be8ed228-7b9f-4d88-9521-f6039e697cd5 52 3 5 false false 0 decimal
&[DATE] &[TIME] - &[FILENAME]
&[PAGENUM] / &[COUNT]

Stückweise stetige Funktionen

Piecewise continuous functions

Mathematik

Mathematics

Inhalt

Contents

 Restart complete. diff(), int(), lim(), sum(), det() handled by Maxima

Sprungfunktion

Step function

Die Sprungfunktion kann auf viele verschiedene Arten dargestellt werden.

There are several ways to represent the step function.

Boolsche Operatoren

boolean operators

 0 x 1 step 0.9967 Received Bytes: 39 (%i22) integrate(x>1,x,0,2); (%o22) 'integrate(x > 1,x,0,2)

Signum-Funktion

sign function

 0.5 x 1 step 1 Received Bytes: 17 (%i23) integrate((1+signum(-1+x))/2,x,0,2); (%o23) 1

Betragsfunktion

absolute value

 # x 1 step Division durch Null. Principal Value 1 2 1 sys Received Bytes: 16Received Bytes: 16 (%i24) integrate((-1+x+abs(-1+x))/(2*(-1+x)),x,0,2);Principal Value (%o24) 1

Heaviside-Sprungfunktion aus dem Plugin

Heaviside step function from the plugin

Statistical Tools

 0.5 x 1 step 1 Received Bytes: 17 (%i25) integrate((1+signum(-1+x))/2,x,0,2); (%o25) 1 1 x 1 step 1.0033 Received Bytes: 40 (%i26) integrate(x >= 1,x,0,2); (%o26) 'integrate(x >= 1,x,0,2) Received Bytes: 40 (%i26) integrate(x >= 1,x,0,2); (%o26) 'integrate(x >= 1,x,0,2)

Gerundeter Tangens hyperbolicus

rounded hyperbolic tangent

 0 x 1 step # Received Bytes: 57 (%i27) integrate(round2((1+tanh(-1+x))/2,0),x,0,2); (%o27) 'integrate('round((tanh(x-1)+1)/2),x,0,2)

Lineare Interpolation

linear interpolation

 0.4737 x 1 step 1.0033 Received Bytes: 123 (%i28) integrate(linterp(matrix([0],[999999999999999/1000000000000000],[1],[2]),matrix([0],[0],[1],[1]),x),x,0,2); (%o28) 'integrate(linterp(matrix([0],[999999999999999/1000000000000000],[1],[2]),matrix([0],[0],[1],[1]),x),x,0,2)

Mathematik

Mathematics

Inhalt

Contents

$Author: mkraska $ $Date: 2018-09-15 10:38:13 +0200 (Sa, 15 Sep 2018) $

pid=10964 Maxima 5.41.0 http://maxima.sourceforge.net using Lisp SBCL 1.3.18 Distributed under the GNU Public License. See the file COPYING. Dedicated to the memory of William Schelter. The function bug_report() provides bug reporting information. (%i1) display2d:false$ (%i2) linel:700$ (%i3) simpsum:true$ (%i4) logsimp:true$ (%i5) keepfloat:true$ (%i6) ratprint:false$ (%i7) load(vect)$ (%i8) load(abs_integrate)$ WARNING: redefining MAXIMA::OPAPPLY in DEFMACRO WARNING: redefining MAXIMA::OPCONS in DEFMACRO ARRSTORE: use_fast_arrays=false; allocate a new property hash table for $INTABLE2 (%i9) setup_autoload(mnewton, mnewton)$ (%i10) setup_autoload(draw, draw2d, draw3d)$ (%i11) load(lsquares)$ (%i12) logb(x,y):=log(x)/log(y)$ (%i13) ntewurzel(x,n):=x^(1/n)$ (%i14) el(x,y):=x[y]$ (%i15) el(x,[y]):=if equal(length(y),1) then x[y[1]] else x[y[1],y[2]]$ (%i16) Fit(Data,vars,fun,par,init):=lsquares_estimates_approximate(lsquares_mse(Data,vars,fun),par,initial=init,iprint=[-1,0])$ (%i17) Fit6(Data,vars,fun,par,init,t):=lsquares_estimates_approximate(lsquares_mse(Data,vars,fun),par,initial=init,tol=float(t),iprint=[-1,0])[1]$ (%i18) Residuals(Data,vars,fun,[par]):=float(transpose(matrix(lsquares_residuals(Data,vars,fun,par))))$ (%i19) MSE(Data,vars,fun,[par]):=float(lsquares_residual_mse(Data,vars,fun,par))$ (%i20) round2(x,n):=round(x*10^n)/10^n$ (%i21) CustomInitExample; (%o21) CustomInitExample (%i22) integrate(x>1,x,0,2); (%o22) 'integrate(x > 1,x,0,2) (%i23) integrate((1+signum(-1+x))/2,x,0,2); (%o23) 1 (%i24) integrate((-1+x+abs(-1+x))/(2*(-1+x)),x,0,2);Principal Value (%o24) 1 (%i25) integrate((1+signum(-1+x))/2,x,0,2); (%o25) 1 (%i26) integrate(x >= 1,x,0,2); (%o26) 'integrate(x >= 1,x,0,2) (%i27) integrate(round2((1+tanh(-1+x))/2,0),x,0,2); (%o27) 'integrate('round((tanh(x-1)+1)/2),x,0,2) (%i28) integrate(linterp(matrix([0],[999999999999999/1000000000000000],[1],[2]),matrix([0],[0],[1],[1]),x),x,0,2); (%o28) 'integrate(linterp(matrix([0],[999999999999999/1000000000000000],[1],[2]),matrix([0],[0],[1],[1]),x),x,0,2) (%i29)