Bisection Method

From the book "Numerical Methods for Engineers", by Steven C. Chapra, they state the true error is always less than the approximate error, and therefore, it is safe

approximate square roots of fractions with rationals

approximate square roots of fractions with rationals Ask Question Asked 1 year, 9 months ago Modified 1 year, 9 months ago

How do Taylor polynomials work to approximate functions?

I (sort of) understand what Taylor series do, they approximate a function that is infinitely differentiable. Well, first of all, what does infinitely differentiable mean? Does it mean that the fu...

Difference between "≈", "≃", and "≅"

In mathematical notation, what are the usage differences between the various approximately-equal signs "≈", "≃", and "≅"? The Unicode standard lists all of them inside the Mathematical Operators B...

calculus

Finding the number of terms needed to approximate a series with a given accuracy Ask Question Asked 2 years, 3 months ago Modified 2 years, 3 months ago

calculus

Use Euler''s method to approximate the solution for the following initial value problem. Ask Question Asked 8 years ago Modified 8 years ago

Calculating approximate value for some variable much bigger than

Often in physics problems, we derive some kind of function f(x) for some physical quantity and we try to find the approximate value of the function as some variable gets too big, or close to

spectral theory

@DeanMiller: I think it helps, but it is a bit confusing as the OP uses a definition of approximate spectrum that differs from Wikipedia''s but which according to the addendum of the

Approximating the error function erf by analytical functions

My question is if I can find, or if there are known, substitutions for this non-elementary function in terms of elementary ones. In the sense above, i.e. the approximation is

Approximating square roots using binomial expansion.

We want to (manually) approximate $sqrt {2}$ by using the first few terms of the binomial series expansion of begin {align*} sqrt {1-2x}&= sum_ {n=0}^infty binom {frac {1} {2}} {n} (