TERADA Bunkoo, SAKATA Hirosi, SAITOO Teisiroo：
Prakatika ekzerco por diferencialo kaj integralo

Deziro

La libro enkondukas fundamentan analitikon, por ekzemple difinon de ε-δ de limeso.

Impreso

http://www.asciimathml.com/dredging/media/excersises/graphtypes.html (rompita ligo)

kateno

` y = a / 2 (e^(x/a) + e^(-x/a)) `

agraph plot(0.5*(e^(x)+e^(-x))) endgraph

Trifoio

`r = a sin 3 theta`

agraph TypeOfGraph=Polar; setViewport(600,600,60); setGraphArea(-5,5,-5,5); setGridandTicks(1,1/24,1,1); setLabelsandTitle(Automatic,"Im","Re","Trifolio"); axes(); setPen("2","green"); polarplot("4*sin(3*t)",0, 2*pi); axesBorder("1","light"+gridstroke); viewportBorder("3","black"); endagraph

Cikloid

` x=a(theta - sin theta) `
` y=a(1 - cos theta) `

agraph TypeOfGraph=Polar; setViewport(600,600,60); setGraphArea(-5,5,-5,5); setGridandTicks(1,1/24,1,1); setLabelsandTitle(Automatic,"Im","Re","Cikloid"); axes(); setPen("2","blue"); plot(["0.5*(t-sin(t))", "0.5*(1-cos(t))"],0,10); axesBorder("1","light"+gridstroke); viewportBorder("3","black"); endagraph

asteroido(hipocikloido)

` x^(2/3) + y^(2/3) = a^(2/3) `

agraph TypeOfGraph=Polar; setViewport(600,600,60); setGraphArea(-5,5,-5,5); setGridandTicks(1,1/24,1,1); setLabelsandTitle(Automatic,"Im","Re","asteroido(hipocikloido)"); axes(); setPen("2","green"); plot(["cos(t)*cos(t)*cos(t)", en:"sin(t)*sin(t)*sin(t)"], 0, 2 * pi); axesBorder("1","light"+gridstroke); viewportBorder("3","black"); endagraph

lemniskato

` (x^2 + y^2)^2 - 2a^2(x^2 - y^2) = 0 `

` r^2 = a^2 cos (2 theta) `

agraph TypeOfGraph=Polar; setViewport(600,600,60); setGraphArea(-5,5,-5,5); setGridandTicks(1,1/24,1,1); setLabelsandTitle(Automatic,"Im","Re","lemniskato"); axes(); setPen("2","green"); polarplot("sqrt(cos(2*t))",0, pi); polarplot("-sqrt(cos(2*t))",0, pi); axesBorder("1","light"+gridstroke); viewportBorder("3","black"); endagraph

kartecia folio

`x^3 + y^3 - 3 a x y = 0`

`x = 3at/(1+t^3), y=3at^2/(1+t^3) (t != -1)`

agraph TypeOfGraph=Polar; setViewport(600,600,60); setGraphArea(-5,5,-5,5); setGridandTicks(1,1/24,1,1); setLabelsandTitle(Automatic,"Im","Re","kartecia folio"); axes(); setPen("2","green"); plot(["3*t/(1+t^3)","3*(t^2)/(1+t^3)"], -0.8, 20); plot(["3*t/(1+t^3)","3*(t^2)/(1+t^3)"], -20, -1.2); axesBorder("1","light"+gridstroke); viewportBorder("3","black"); endagraph

strofoido

` (x + a)x^2 + (x - a)y^2 = 0`

` x = a(t^2 - 1)/(t^2 + 1), y = at(t^2 - 1)/(t^2 + 1) `

agraph TypeOfGraph=Polar; setViewport(600,600,60); setGraphArea(-5,5,-5,5); setGridandTicks(1,1/24,1,1); setLabelsandTitle(Automatic,"Im","Re","strofoido"); axes(); setPen("2","green"); plot(["(t^2-1)/(1+t^2)","t*(t^2-1)/(1+t^2)"], -10, 10); axesBorder("1","light"+gridstroke); viewportBorder("3","black"); endagraph

Cisoido

` x^3 + (x - a)y^2 = 0`

` x = at^2/(1 + t^2), y = at^3/(1 + t^2) `

agraph TypeOfGraph=Polar; setViewport(600,600,60); setGraphArea(-5,5,-5,5); setGridandTicks(1,1/24,1,1); setLabelsandTitle(Automatic,"Im","Re","Cisoido"); axes(); setPen("2","green"); plot(["t^2/(1+t^2)","t^3/(1+t^2)"], -10, 10); axesBorder("1","light"+gridstroke); viewportBorder("3","black"); endagraph

paskala limako

` r = b - a cos theta`

agraph TypeOfGraph=Polar; setViewport(600,600,60); setGraphArea(-5,5,-5,5); setGridandTicks(1,1/24,1,1); setLabelsandTitle(Automatic,"Im","Re","paskala limako"); axes(); setPen("2","green"); plot(["2(cos(t))^2+cos(t)","2cos(t)sin(t)+sin(t)"], 0, 2*pi); axesBorder("1","light"+gridstroke); viewportBorder("3","black"); endagraph

parabolo

` x^(1/2) + y^(1/2) = a^(1/2) `

agraph TypeOfGraph=Polar; setViewport(600,600,60); setGraphArea(-5,5,-5,5); setGridandTicks(1,1/24,1,1); setLabelsandTitle(Automatic,"Im","Re","parabolo"); axes(); setPen("2","green"); plot(["(cos(t))^4","(sin(t))^4"], 0, 0.5*pi); axesBorder("1","light"+gridstroke); viewportBorder("3","black"); endagraph

konkoido

` b^2 y^2 = (y - a)^2(x^2 + y^2) `

` x = a + b cos theta, y = a tan theta + b sin theta

` r = a / (cos theta) + b `

agraph TypeOfGraph=Polar; setViewport(600,600,60); setGraphArea(-5,5,-5,5); setGridandTicks(1,1/24,1,1); setLabelsandTitle(Automatic,"Im","Re","Konkoido"); axes(); setPen("2","green"); plot(["1+2*cos(t)", "tan(t)+2*sin(t)"], -1.3, 1.3); axesBorder("1","light"+gridstroke); viewportBorder("3","black"); endagraph

kardioido

` r = a(1 - cos theta) `

agraph TypeOfGraph=Polar; setViewport(600,600,60); setGraphArea(-5,5,-5,5); setGridandTicks(1,1/24,1,1); setLabelsandTitle(Automatic,"Im","Re","kardioido"); axes(); setPen("2","green"); plot(["(1+cos(t))cos(t)", "(1+cos(t))sin(t)"],0,2*pi); axesBorder("1","light"+gridstroke); viewportBorder("3","black"); endagraph

kvarfolio

`r = a cos 2 theta`

agraph TypeOfGraph=Polar; setViewport(600,600,60); setGraphArea(-5,5,-5,5); setGridandTicks(1,1/24,1,1); setLabelsandTitle(Automatic,"Im","Re","kvarfolio"); axes(); setPen("2","green"); polarplot("4*sin(2*t)",0, 2*pi); axesBorder("1","light"+gridstroke); viewportBorder("3","black"); endagraph

hiperbola spiralo

` r theta = a `

agraph
TypeOfGraph=Polar;
setViewport(600,600,60);
setGraphArea(-5,5,-5,5);
setGridandTicks(1,1/24,1,1);
setLabelsandTitle(Automatic,"Im","Re","hiperbola spiralo");
axes(); 
setPen("2","green");
polarplot("-pi/t",0, 5*pi);
axesBorder("1","light"+gridstroke);
viewportBorder("3","black");
endagraph

logaritma spiralo

` r = e^(a theta) `

agraph
TypeOfGraph=Polar;
setViewport(600,600,60);
setGraphArea(-5,5,-5,5);
setGridandTicks(1,1/24,1,1);
setLabelsandTitle(Automatic,"Im","Re","logaritma spiralo");
axes(); 
setPen("2","green");
polarplot("exp(t/pi)",-4*pi, 4*pi);
axesBorder("1","light"+gridstroke);
viewportBorder("3","black");
endagraph

arkimeda spiralo

agraph TypeOfGraph=Polar; setViewport(600,600,60); setGraphArea(-5,5,-5,5); setGridandTicks(1,1/24,1,1); setLabelsandTitle(Automatic,"Im","Re","arkimeda spiralo"); axes(); setPen("2","blue"); plot(["t*cos(pi*t)", "t*sin(pi*t)"],0,5); setPen("2","green"); polarplot("-t/pi",0,5*pi); axesBorder("1","light"+gridstroke); viewportBorder("3","black"); endagraph

ekspresion

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Informoj

Lernejo de Marinkjo > Libroj de matematiko > TERADA Bunkoo, SAKATA Hirosi, SAITOO Teisiroo:Ekzerco por diferencialo kaj integralo