Short programs for some basic probability applications. Solves binomial problems, computes the cumulative value of a binomial distribution, solves geometric, hypergeometric, and negative binomial distributions, computers the inverse probability of an event, and more.
Calculates Bernoulli numbers. Both integer and real versions for returning the nth Bernoulli number or the list of Bernoulli numbers from 0 through n. On the 49, is substantially faster than the built-in IBERNOULLI command. On the 48/28, is limited to smaller numbers for integers.
Reads the scatter data in the 'sDAT' (SigmaDAT) variable and performs a connect the dots output. The user can scale and translate the graphical output exactly like any normal graphical operation.
Prior to development of the Finite Element Method, there existed an approximation technique for solving differential equations called the Method of Weighted Residuals (MWR). For Galerkin's method, the test function w comes from the chosen trial function, i.e. w = du/da and the weighted average of the residual over the problem domain is set to zero. This program returns the trial function. It is shown plotted with the exact solution for 0<x<1.
Two programs for linear algebra, one to decompose a real matrix A into a real orthogonal matrix Q and a real upper triangular matrix R such that A=Q*R, and the other to do singular value decomposition.
A set of programs which accomplish a lot in the way of state-space system manipulation, as well as a
few programs which could be separated from this list to handle polynomials and the like. The functions that they perform include transfer function calculation (which means calculation of det(sI-A) and adj(sI-A)), state feedback gain calculations, observability matrix and controllability matrix determination, manual root finding, and so forth.
Tiny MSLV (multiple equation solver) for all RPL calculators. Program is 333.5 bytes on the 48GX. On the HP-28C it can find a simultaneous root of five nonlinear real-valued expressions. Uses successive approximation and the calculator's built-in matrix functions.