Pre-Engineering 220 Introduction to MatLab ® & Scientific Programming j kiefer
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- 2. Integration
MatLab® Sidelight Number Two1. Nonlinear Equationsa. Fzero
The built-in MatLab® command for solving individual equations is named fzero. x = fzero(‘function’,x0) The initial guess is x0; ‘function’ is either a mathematical expression typed as a string, or the name of a user defined function. The function has to entered in standard form: f(x) = 0. ‘function’ is the f(x). If entered as a string, the function cannot include redefined variables. The initial guess can be entered as a single value, or as a 2-element vector such that the function crosses the x-axis between x0(1) and x0(2). (As in the bisection or secant methods.) b. Maximun/minimum A function to find the minimum of a function is fminbnd. [x fval] = fminbnd(‘function’,x1,x2) The command finds the minimum of the function, if any, lying in the interval (x1,x2). 2. Integrationa. Integrand as function The quad command evaluates a definite integral using an elaborated version of Simpson’s Rule. The method adjusts the step size as it goes along.  q = quad(‘function’,a,b,tol)
The parameter tol is an optional tolerance. If tol is not specified, MatLab® assumes  .
The quadl command carries out the integration using another method, the adaptive Lobatto method. That’s quad-L. b. Integrand as data table When the integrand is available as a table of data pairs, MatLab® uses the Trapezoid Rule. q = trapz(x,y) For generating uniformly distributed pseudorandom numbers, MatLab® has the command rand.
m = randperm(n) Directory: physics physics -> Photometer and Optical Link Sensitivity issues, needs editing 1/2010 Purpose physics -> Photometer and Optical Link Purpose physics -> - physics -> Teacher Notes – Activity 14: Momentum in Collisions physics -> Teacher Notes – Activity 15: Impulse and Change in Momentum physics -> Linear Momentum Definition Download 8.69 Mb. Share with your friends:
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