Source: bsp_20_fkt.hpp


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//    Dokumentation
//         kdoc -p -d bsp_20 bsp_20_fkt.hpp
//         kdoc -p -d tex_bsp_20 -f latex bsp_20_fkt.hpp

#ifndef BSP_20_FKT
#define BSP_20_FKT

/**
The functions for examples 20, 21, 22
@short		The functions for examples 20, 21, 22
@author		Gundolf Haase
@version	SS07
*/


//                       Funktionen aus Aufgabe 20
//    Riemann-Integration
/**
     Calculates the integral value.of a 1D-function by the Riemann formula
     @param	func	function func(x) to integrate
     @param	a	interval [a,b]
     @param	b     interval [a,b]
     @param	n	number of subintervals of [a,b]
     @return	integral f(x) from a to b
*/
double riemann( double (* const func)(double), const double &a, const double &b,
		const int n);

//    Differenzieren
/**
     Calculates the first derivative f'(x) of a 1D-function by the finite difference.
     @param	func	function func(x) to differentiate
     @param	x	point for evaluation
     @param	h	distance from x in the finite difference formula
     @return	f'(x)
*/
double derivative( double (* const func)(double), const double &x, const double &h);

//                       Funktionen aus Aufgabe 21

//    Riemann-Integration (hier klappt Overloading da 4. Parameter anders)
/**
     Calculates the integral value.of a 1D-function for a given accuracy
     by the Riemann formula
     @param	func	function func(x) to integrate
     @param	a	interval [a,b]
     @param	b     interval [a,b]
     @param	eps	absolute numerical accuracy
     @return	integral f(x) from a to b
*/

double riemann( double (* const func)(double), const double &a, const double &b,
		const double eps=1e-4);

//    Differenzieren (andere Funktionsname, da alle Parameter gleich sind
//                    und die Parameterliste nicht umgestellt wurde)
/**
     Calculates the first derivative f'(x) of a 1D-function with a given accuracy
     by the finite difference.
     @param	func	function func(x) to differentiate
     @param	x	point for evaluation
     @param	eps	absolute numerical accuracy
     @return	f'(x)
*/

double derivative2( double (* const func)(double), const double &x, const double eps=1e-4);

//    Newton solver fuer func(x) mit x aus [a,b]
/**
     Solves the equation f(x)=0 in the interval [a,b] with the Newton iteration using
     the finite difference to approximate the needed first derivative.
     Calculates the first derivative f'(x) of a 1D-function with a given accuracy
     by the finite difference.
     @param	func	1D-function func(x)
     @param	a	interval [a,b]
     @param	b     interval [a,b]
     @param	eps	absolute numerical accuracy
     @return	one root of func(x) in the given interval
*/

double newton_diff_approx
 ( double (* const func)(double), const double &a, const double &b, const double eps=1e-4);



#endif

Generated by: ghaase on mephisto on Thu May 24 08:44:56 2007, using kdoc 2.0a54.