Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [computational-mathematics]

This tag concerns computational problems central to mathematical and scientific computing. The scope includes algorithms, numerical analysis, optimization, and linear algebra, computational topology, computational geometry, symbolic methods, and inverse problems.

Computational mathematics involves mathematical research in areas of science where computing plays a central and essential role, emphasizing algorithms, numerical methods, and symbolic methods. Subtopics include numerical linear algebra, numerical optimization, computational geometry, numerical PDEs and inverse problems.

Consider also posting your question at Computational Science Stack Exchange.

1945 questions
23
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6 answers

Calculating logs and fractional exponents by hand

In view of what we can compute by hand, on a piece of paper, without having to use a computer or a calculator, how far can we go with the evaluation of $\log$-functions and fractional powers? More concretely, are there practical methods, that work…
user929304
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6
votes
1 answer

Wolfram Alpha error?

I was seeing some equations in WA, and i got with http://www.wolframalpha.com/input/?i=%28k%2B1%29%5E2%3E%3D4%28k-1%29%5E2 Let's manually solve the equation $$(k+1)^2\ge4(k-1)^2$$ $$(k+1)^2-(2k-2)^2\ge0$$ $$(-k+3)(3k-1)\ge0$$ But in alternate forms,…
chubakueno
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4
votes
5 answers

could someone please explain this proof to me? $d(x^2)=2xdx+dxdx$

I know that $d(xy)=ydx+xdy$ and $d(x^2)=2xdx+dxdx$ I want to calculate $d(x^3)$ and $d(x^4)$?? can anyone explain that how can I calculate it? and what is the name of this rule? Regards
user406745
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4
votes
0 answers

Algorithm for numerically calculating $\log x$

It was while fiddling yesterday that I came up with this rather pretty approximation: $$\log x = \frac{1}{2\epsilon}(x^{\epsilon}-x^{-\epsilon})+\mathcal{O}(\epsilon^2)$$ To be more precise, $$\log x =…
ShakesBeer
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4
votes
5 answers

A equation of Trigonometry

hello dear friends please help me to solve this problem.Thanks very much. How much are $a$ and $b$ in the problem below? $$1-2\cos 3a +2\cos 3b=0$$$$1-2\cos 5a +2\cos 5b=0$$
nickol
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3
votes
0 answers

Clarification on different types of solutions: analytical, closed form, iterative, algorithmic,

When doing computation, there are different types of solutions: analytical, closed form, iterative, algorithmic, exact, approximate, ... (there are probably more than I just listed and please don't hesitate to add more) I was wondering what these…
Tim
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3
votes
2 answers

Is all mathematics computable?

No matter how good a computer is, it will never compute the whole sequence of PI, but we can approximate it to arbitrary degeree. We can also implement programs that can do calculus and linear algebra. But what about other subjects, Group theory,…
user29163
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2
votes
1 answer

Find regular expression for a binary sequence dividable by 3

I am trying to find a short regular expression that matches to all binary sequences that are dividable by 3. This is homework. It would be great if I could only get some hints before the final solution :D Using the DFA I would get the following…
Chris
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2
votes
2 answers

Uniform grid on a disc

Do there exist any known methods of drawing a uniform grid on a disk ? I am looking for a map that converts a grid on a square to a grid on a disk.
nonlinearism
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2
votes
1 answer

Calculation Mismatch for WolframAlpha vs RConsole

Getting different answers when the same input is entered on the mentioned consoles known as $W$ and $R$ respectively. Any ideas on the root cause? The first example shows a difference of $128$. > 17*13^2*11^3*7^4*5^5*3^6*2^7 W -> 2677277333530800000…
Rohit
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2
votes
0 answers

Summation of n terms of a series$ 1+2+8+64+.........$

In one of my problem , I got a series as $1$,$2$,$8$,$64$,$1024$...and so on. can we really get a sum expression for that series$???$ If yes, then what is the expression $f$ $?$ or the sum of $n$ terms of a series…
Ajay shifu
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2
votes
3 answers

Let $x$ be an integer and $n$ be a positive integer. Find the smallest $n$ such that $x^4+n^2$ is not a prime for any $x$.

I need help proving the following: Let $x$ be an integer and $n$ be a positive integer. Find the smallest $n$ such that $x^4+n^2$ is not a prime for any $x$. I know that the smallest $n$ is 8 by testing $n=1,2,3,...$. I need help proving that $n=8$…
Dawn AM
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2
votes
0 answers

numerically solving linear integral equations

I want to solve a 3*3 linear equation system but the equations are integral equations and he coefficients of solutions are to be extracted NUMERICALLY from some other integrals.I do not know how. I can locate the coefficients into the Ax = b system…
MEVA
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2
votes
1 answer

Intersection symbols

I am writing a scientific paper. I need to express the intersection of two space, e.g. A and B where A and B can be a line, plane or a 3-D space. What is the appropriate symbol to state this concept. I used the intersections used in the set theory.…
Amir
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1
vote
0 answers

Metaprogram and Metametaprogram with BLOOP

I'm solving one question and have a problem. Problem is this: Imagine $f(x)$ in the following way. We give an input $x$ to a BLOOP program $Π$ , which prints out another BLOOP program $Π_x$. Then run $Π_x$ (no input) which produces $f(x)$. I need…
Minaj
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