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.

Filter by
Sorted by
Tagged with
10
votes
2answers
864 views

Interpolating an Antiderivative

I'd like to be able to make InterpolatingFunctions for antiderivatives of functions that can't be integrated symbolically. However, the following code returns ...
2
votes
3answers
356 views

Evaluate a certain three-dimensional constrained integral

The result of the three-dimensional integration ...
-1
votes
3answers
7k views

How do I determine the maximum value for a polynomial, given a range of x values?

I need to determine the maximum value for y = a x^2 + b x + c, where I know the coefficients and the upper and lower x values. ...
31
votes
4answers
24k views

Finding Limits in several variables

Is there a way to find a limit of a multivariable function, like $$\lim_{(x,y)\to (0,0)} f(x,y)$$ with Mathematica? When $f$ is continuous, we can use $$\lim_{(x,y)\to (0,0)} f(x,y)=\lim_{(x,0)\...
31
votes
5answers
12k views

How can I differentiate numerically?

Mathematica has two ways to integrate: Integrate and NIntegrate. But what about D? ...
20
votes
3answers
8k views

Derivative of real functions including Re and Im

When deriving functions using Re, Im or Arg (and probably some other functions as well), ...
30
votes
4answers
6k views

How to find the period of an arbitrary mathematical function?

Is there a function to find the period of an arbitrary (possibly complex) function in Mathematica?
8
votes
2answers
416 views

Working with a system of differential equations that cannot be solved explicitly

I have to work a lot with three functions $\;o_1(t), o_2(t), o_3(t)\;$ that are solutions to a certain system of differential equations: ...
22
votes
2answers
699 views

Derivative of a pure function with SlotSequence

I can live with this but I can't figure out why the following is 0: Derivative[1][f[##] &][x] 0 From documentation for ...
22
votes
1answer
669 views

Teaching Mathematica more about DiracDelta and KroneckerDelta

As the documentation and some experimentation indicates, Mathematica contains little information about representations of the DiracDelta and ...
3
votes
4answers
2k views

How do I evaluate several n-th derivatives of a function at one point?

I have a question where I have to compute a Table containing $f^{(n)}(0)$ for n = 1, ..., 5, where $f^{(n)}$ denotes the $n$th ...
10
votes
4answers
771 views

Mathematica complaints that convergent integral diverges

Bug introduced in 10.0 and fixed in 10.0.2 Trying to do the integral ...
3
votes
4answers
1k views

Integrate full derivative

I want mathematica to do Integrate[D[f[x],x], {x,0,t}] and achieve the answer f[t]-f[0]. But Mathematica doesn't intergrate ...
8
votes
1answer
459 views

ReplaceAll[] and Limit[] don't give correct results for this expression under extreme variables [duplicate]

Possible Duplicate: Funny behaviour when plotting a polynomial of high degree and large coefficients 1/x^2 + (3 + x)/(6 (1 - Exp[x] + x)) ——This is a ...
7
votes
1answer
387 views

Products of Differential Operators

I have a differential equation defined as the product of operators which I want to expand out into a polynomial in powers of $z\frac{d}{dz}$ $\qquad \prod_{n=1}^p(z\frac{d}{dz}+a_n)$ However when I ...
2
votes
3answers
283 views

Optimization of ODE with respect to the initial condition

One has a (system) of ODEs with a one-parameter family of initial conditions. For example, ...
0
votes
3answers
182 views

How to write a custom function to judge whether a bivariate function is differentiable at a certain point?

We know that the necessary and sufficient conditions for a multivariate function to be differentiable at a certain point are complicated: Suppose the function $z = f (x_ 1, x_ 2, ..., x_n) $ is ...
0
votes
1answer
915 views

Plot[ D[Sin[x]] ] and Evaluate[] [duplicate]

Why does t = 2 Pi; Plot[D[Sin[x],x], {x,0,t}] (* Plotting the derivative of Sin[x] *) not work, but ...
46
votes
1answer
11k views

How to visualize Riemann surfaces?

In WolframAlpha we can easily visualize Riemann surfaces of arbitrary functions, can we plot the Riemann surface of an arbitrary function using Mathematica and ...
38
votes
6answers
2k views

Finding length of intersection of two surfaces

I would like to know how we find the length of the intersection of two surfaces. For instance, in the following example,a surface intersects with a plane: How do we find the length of intersection ...
37
votes
1answer
934 views

How to augment the realm of functions Mathematica thinks it knows how to integrate symbolically

My question involves extending the functionality of Integrate over specific integrals in the most generic manner. Specifically, is it possible to "hack into" ...
14
votes
3answers
3k views

Determine frequency of oscillations

I am wondering how I could determine the frequency of oscillations of a differential model equation? How could I find the frequency from this example given in Mathematica Documentation: ...
17
votes
2answers
853 views

What kind of hypergeometric function is it?

I found a formula for an integral of a product of three Bessel functions at The Wolfram Functions Site: I cannot understand what kind of hypergeometric function it is. The Mathematica code given for ...
3
votes
1answer
4k views

Complex line integral

Can someone recommend an online article or introductory tutorial that will show me how to do real and complex line integrals using Mathematica?
16
votes
2answers
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: ...
11
votes
2answers
7k views

How to find the non-differentiable point(s) of a given continuous function?

For example, the non-differentiable point of the function $f(x)=|x|$ is at $x=0$. How to find the non-differentiable points of a continuous function that is defined numerically?
10
votes
1answer
591 views

Mathematica implementation of Zeilberger's algorithm (previously done in Maple)

I have this Mathematica code: ...
8
votes
2answers
1k views

Three dimensional Laplacian insulated on lateral faces and convectively exposed on transverse faces (updated)

I have the three dimensional Laplacian $\nabla^2 T(x,y,z)=0$ representing temperature distribution in a cuboid shaped wall which is exposed to two fluids flowing perpendicular to each other on either ...
10
votes
1answer
927 views

Why should the spatial derivative order of the ODE *not* exceed two?

Following this question I came across this strange behaviour. Let me define a 1 D interval implicitely ...
10
votes
3answers
656 views

Maximize violating constraints

I have Maximize[{(h*10)/(300*(100 - (l^.5 + d^.4 + H^.6))), (l + d + H + h) == 669, l > 0, d > 0, H > 0, h > 0}, {h, l, d, H}] I believe ...
5
votes
2answers
1k views

Compute Hessian of function symbolically

This question could equally apply to the computation of other symbolic transformations of a function, but I use the Hessian as an example here. Consider a two-variable function ...
2
votes
2answers
937 views

Finding the volume enclosed by two surfaces of revolution

I've come this far as to combine both functions in a graph: f = Plot[4 - x^2, {x, -10, 10}] g = Plot[-1 + 4 x, {x, -10, 10}] Show[g, f, PlotRange -> All] ...
1
vote
1answer
167 views

Continuation of a Problem with Manipulate

For the beginning of this discussion, see: A problem with Manipulate. Now, the final use of the Initialization command doesn't protect the Global workspace. What I am discussing is not a single ...
1
vote
3answers
414 views

Problem solving Third order non-linear differential equation in Mathematica

I am trying to find an analytical solution of the following 3rd order non-linear differential equation in Mathematica: $a (f'(x))^2+f'''(x)=0$ with boundary conditions $f(0)=0$, $f'(0)=0$, $f(1)=1$, $...
27
votes
1answer
2k views

Undocumented use of Integrate: Integrating over regions

I have come across a few questions asking about integrating over regions. And while the answers are impressive there should be a better more consistent way. So my question is, are there ways, ...
19
votes
2answers
2k views

Differentiating functions of vectors/matrices?

I'm dealing with derivatives of scalar functions of matrices and wondering if Mathematica can help me here. The standard approach of expanding it in terms of components is cumbersome. As an ...
12
votes
1answer
2k views

Lagrange Multiplier

We are asked to maximize and minimize $f(x,y)=4xy$, given the constraint $4x^2+y^2=8$, using the Lagrange Multiplier method. First, I enter the functions f and g. ...
10
votes
3answers
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 ...
3
votes
1answer
341 views

Cartesian tensor gradient

Let $\mathbf{R} = [x,y,z]$ be a cartesian vector, $R_\alpha$ it's tensor representation with $\alpha = x,y,z$ and let $R=\sqrt{x^2 + y^2 + z^2}$ be its norm. I want to do tensor derivatives of the ...
17
votes
4answers
11k views

How to do implicit differentiation in Mathematica?

I have an equation which is K^(1/2)*L^(1/2)-(K+L) = 24 but I don't know how to do implicit differentiation to find dK/dL because I only know how to do the normal ...
13
votes
3answers
2k views

Different results for integration using Mathematica and MATLAB

I have the following integration: $$\text{y}=2 \sqrt{\frac{1}{\pi }} \int_0^{\infty } \frac{e^{-z} \left(1-e^{-\frac{z}{b}} \left(\frac{a}{a+c z}\right)^L\right)}{\sqrt{z}} \, dz$$ I get different ...
11
votes
2answers
2k views

Find closed form expression for series expansion coefficients [duplicate]

Is there a built-in function that will find a general expression for the coefficient of the series expansion of a function? Series will only give the explicit ...
9
votes
5answers
3k views

Is there a way to rewrite integrals in Mathematica using u substitution?

In Mathematica, can I give it an integral and a few substitution rules and have it rewrite the integral in terms of those variables?
2
votes
1answer
2k views

Finding residues of multi-dimensional complex functions

Say I have a function $f$ of $n$ complex variables, $\{ z_i \}_{i=1}^{i=Nc}$. And then I want to contour integrate the expression such that for each $z_i$ its an integration on an unit circle about ...
6
votes
4answers
3k views

3N-dimensional integral

I'm trying to compute a multidimensional integral with a variable number of dimensions. The integral is as follows: $$ \int d^{3N}\!p~e^{-\frac{\beta}{2m}\vec p^2}. $$ I have tried this ...
8
votes
3answers
840 views

Finding volume of a segment

I'm still pretty new to Mathematica, so I would like to seek advice regarding a geometrical problem. I am currently trying to define that as an extra condition in the Mathematica code below. ...
12
votes
2answers
543 views

Can we abuse notation and write equations in differential one-form?

Consider a simple equation with a one-form on both sides (mathworld.wolfram is also aware of this): $$ y\mathrm{d}x = \mathrm{d}y $$ This is a perfectly valid abuse of notation. We can carry the $y$ ...
9
votes
2answers
1k views

Bug in Integrate for Mathematica

Bug introduced in 8.0.0 and fixed in 9.0.0 Consider the following: ...
9
votes
2answers
5k 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 $1<|z|<2$?
7
votes
1answer
315 views

Length of a curve parallel to a spline

I have constructed a BSplineFunction through a set of random points: ...

1
2
3 4 5
14