# Calculus

### Numerical analysis for statisticians

August 25, 2011 |

“In the end, it really is just a matter of choosing the relevant parts of mathematics and ignoring the rest. Of course, the hard part is deciding what is irrelevant.” Somehow, I had missed the first edition of this book and thus I started reading it this afternoon with a ... [Read more...]

### Example 8.36: Quadratic equation with real roots

April 29, 2011 |

We often simulate data in SAS or R to confirm analytical results. For example, consider the following problem from the excellent text by Rice:Let U1, U2, and U3 be independent random variables uniform on [0, 1]. What is the probability that the roots... ### Single variable optimization

January 1, 2011 |

Optimization means to seek minima or maxima of a funtion within a given defined domain. If a function reach its maxima or minima, the derivative at that point is approaching to 0. If we apply Newton-Raphson method for root finding to f’, we can get the optimizing f. Read More: 223 Words ... [Read more...]

### one-dimensional integrals

December 25, 2010 |

The foundamental idea of numerical integration is to estimate the area of the region in the xy-plane bounded by the graph of function f(x). The integral was esimated by divide x to small intervals, then add all the small approximations to give a total approximation. Read More: 468 Words Totally [Read more...]

### Root finding

December 4, 2010 |

Numerical root finding methods use iteration, producing a sequence of numbers that hopefully converge towards a limits which is a root. In this post, only focus four basic algorithm on root finding, and covers bisection method, fixed point method, Newton-Raphson method, and secant method. Read More: 1896 Words Totally [Read more...]