Thursday, November 5th, 2009
Saddle-Point Approximation Explained
Description
A detailed tutorial on saddle-point approximation. Step by step tutorial including several examples of saddle-point approximation for reference.
Overview
Saddle-point approximation is also referred to as the method of steepest descent and Laplace’s method. It is a way of approximating integrals in the form
. f(x) is some twice-differentiable function, M is a large number, and the integral endpoints a and b have a possibilty of being infinite.
Tags: a, approximation, b, Calculus, descent, differentiable, function, infinite, infinity, integral, Laplace, large, m, method, number, point, saddle, saddle-point, steepest, twice, twice-differentiable
Posted in Calculus | No Comments »
Thursday, October 8th, 2009
Introduction to Inflection Points
Description
A detailed tutorial on inflection points. Step by step tutorial including several examples of inflection points and how to locate inflection points for reference.
Overview
An inflection point, sometimes also known as a point of inflection, is a point on the graph of a function at which the function changes sign. This means that a concave up curve will become a concave down curve, or a concave down curve will become a concave up curve. Inflection points are also points of local maxima and local minima of a function. There are two ways to categorize inflection points. There are stationary points of inflection, and non-stationary points of inflection. Stationary points are formed when the function is zero, and non-stationary points are when the function is not zero.
Tags: Calculus, concave, curve, down, function, inflection, inflexion, local, Math, maxima, minima, non-stationary, point, saddle-point, sign, stationary, up
Posted in Calculus | No Comments »