Riemann integrability - Revision history

Michael at 19:09, 18 January 2013

2013-01-18T19:09:37Z

← Older revision		Revision as of 19:09, 18 January 2013
Line 8:		Line 8:
	p.push(brd.create('point',[2.7,(Math.random()-0.2)*5]));		p.push(brd.create('point',[2.7,(Math.random()-0.2)*5]));

	var f = ~~brd~~.lagrangePolynomial(p);		var f = JXG.Math.Numerics.lagrangePolynomial(p);
	var n = brd.create('slider',[[-1,3],[2,3],[1,10,50]],{name:'n',snapWidth:1});		var n = brd.create('slider',[[-1,3],[2,3],[1,10,50]],{name:'n',snapWidth:1});
	var plot = brd.create('functiongraph',[f,-3,3]);		var plot = brd.create('functiongraph',[f,-3,3]);
Line 15:		Line 15:
	var lo = brd.create('riemannsum',[f,function(){ return n.Value();}, 'lower',-3,3],{fillColor:'#ffff00', fillOpacity:0.3});		var lo = brd.create('riemannsum',[f,function(){ return n.Value();}, 'lower',-3,3],{fillColor:'#ffff00', fillOpacity:0.3});

	brd.create('text',[-2,-2,function(){ return 'Diff='+(~~brd~~.riemannsum(f,n.Value(),'upper',-3,3)-~~brd~~.riemannsum(f,n.Value(),'lower',-3,3)).toFixed(4); }]);		brd.create('text',[-2,-2,function(){ return 'Diff='+(JXG.Math.Numerics.riemannsum(f,n.Value(),'upper',-3,3)-JXG.Math.Numerics.riemannsum(f,n.Value(),'lower',-3,3)).toFixed(4); }]);
	</jsxgraph>		</jsxgraph>

Line 28:		Line 28:
	p.push(brd.create('point',[2.7,(Math.random()-0.2)*5]));		p.push(brd.create('point',[2.7,(Math.random()-0.2)*5]));

	var f = ~~brd~~.lagrangePolynomial(p);		var f = JXG.Math.Numerics.lagrangePolynomial(p);
	var n = brd.create('slider',[[-1,3],[2,3],[1,10,50]],{name:'n',snapWidth:1});		var n = brd.create('slider',[[-1,3],[2,3],[1,10,50]],{name:'n',snapWidth:1});
	var plot = brd.create('functiongraph',[f,-3,3]);		var plot = brd.create('functiongraph',[f,-3,3]);
Line 35:		Line 35:
	var lo = brd.create('riemannsum',[f,function(){ return n.Value();}, 'lower',-3,3],{fillColor:'#ffff00', fillOpacity:0.3});		var lo = brd.create('riemannsum',[f,function(){ return n.Value();}, 'lower',-3,3],{fillColor:'#ffff00', fillOpacity:0.3});

	brd.create('text',[-2,-2,function(){ return 'Diff='+(~~brd~~.riemannsum(f,n.Value(),'upper',-3,3)-~~brd~~.riemannsum(f,n.Value(),'lower',-3,3)).toFixed(4); }]);		brd.create('text',[-2,-2,function(){ return 'Diff='+(JXG.Math.Numerics.riemannsum(f,n.Value(),'upper',-3,3)-JXG.Math.Numerics.riemannsum(f,n.Value(),'lower',-3,3)).toFixed(4); }]);
	</source>		</source>

	[[Category:Calculus]]		[[Category:Calculus]]
	[[Category:Examples]]		[[Category:Examples]]

A WASSERMANN at 12:47, 11 May 2010

2010-05-11T12:47:00Z

← Older revision		Revision as of 12:47, 11 May 2010
Line 9:		Line 9:

	var f = brd.lagrangePolynomial(p);		var f = brd.lagrangePolynomial(p);
	var n = brd.create('slider',[[-1,3],[2,3],[1,10,~~100~~]],{name:'n',snapWidth:1});		var n = brd.create('slider',[[-1,3],[2,3],[1,10,50]],{name:'n',snapWidth:1});
	var plot = brd.create('functiongraph',[f,-3,3]);		var plot = brd.create('functiongraph',[f,-3,3]);

Line 15:		Line 15:
	var lo = brd.create('riemannsum',[f,function(){ return n.Value();}, 'lower',-3,3],{fillColor:'#ffff00', fillOpacity:0.3});		var lo = brd.create('riemannsum',[f,function(){ return n.Value();}, 'lower',-3,3],{fillColor:'#ffff00', fillOpacity:0.3});

	brd.~~createElement~~('text',[-2,-2,function(){ return 'Diff='+(brd.riemannsum(f,n.Value(),'upper',-3,3)-brd.riemannsum(f,n.Value(),'lower',-3,3)).toFixed(4); }]);		brd.create('text',[-2,-2,function(){ return 'Diff='+(brd.riemannsum(f,n.Value(),'upper',-3,3)-brd.riemannsum(f,n.Value(),'lower',-3,3)).toFixed(4); }]);
	</jsxgraph>		</jsxgraph>

			===The underlying JavaScript code===
			<source lang="javascript">
			var brd = JXG.JSXGraph.initBoard('box', {boundingbox:[-3,5,3,-3],axis:true});
			var p = [];
			p.push(brd.create('point',[-2.7,(Math.random()-0.2)*5]));
			p.push(brd.create('point',[-1,(Math.random()-0.2)*5]));
			p.push(brd.create('point',[0,(Math.random()-0.2)*5]));
			p.push(brd.create('point',[1,(Math.random()-0.2)*5]));
			p.push(brd.create('point',[2.7,(Math.random()-0.2)*5]));

			var f = brd.lagrangePolynomial(p);
			var n = brd.create('slider',[[-1,3],[2,3],[1,10,50]],{name:'n',snapWidth:1});
			var plot = brd.create('functiongraph',[f,-3,3]);

			var up = brd.create('riemannsum',[f,function(){ return n.Value();}, 'upper',-3,3],{fillColor:'#ff0000', fillOpacity:0.3});
			var lo = brd.create('riemannsum',[f,function(){ return n.Value();}, 'lower',-3,3],{fillColor:'#ffff00', fillOpacity:0.3});

			brd.create('text',[-2,-2,function(){ return 'Diff='+(brd.riemannsum(f,n.Value(),'upper',-3,3)-brd.riemannsum(f,n.Value(),'lower',-3,3)).toFixed(4); }]);
			</source>

	[[Category:Calculus]]		[[Category:Calculus]]
	[[Category:Examples]]		[[Category:Examples]]

A WASSERMANN at 12:45, 11 May 2010

2010-05-11T12:45:17Z

← Older revision		Revision as of 12:45, 11 May 2010
Line 9:		Line 9:

	var f = brd.lagrangePolynomial(p);		var f = brd.lagrangePolynomial(p);
	var n = brd.create('slider',[[-1,3],[2,3],[1,10,50]],{name:'n',snapWidth:1});		var n = brd.create('slider',[[-1,3],[2,3],[1,10,100]],{name:'n',snapWidth:1});
	var plot = brd.create('functiongraph',[f,-3,3]);		var plot = brd.create('functiongraph',[f,-3,3]);

A WASSERMANN at 12:44, 11 May 2010

2010-05-11T12:44:16Z

← Older revision		Revision as of 12:44, 11 May 2010
Line 15:		Line 15:
	var lo = brd.create('riemannsum',[f,function(){ return n.Value();}, 'lower',-3,3],{fillColor:'#ffff00', fillOpacity:0.3});		var lo = brd.create('riemannsum',[f,function(){ return n.Value();}, 'lower',-3,3],{fillColor:'#ffff00', fillOpacity:0.3});

	brd.createElement('text',[-2,-3,function(){ return 'Diff='+(brd.riemannsum(f,n.Value(),'upper',-3,3)-brd.riemannsum(f,n.Value(),'lower',-3,3)).toFixed(4); }]);		brd.createElement('text',[-2,-2,function(){ return 'Diff='+(brd.riemannsum(f,n.Value(),'upper',-3,3)-brd.riemannsum(f,n.Value(),'lower',-3,3)).toFixed(4); }]);
	</jsxgraph>		</jsxgraph>

	[[Category:Calculus]]		[[Category:Calculus]]
	[[Category:Examples]]		[[Category:Examples]]

A WASSERMANN at 12:44, 11 May 2010

2010-05-11T12:44:05Z

← Older revision		Revision as of 12:44, 11 May 2010
Line 1:		Line 1:
	<jsxgraph width="800" height="400" box="box">		<jsxgraph width="800" height="400" box="box">
	var brd = JXG.JSXGraph.initBoard('box', {boundingbox:[-3,4,3,-4],axis:true});		var brd = JXG.JSXGraph.initBoard('box', {boundingbox:[-3,5,3,-3],axis:true});
	var p = [];		var p = [];
	p.push(brd.create('point',[-2.7,(Math.random()-0.5)*5]));		p.push(brd.create('point',[-2.7,(Math.random()-0.2)*5]));
	p.push(brd.create('point',[-1,(Math.random()-0.5)*5]));		p.push(brd.create('point',[-1,(Math.random()-0.2)*5]));
	p.push(brd.create('point',[0,(Math.random()-0.5)*5]));		p.push(brd.create('point',[0,(Math.random()-0.2)*5]));
	p.push(brd.create('point',[1,(Math.random()-0.5)*5]));		p.push(brd.create('point',[1,(Math.random()-0.2)*5]));
	p.push(brd.create('point',[2.7,(Math.random()-0.5)*5]));		p.push(brd.create('point',[2.7,(Math.random()-0.2)*5]));

	var f = brd.lagrangePolynomial(p);		var f = brd.lagrangePolynomial(p);
Line 12:		Line 12:
	var plot = brd.create('functiongraph',[f,-3,3]);		var plot = brd.create('functiongraph',[f,-3,3]);

	var up = brd.~~createElement~~('riemannsum',[f,function(){ return n.Value();}, 'upper',-3,3],{fillColor:'#ff0000', fillOpacity:0.3});		var up = brd.create('riemannsum',[f,function(){ return n.Value();}, 'upper',-3,3],{fillColor:'#ff0000', fillOpacity:0.3});
	var lo = brd.~~createElement~~('riemannsum',[f,function(){ return n.Value();}, 'lower',-3,3],{fillColor:'#ffff00', fillOpacity:0.3});		var lo = brd.create('riemannsum',[f,function(){ return n.Value();}, 'lower',-3,3],{fillColor:'#ffff00', fillOpacity:0.3});

	/*		brd.createElement('text',[-2,-3,function(){ return 'Diff='+(brd.riemannsum(f,n.Value(),'upper',-3,3)-brd.riemannsum(f,n.Value(),'lower',-3,3)).toFixed(4); }]);
	brd.createElement('text',[-6,-3,function(){ return '~~Sum~~='+(brd.riemannsum(f,s.Value(),~~document.getElementById(~~'~~sumtype~~').~~value~~,a.Value(),~~b.Value()~~)).toFixed(4); }]);
	~~brd.create('text',[3,-3,'`sum_(i=0)^n i^2`']);~~
	*/
	</jsxgraph>		</jsxgraph>

	[[Category:Calculus]]		[[Category:Calculus]]
	[[Category:Examples]]		[[Category:Examples]]

A WASSERMANN at 12:40, 11 May 2010

2010-05-11T12:40:56Z

← Older revision		Revision as of 12:40, 11 May 2010
Line 2:		Line 2:
	var brd = JXG.JSXGraph.initBoard('box', {boundingbox:[-3,4,3,-4],axis:true});		var brd = JXG.JSXGraph.initBoard('box', {boundingbox:[-3,4,3,-4],axis:true});
	var p = [];		var p = [];
	p.push(brd.create('point',[-2,(Math.random()-0.5)*5]));		p.push(brd.create('point',[-2.7,(Math.random()-0.5)*5]));
	p.push(brd.create('point',[-1,(Math.random()-0.5)*5]));		p.push(brd.create('point',[-1,(Math.random()-0.5)*5]));
	p.push(brd.create('point',[0,(Math.random()-0.5)*5]));		p.push(brd.create('point',[0,(Math.random()-0.5)*5]));
	p.push(brd.create('point',[1,(Math.random()-0.5)*5]));		p.push(brd.create('point',[1,(Math.random()-0.5)*5]));
	p.push(brd.create('point',[2,(Math.random()-0.5)*5]));		p.push(brd.create('point',[2.7,(Math.random()-0.5)*5]));

	var f = brd.lagrangePolynomial(p);		var f = brd.lagrangePolynomial(p);
Line 12:		Line 12:
	var plot = brd.create('functiongraph',[f,-3,3]);		var plot = brd.create('functiongraph',[f,-3,3]);

	var os = brd.createElement('riemannsum',[f,		var up = brd.createElement('riemannsum',[f,function(){ return n.Value();}, 'upper',-3,3],{fillColor:'#ff0000', fillOpacity:0.3});
	function(){ return n.Value();}, 'upper',		var lo = brd.createElement('riemannsum',[f,function(){ return n.Value();}, 'lower',-3,3],{fillColor:'#ffff00', fillOpacity:0.3});
	-3,3],
	{fillColor:'#ffff00', fillOpacity:0.3});

	/*		/*

A WASSERMANN at 12:39, 11 May 2010

2010-05-11T12:39:42Z

← Older revision		Revision as of 12:39, 11 May 2010
Line 13:		Line 13:

	var os = brd.createElement('riemannsum',[f,		var os = brd.createElement('riemannsum',[f,
	function(){ return n.Value();}, 'upper'},		function(){ return n.Value();}, 'upper',
	-3,3],		-3,3],
	{fillColor:'#ffff00', fillOpacity:0.3});		{fillColor:'#ffff00', fillOpacity:0.3});

A WASSERMANN at 12:39, 11 May 2010

2010-05-11T12:39:32Z

← Older revision		Revision as of 12:39, 11 May 2010
Line 12:		Line 12:
	var plot = brd.create('functiongraph',[f,-3,3]);		var plot = brd.create('functiongraph',[f,-3,3]);

	/*
	var os = brd.createElement('riemannsum',[f,		var os = brd.createElement('riemannsum',[f,
	function(){ return s.Value();}, ~~function(){ return document.getElementById(~~'~~sumtype~~'~~).value;~~},		function(){ return n.Value();}, 'upper'},
	~~function(){return a.Value();}~~,		-3,3],
	~~function(){return b.Value();}~~
	],
	{fillColor:'#ffff00', fillOpacity:0.3});		{fillColor:'#ffff00', fillOpacity:0.3});

			/*
	brd.createElement('text',[-6,-3,function(){ return 'Sum='+(brd.riemannsum(f,s.Value(),document.getElementById('sumtype').value,a.Value(),b.Value())).toFixed(4); }]);		brd.createElement('text',[-6,-3,function(){ return 'Sum='+(brd.riemannsum(f,s.Value(),document.getElementById('sumtype').value,a.Value(),b.Value())).toFixed(4); }]);

	brd.create('text',[3,-3,'`sum_(i=0)^n i^2`']);		brd.create('text',[3,-3,'`sum_(i=0)^n i^2`']);
	*/		*/

A WASSERMANN at 12:38, 11 May 2010

2010-05-11T12:38:04Z

← Older revision		Revision as of 12:38, 11 May 2010
Line 2:		Line 2:
	var brd = JXG.JSXGraph.initBoard('box', {boundingbox:[-3,4,3,-4],axis:true});		var brd = JXG.JSXGraph.initBoard('box', {boundingbox:[-3,4,3,-4],axis:true});
	var p = [];		var p = [];
	p.push(brd.create('point',[-2,(Math.random()-0.5)*5]);		p.push(brd.create('point',[-2,(Math.random()-0.5)*5]));
	p.push(brd.create('point',[-1,(Math.random()-0.5)*5]);		p.push(brd.create('point',[-1,(Math.random()-0.5)*5]));
	p.push(brd.create('point',[0,(Math.random()-0.5)*5]);		p.push(brd.create('point',[0,(Math.random()-0.5)*5]));
	p.push(brd.create('point',[1,(Math.random()-0.5)*5]);		p.push(brd.create('point',[1,(Math.random()-0.5)*5]));
	p.push(brd.create('point',[2,(Math.random()-0.5)*5]);		p.push(brd.create('point',[2,(Math.random()-0.5)*5]));

	var f = brd.lagrangePolynomial(p);		var f = brd.lagrangePolynomial(p);

A WASSERMANN: New page: var brd = JXG.JSXGraph.initBoard('box', {boundingbox:[-3,4,3,-4],axis:true}); var p = []; p.push(brd.create('point',[-2,(Math.random()-0.5)*5]...

2010-05-11T12:37:30Z

New page: <jsxgraph width="800" height="400" box="box"> var brd = JXG.JSXGraph.initBoard('box', {boundingbox:[-3,4,3,-4],axis:true}); var p = []; p.push(brd.create('point',[-2,(Math.random()-0.5)*5]...

New page

<jsxgraph width="800" height="400" box="box">
var brd = JXG.JSXGraph.initBoard('box', {boundingbox:[-3,4,3,-4],axis:true});
var p = [];
p.push(brd.create('point',[-2,(Math.random()-0.5)*5]);
p.push(brd.create('point',[-1,(Math.random()-0.5)*5]);
p.push(brd.create('point',[0,(Math.random()-0.5)*5]);
p.push(brd.create('point',[1,(Math.random()-0.5)*5]);
p.push(brd.create('point',[2,(Math.random()-0.5)*5]);

var f = brd.lagrangePolynomial(p);
var n = brd.create('slider',[[-1,3],[2,3],[1,10,50]],{name:'n',snapWidth:1});
var plot = brd.create('functiongraph',[f,-3,3]);

/*
var os = brd.createElement('riemannsum',[f,
function(){ return s.Value();}, function(){ return document.getElementById('sumtype').value;},
function(){return a.Value();},
function(){return b.Value();}
],
{fillColor:'#ffff00', fillOpacity:0.3});

brd.createElement('text',[-6,-3,function(){ return 'Sum='+(brd.riemannsum(f,s.Value(),document.getElementById('sumtype').value,a.Value(),b.Value())).toFixed(4); }]);

brd.create('text',[3,-3,'`sum_(i=0)^n i^2`']);
*/
</jsxgraph>

[[Category:Calculus]]
[[Category:Examples]]