ I've shown that ...
3k views

### Numerical partial derivative

For a one-variable numerical function, it's simple to calculate the derivative at a point with Derivative as Szabolcs has pointed out before: ...
1k views

### Sum and NSum gives different solutions

I'm working on a Mathematica lab for Calc. 2, and I ran into a problem last night. I was trying to calculate the midpoint approximation of the definite integral of ...
187 views

### Manipulate fails with f[x]=x^k/(1+x^k)

I have this code: Clear[f] f = Function[x, x^k/(1 + x^k)]; Manipulate[Plot[f[x], {x, 0, 5}], {k, 1, 10}] But nothing draws as I move the slider. Am I missing ...
889 views

### Solve f'[x]==0 for x

I tried the following: f[x_] := x^n/(k + x^(2 n)); Solve[f'[x] == 0, x] But I got the following response: Solve::nsmet: This system cannot be solved with the ...
1k views

### Evaluating the integral of $\cos (\theta )\cos\left[\tan ^{-1}\left(\frac{a^2 \tan (\phi )}{b^2}\right)\right]$

I am trying to evalute the following integral: Integrate[Cos[θ] Cos[ArcTan[a^2/b^2 Tan[φ]]], {φ, 0, 2π}] I know that for $a=b$ I should get 0 out of the integral ...
245 views

### Only perform a symbolic differentiation once

I want to define a function that involves a differentiation step that Mathematica can do easily, which might be of the form ...
943 views

813 views

### Volterra integral equation : 'literally match the independent variables' message

I want to solve an Volterra type Integral equation, and as a practice I entered the following code to my mathematica: ...
3k views

### How to change coordinates of integration?

Is there some built-in routine, some easier method to change variables of integration, without/before solving the integral? Say I have ...
7k views

### Multiple assumptions in integral

I want to add two assumptions, so I can get this probability density function to equal 1, though I can't get a solution. ...
1k views

### Why does the first derivative of a piecewise continuous function have discontinuities?

I have this piecewise continuous function which is also continuously differentiable over time : ...
555 views

### NumericQ prevents evaluation at a numerical value sometimes

I set up a symbolic integral, to be evaluated only when some of the symbols have been replaced by numbers. The evaluation after assigning numbers to the symbols is still symbolic for some reason. The ...
415 views

### Integrate[(1 + x/n)^n*Exp[-x], {x, 0, Infinity}]

I evaluated Integrate[(1 + x/n)^n*Exp[-x], {x, 0, Infinity}] . thinking the answer should be approximately $\sqrt{\pi n/2}$. Mathematica gave me ...
487 views

### Integration gives ComplexInfinity when it shouldn't

A simple example of my problem is that Assuming[k ∈ Reals, Integrate[Exp[l]/((1 + Exp[l])*Exp[k l]), l]] /. {k -> 2} gives ...
220 views

### Version 8.0 integrates but Version 9.0.1 doesn't

Bug introduced in 9.0 and fixed in 10.1 I am trying to run the following integral in version 9.0, but it fails: ...
In my calculus 3 course, we're studying gradients and have a project that takes a combination of 3D Gaussian radial surfaces and a basic parametric path $r(t) = \{x(t),y(t)\}$ to see how the gradient ...