Modern alkalmazott anal\303\255 zis
J\303\241rai Antal
Ezek a programok csak szeml\303\251ltet\303\251sre szolg\303\241lnak
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn
Bevezet\303\251 s
I. M\303\251 rt\303\251 k \303\251 s integr\303\241 l
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn
1. M\303\251 rt\303\251 kelm\303\251let
2. Integr\303\241 l\303\241 s
II. Funkcion\303\241 lanal\303\255 zis
5. Line\303\241 ris oper\303\241 torok
7. Spektr\303\241 lelm\303\251 let
8. Kompakt oper\303\241 torok
9. Differenci\303\241 lsz\303\241 m\303\255 t\303\241 s
III. Vektoranal\303\255 zis
10. A differenci\303\241 lgeometria alapjai
11. Stieltjes-integr\303\241 l \303\251 s g\303\266 rbe menti integr\303\241 l
12. Differenci\303\241 lform\303\241 k integr\303\241 l\303\241 sa
IV. Komplex f\303\274ggv\303\251nytan
13. Analitikus f\303\274ggv\303\251nyek
14. Holomorf f\303\274ggv\303\251nyek
15. Meromorf f\303\274ggv\303\251nyek
V. Fourier-elm\303\251 let
16. Klasszikus Fourier-sorok
17. Ortogon\303\241 lis polinomok
*17.26. Inverz interpol\303\241 ci\303\263 .
x:='x'; fsolve(2*sin(x)=x,x);
SSJ4RzYi
JCIiIUYj
x:=1.;2*sin(%);2*sin(%);2*sin(%);2*sin(%);2*sin(%);2*sin(%);2*sin(%);2*sin(%);2*sin(%);2*sin(%);2*sin(%);2*sin(%);2*sin(%);2*sin(%);2*sin(%);2*sin(%);2*sin(%);2*sin(%);2*sin(%);2*sin(%);2*sin(%);2*sin(%);2*sin(%);2*sin(%);2*sin(%);2*sin(%);2*sin(%);2*sin(%);2*sin(%);2*sin(%);2*sin(%);2*sin(%);2*sin(%);2*sin(%);2*sin(%);2*sin(%);2*sin(%);2*sin(%);2*sin(%);2*sin(%);2*sin(%);2*sin(%);2*sin(%);2*sin(%);2*sin(%);2*sin(%);2*sin(%);
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halfing:=proc(a,b,f::procedure,eps,feps,N) local aa,bb,ab,ff,delta,n;
if f(a)<0 then aa:=a; bb:=b; else aa:=b; bb:=a; fi;
if f(a)*f(b)>0 then error "bad interval" fi;
delta:=abs(a-b);
for n to N do
ab:=(aa+bb)/2.;
delta:=delta/2.;
ff:=f(ab);
if abs(ff)<feps and delta<eps then return ab fi;
if ff<0 then aa:=ab else bb:=ab fi;
od;
FAIL;
end;
Zio2KEkiYUc2IkkiYkdGJSdJImZHRiVJKnByb2NlZHVyZUclKnByb3RlY3RlZEdJJGVwc0dGJUklZmVwc0dGJUkiTkdGJTYoSSNhYUdGJUkjYmJHRiVJI2FiR0YlSSNmZkdGJUkmZGVsdGFHRiVJIm5HRiVGJUYlQydAJTItRig2I0YkIiIhQyQ+Ri9GJD5GMEYmQyQ+Ri9GJj5GMEYkQCQyRjoqJkY4IiIiLUYoNiNGJkZEWVEtYmFkfmludGVydmFsRiU+RjMtSSRhYnNHRio2IywmRiRGREYmISIiPyhGNEZERkRGLUkldHJ1ZUdGKkMnPkYxKiYsJkYvRkRGMEZERkQkIiIjRjpGTj5GMyomRjNGREZVRk4+RjItRig2I0YxQCQzMi1GSzYjRjJGLDJGM0YrT0YxQCUyRjJGOj5GL0YxPkYwRjFJJUZBSUxHRipGJUYlRiU=
halfing(-1,1,x->x^2,1,1,10);
Error, (in halfing) bad interval
halfing(1.,2.,x->2*sin(x)-x,0.0000001,100,10);
SSVGQUlMRyUqcHJvdGVjdGVkRw==
debug(halfing); halfing(1.,2.,x->2*sin(x)-x,0.000001,100,20);
SShoYWxmaW5nRzYi
{--> enter halfing, args = 1., 2., proc (x) options operator, arrow; 2*sin(x)-x end proc, 0.1e-5, 100, 20
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JCIrSVhSSHchIzo=
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JCIrSydbdCE+ISM6
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<-- exit halfing (now at top level) = 1.895493506}
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regulafalsi:=proc(a,b,f::procedure,eps,feps,N) local aa,bb,ab,ff,fa,fb,delta,n;
if f(a)<0 then aa:=a; bb:=b; else aa:=b; bb:=a; fi;
fa:=f(aa); fb:=f(bb);
if fa*fb>0 then error "bad interval" fi;
delta:=abs(aa-bb);
for n to N do
ab:=aa-fa/(fb-fa)*(bb-aa);
ff:=f(ab);
if ff<0 then delta:=abs(aa-ab); aa:=ab; fa:=ff;
else delta:=abs(ab-bb); bb:=ab; fb:=ff fi;
if abs(ff)<feps and delta<eps then return ab fi;
od;
FAIL;
end;
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
regulafalsi(-1,1,x->x^2,1,1,10);
Error, (in regulafalsi) bad interval
regulafalsi(1.,2.,x->2*sin(x)-x,0.000001,100,7);
JCIra1VcJio9ISIq
secant:=proc(a,b,f::procedure,eps,feps,N) local aa,bb,ab,ff,fa,fb,delta,n;
aa:=a; bb:=b;
fa:=f(aa); fb:=f(bb);
delta:=abs(aa-bb);
for n to N do
ab:=aa-fa/(fb-fa)*(bb-aa);
ff:=f(ab);
aa:=bb; fa:=fb; bb:=ab; fb:=ff;
delta:=abs(aa-bb);
if abs(ff)<feps and delta<eps then return ab fi;
od;
FAIL;
end;
Zio2KEkiYUc2IkkiYkdGJSdJImZHRiVJKnByb2NlZHVyZUclKnByb3RlY3RlZEdJJGVwc0dGJUklZmVwc0dGJUkiTkdGJTYqSSNhYUdGJUkjYmJHRiVJI2FiR0YlSSNmZkdGJUkjZmFHRiVJI2ZiR0YlSSZkZWx0YUdGJUkibkdGJUYlRiVDKT5GL0YkPkYwRiY+RjMtRig2I0YvPkY0LUYoNiNGMD5GNS1JJGFic0dGKjYjLCZGLyIiIkYwISIiPyhGNkZFRkVGLUkldHJ1ZUdGKkMqPkYxLCZGL0ZFKihGM0ZFLCZGNEZFRjNGRkZGLCZGMEZFRi9GRkZFRkY+RjItRig2I0YxPkYvRjA+RjNGND5GMEYxPkY0RjJGQEAkMzItRkI2I0YyRiwyRjVGK09GMUklRkFJTEdGKkYlRiVGJQ==
secant(-1.,1.,x->x^2,10.,10.,10);
SSVGQUlMRyUqcHJvdGVjdGVkRw==
debug(secant); secant(-1.,1.,x->x^2,10.,10.,2);
SSdzZWNhbnRHNiI=
{--> enter secant, args = -1., 1., proc (x) options operator, arrow; x^2 end proc, 10., 10., 2
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<-- exit secant (now at top level) = FAIL}
SSVGQUlMRyUqcHJvdGVjdGVkRw==
secant(-1.,0.5,x->x^2,0.01,100.,10);
{--> enter secant, args = -1., .5, proc (x) options operator, arrow; x^2 end proc, 0.1e-1, 100., 10
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<-- exit secant (now at top level) = 0.1315789474e-1}
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secant(1.,2.,x->2*sin(x)-x,0.000001,100,10);
{--> enter secant, args = 1., 2., proc (x) options operator, arrow; 2*sin(x)-x end proc, 0.1e-5, 100, 10
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<-- exit secant (now at top level) = 1.895494267}
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debug(secant); secant(1.,2.,x->2*sin(x)-x,0.000001,100,6);
SSdzZWNhbnRHNiI=
{--> enter secant, args = 1., 2., proc (x) options operator, arrow; 2*sin(x)-x end proc, 0.1e-5, 100, 6
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<-- exit secant (now at top level) = 1.895494267}
JCIrblVcJio9ISIq
Student[Calculus1][NewtonsMethodTutor](x-cos(x),0);
Error, (in Student:-Calculus1:-NewtonsMethodTutor) the derivative is 0 after the 1st iteration
Newton:=proc(x0,f::procedure,fp::procedure,eps,feps,N) local x,xx,delta,n;
x:=x0;
for n to N do
xx:=x-evalf(f(x)/fp(x));
delta:=abs(x-xx);
if abs(f(xx))<feps and delta<eps then return xx fi;
x:=xx;
od; FAIL; end;
Zio2KEkjeDBHNiInSSJmR0YlSSpwcm9jZWR1cmVHJSpwcm90ZWN0ZWRHJ0kjZnBHRiVGKEkkZXBzR0YlSSVmZXBzR0YlSSJOR0YlNiZJInhHRiVJI3h4R0YlSSZkZWx0YUdGJUkibkdGJUYlRiVDJT5GMEYkPyhGMyIiIkY3Ri5JJXRydWVHRilDJj5GMSwmRjBGNy1JJmV2YWxmR0YpNiMqJi1GJzYjRjBGNy1GK0ZBISIiRkM+RjItSSRhYnNHRik2IywmRjBGN0YxRkNAJDMyLUZGNiMtRic2I0YxRi0yRjJGLE9GMT5GMEYxSSVGQUlMR0YpRiVGJUYl
Newton(1.,x->2*sin(x)-x,x->2*cos(x)-1,0.000001,100,6);
SSVGQUlMRyUqcHJvdGVjdGVkRw==
debug(Newton); Newton(1.,x->2*sin(x)-x,x->2*cos(x)-1,0.000001,100,6);
SSdOZXd0b25HNiI=
{--> enter Newton, args = 1., proc (x) options operator, arrow; 2*sin(x)-x end proc, proc (x) options operator, arrow; 2*cos(x)-1 end proc, 0.1e-5, 100, 6
JCIiIiIiIQ==
JCErPDF1c3UhIio=
JCIrPDF1cyUpISIq
JCErPDF1c3UhIio=
JCIraUMmeVciISIp
JCIrQ2w3Jj4jISIp
JCIraUMmeVciISIp
JCIrIlFZXiRwISIq
JCIrUiN5TGEoISIq
JCIrIlFZXiRwISIq
JCIrSC1qajshIik=
JCIrNGY6LCgqISIq
JCIrSC1qajshIik=
JCIrV1o/UyQpISIq
JCIrWXY0J0gpISIq
JCIrV1o/UyQpISIq
JCIrTXAzVlwhIio=
JCIrNXk2KFIkISIq
JCIrTXAzVlwhIio=
SSVGQUlMRyUqcHJvdGVjdGVkRw==
<-- exit Newton (now at top level) = FAIL}
SSVGQUlMRyUqcHJvdGVjdGVkRw==
Newton(1.5,x->2*sin(x)-x,x->2*cos(x)-1,0.000001,100,6);
{--> enter Newton, args = 1.5, proc (x) options operator, arrow; 2*sin(x)-x end proc, proc (x) options operator, arrow; 2*cos(x)-1 end proc, 0.1e-5, 100, 6
JCIjOiEiIg==
JCIrKyNlbDIjISIq
JCIqKyNlbGQhIio=
JCIrKyNlbDIjISIq
JCIrO21dNT4hIio=
JCIqJWVeZzshIio=
JCIrO21dNT4hIio=
JCIrLj9pJio9ISIq
JCIpOFkpWyIhIio=
JCIrLj9pJio9ISIq
JCIrd1VcJio9ISIq
JCInRng3ISIq
JCIrd1VcJio9ISIq
JCIrblVcJio9ISIq
JCIiKiEiKg==
<-- exit Newton (now at top level) = 1.895494267}
JCIrblVcJio9ISIq
modNewton:=proc(x0,f::procedure,q,eps,feps,N) local x,xx,delta,n;
x:=x0;
for n to N do
xx:=x-evalf(f(x)/q);
delta:=abs(x-xx);
if abs(f(xx))<feps and delta<eps then return xx fi;
x:=xx;
od; FAIL; end;
Zio2KEkjeDBHNiInSSJmR0YlSSpwcm9jZWR1cmVHJSpwcm90ZWN0ZWRHSSJxR0YlSSRlcHNHRiVJJWZlcHNHRiVJIk5HRiU2JkkieEdGJUkjeHhHRiVJJmRlbHRhR0YlSSJuR0YlRiVGJUMlPkYvRiQ/KEYyIiIiRjZGLUkldHJ1ZUdGKUMmPkYwLCZGL0Y2LUkmZXZhbGZHRik2IyomLUYnNiNGL0Y2RiohIiJGQT5GMS1JJGFic0dGKTYjLCZGL0Y2RjBGQUAkMzItRkQ2Iy1GJzYjRjBGLDJGMUYrT0YwPkYvRjBJJUZBSUxHRilGJUYlRiU=
modNewton(2.,x->2*sin(x)-x,2*cos(2.)-1,0.000001,100,10);
JCIrUVZcJio9ISIq
debug(modNewton); modNewton(1.5,x->2*sin(x)-x,2*cos(1.5)-1,0.000001,100,10);
SSptb2ROZXd0b25HNiI=
{--> enter modNewton, args = 1.5, proc (x) options operator, arrow; 2*sin(x)-x end proc, -.8585255967, 0.1e-5, 100, 10
JCIjOiEiIg==
JCIrKyNlbDIjISIq
JCIqKyNlbGQhIio=
JCIrKyNlbDIjISIq
JCIrRFd0JnAiISIq
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JCIrRFd0JnAiISIq
JCIrZTUpPi4jISIq
JCIqTG1DTyQhIio=
JCIrZTUpPi4jISIq
JCIrZidcOHYiISIq
JCIqKlJKMUchIio=
JCIrZidcOHYiISIq
JCIrVmc1Lj8hIio=
JCIqJVFjPEQhIio=
JCIrVmc1Lj8hIio=
JCIrUSRvXnkiISIq
JCIqMHgkekAhIio=
JCIrUSRvXnkiISIq
JCIrWSF5Pyk+ISIq
JCIqMyg0cD4hIio=
JCIrWSF5Pyk+ISIq
JCIrKTMpbzM9ISIq
JCIqZSoqUXQiISIq
JCIrKTMpbzM9ISIq
JCIrIyp5ImYnPiEiKg==
JCIqLylIczohIio=
JCIrIyp5ImYnPiEiKg==
JCIrPj83RT0hIio=
JCIqdGV6UiIhIio=
JCIrPj83RT0hIio=
SSVGQUlMRyUqcHJvdGVjdGVkRw==
<-- exit modNewton (now at top level) = FAIL}
SSVGQUlMRyUqcHJvdGVjdGVkRw==
*17.27. Egy p\303\251 lda: a konvergencia rendje.
quasiNewton:=proc(x0,f::procedure,fp::procedure,alpha,eps,feps,N) local x,xx,delta,n;
x:=x0;
for n to N do
xx:=x-alpha*evalf(f(x)/fp(x));
delta:=abs(x-xx);
if abs(f(xx))<feps and delta<eps then return xx fi;
x:=xx;
od; FAIL; end;
Zio2KUkjeDBHNiInSSJmR0YlSSpwcm9jZWR1cmVHJSpwcm90ZWN0ZWRHJ0kjZnBHRiVGKEkmYWxwaGFHRiVJJGVwc0dGJUklZmVwc0dGJUkiTkdGJTYmSSJ4R0YlSSN4eEdGJUkmZGVsdGFHRiVJIm5HRiVGJUYlQyU+RjFGJD8oRjQiIiJGOEYvSSV0cnVlR0YpQyY+RjIsJkYxRjgqJkYsRjgtSSZldmFsZkdGKTYjKiYtRic2I0YxRjgtRitGQyEiIkY4RkU+RjMtSSRhYnNHRik2IywmRjFGOEYyRkVAJDMyLUZINiMtRic2I0YyRi4yRjNGLU9GMj5GMUYySSVGQUlMR0YpRiVGJUYl
debug(quasiNewton);
quasiNewton(1,x->sin(x)^4,x->4*sin(x)^3*cos(x),1.,0.000001,100,10);
SSxxdWFzaU5ld3Rvbkc2Ig==
{--> enter quasiNewton, args = 1, proc (x) options operator, arrow; sin(x)^4 end proc, proc (x) options operator, arrow; 4*sin(x)^3*cos(x) end proc, 1., 0.1e-5, 100, 10
IiIi
JCIrKW8hWzFoISM1
JCIrNyQ+TipRISM1
JCIrKW8hWzFoISM1
JCIrTTN4Y1YhIzU=
JCIrYSk0KFw8ISM1
JCIrTTN4Y1YhIzU=
JCIrVGAqSD4kISM1
JCIrJFx2UDsiISM1
JCIrVGAqSD4kISM1
JCIrYFtZbUIhIzU=
JCIqKVtJbCMpISM1
JCIrYFtZbUIhIzU=
JCIrLzxiajwhIzU=
JCIqXEoiSGchIzU=
JCIrLzxiajwhIzU=
JCIrJltOIT04ISM1
JCIqPmleWCUhIzU=
JCIrJltOIT04ISM1
JCIrYjswbSkqISM2
JCIrJj4uVkokISM2
JCIrYjswbSkqISM2
JCIrSVhdIlIoISM2
JCIrRHJhdUMhIzY=
JCIrSVhdIlIoISM2
JCIreGREU2IhIzY=
JCIrYChbNyY9ISM2
JCIreGREU2IhIzY=
JCIrbEh4YFQhIzY=
JCIrN0dbJ1EiISM2
JCIrbEh4YFQhIzY=
SSVGQUlMRyUqcHJvdGVjdGVkRw==
<-- exit quasiNewton (now at top level) = FAIL}
SSVGQUlMRyUqcHJvdGVjdGVkRw==
quasiNewton(1,x->sin(x)^4,x->4*sin(x)^3*cos(x),4.,0.000001,100,10);
{--> enter quasiNewton, args = 1, proc (x) options operator, arrow; sin(x)^4 end proc, proc (x) options operator, arrow; 4*sin(x)^3*cos(x) end proc, 4., 0.1e-5, 100, 10
IiIi
JCEqRHhTZCYhIio=
JCIrRHhTZDohIio=
JCEqRHhTZCYhIio=
JCIqQVhPZichIzU=
JCIrczxXTGkhIzU=
JCIqQVhPZichIzU=
JCEoJz5zJiohIzY=
JCIrO3VALm0hIzY=
JCEoJz5zJiohIzY=
JCIjRyEjOQ==
JCIrR2c+cyYqISM5
JCIjRyEjOQ==
JCIiIUYj
JCIjRyEjOQ==
<-- exit quasiNewton (now at top level) = 0.}
JCIiIUYj
adaptiveNewton:=proc(x0,f::procedure,fp::procedure,eps,feps,N)
local x,xx,xxx,alpha,delta,q,n,m;
x:=x0; alpha:=1.;
for n to N do
xx:=x-alpha*evalf(f(x)/fp(x));
xxx:=xx-alpha*evalf(f(xx)/fp(xx));
delta:=abs(xxx-xx);
q:=(xxx-xx)/(xx-x);
m:=alpha/(1-q); alpha:=m;
if abs(f(xxx))<feps and delta<eps then return xxx,alpha fi;
x:=xxx;
od; FAIL; end;
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
adaptiveNewton(1.,x->sin(x)^4,x->4*sin(x)^3*cos(x),0.000001,100,10);
NiQkIiU5PCEjQiQiKysrKytTISIq
debug(adaptiveNewton);
adaptiveNewton(1.,x->sin(x)^4,x->4*sin(x)^3*cos(x),0.000001,100,10);
SS9hZGFwdGl2ZU5ld3Rvbkc2Ig==
{--> enter adaptiveNewton, args = 1., proc (x) options operator, arrow; sin(x)^4 end proc, proc (x) options operator, arrow; 4*sin(x)^3*cos(x) end proc, 0.1e-5, 100, 10
JCIiIiIiIQ==
JCIiIiIiIQ==
JCIrKG8hWzFoISM1
JCIrTDN4Y1YhIzU=
JCIrYSk0KFw8ISM1
JCIrM0ohUlwlISM1
JCIrWyZvaCI9ISIq
JCIrWyZvaCI9ISIq
JCIrTDN4Y1YhIzU=
JCIrJ1FlSkMjISM1
JCIrZmpCMjchIzU=
JCIrRj8jZi4iISM1
JCIrSj4+LFwhIzU=
JCIrcXMlPmMkISIq
JCIrcXMlPmMkISIq
JCIrZmpCMjchIzU=
JCIqN14mcDchIzU=
JCIqVT0oKlEiISM2
JCIreSN6MDgiISM2
JCIrRSxjWTUhIzU=
JCIrPS5JeVIhIio=
JCIrPS5JeVIhIio=
JCIqVT0oKlEiISM2
JCIoQSNRdiEjNw==
JCIpYlUqMyUhIzo=
JCIrWHhLKFwoISM6
JCIrSG1GQ2EhIzc=
JCIrNXUqKioqUiEiKg==
JCIrNXUqKioqUiEiKg==
JCIpYlUqMyUhIzo=
JCIlW0UhIzw=
JCIlOTwhI0I=
JCIrJ0cpKnprIyEjQg==
JCIrcnJCdmshIzs=
JCIrKysrK1MhIio=
JCIrKysrK1MhIio=
<-- exit adaptiveNewton (now at top level) = 0.1714e-19, 4.000000000}
NiQkIiU5PCEjQiQiKysrKytTISIq
*Feladat.
alpha:=1.*10^(-12); beta:=0.025; Gamma:=0.4; mu:=0.001; T:=.4; R:=3333.; e:=evalf(exp(1.));
JCIrKysrKzUhI0A=
JCIjRCEiJA==
JCIiJSEiIg==
JCIiIiEiJA==
JCIiJSEiIg==
JCIlTEwiIiE=
JCIrRz1HPUYhIio=
i:=alpha*(e^(U/beta)-1)-mu*U*(U-Gamma);
LCgqJiQiKysrKys1ISNAIiIiKSQiK0c9Rz1GISIqLCQqJiQiKysrKytTISIpRidJIlVHNiJGJ0YnRidGJ0YkISIiKigkRichIiRGJ0YxRicsJkYxRickIiIlRjNGM0YnRjM=
plot(i,U=0.0..0.45);
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
f:=i*R+U-T;
LCoqJiQiKysrK0xMISM9IiIiKSQiK0c9Rz1GISIqLCQqJiQiKysrKytTISIpRidJIlVHNiJGJ0YnRidGJyQiK0wrKytTISM1ISIiKigkIiVMTCEiJEYnRjFGJywmRjFGJyQiIiVGNkY2RidGNkYxRic=
plot(f,U=0..0.5);
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
halfing(0.2,0.4,x->subs(U=x,f),0.0001,1,30);
{--> enter halfing, args = .2, .4, proc (x) options operator, arrow; subs(U = x, f) end proc, 0.1e-3, 1, 30
JCIiIyEiIg==
JCIiJSEiIg==
JCIiIyEiIg==
JCIrKysrK0khIzU=
JCIrKysrKzUhIzU=
JCIoJWVDYCEjNQ==
JCIrKysrK0khIzU=
JCIrKysrK0QhIzU=
JCIrKysrK10hIzY=
JCEqIiozUlwjISM1
JCIrKysrK0QhIzU=
JCIrKysrXUYhIzU=
JCIrKysrK0QhIzY=
JCEqeWNHLSIhIzU=
JCIrKysrXUYhIzU=
JCIrKysrdkchIzU=
JCIrKysrXTchIzY=
JCEpW0VwViEjNQ==
JCIrKysrdkchIzU=
JCIrKytdUEghIzU=
JCIrKysrXWkhIzc=
JCEpIXo5IT0hIzU=
JCIrKytdUEghIzU=
JCIrKyt2b0ghIzU=
JCIrKysrREohIzc=
JCEoanEwJyEjNQ==
JCIrKyt2b0ghIzU=
JCIrK11QJSlIISM1
JCIrKytdaTohIzc=
JCEnQ1tIISM1
JCIrK11QJSlIISM1
JCIrK3Y9IypIISM1
JCIrKytdN3khIzg=
JCIoY0VgIyEjNQ==
JCIrK3Y9IypIISM1
JCIrXTdHKSlIISM1
JCIrKytEMVIhIzg=
JCIocUw3IiEjNQ==
JCIrXTdHKSlIISM1
JCIrRCJHailIISM1
JCIrK103YD4hIzg=
JCInKFE6JSEjNQ==
JCIrRCJHailIISM1
JCIraTpOJilIISM1
JCIrK11pbCgqISM5
JCImZzAnISM1
<-- exit halfing (now at top level) = .2985351562}
JCIraTpOJilIISM1
T:=0.6; R:=12000.;
JCIiJyEiIg==
JCImKz8iIiIh
f:=i*R+U-T;
LCoqJiQiKysrKys3ISM8IiIiKSQiK0c9Rz1GISIqLCQqJiQiKysrKytTISIpRidJIlVHNiJGJ0YnRidGJyQiKz8sKytnISM1ISIiKigkIiYrPyIhIiRGJ0YxRicsJkYxRickIiIlRjZGNkYnRjZGMUYn
plot(f,U=0..0.5);
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
ff:=x->subs(U=x,f);
Zio2I0kieEc2IkYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLUklc3Vic0clKnByb3RlY3RlZEc2JC9JIlVHRiVGJEkiZkdGJUYlRiVGJQ==
halfing(0.2,0.4,ff,0.0001,1,30);
{--> enter halfing, args = .2, .4, ff, 0.1e-3, 1, 30
JCIiJSEiIg==
JCIiIyEiIg==
JCIiIyEiIg==
JCIrKysrK0khIzU=
JCIrKysrKzUhIzU=
JCIqYi9gPichIzU=
JCIrKysrK0khIzU=
JCIrKysrK04hIzU=
JCIrKysrK10hIzY=
JCEqMXdvYiMhIzU=
JCIrKysrK04hIzU=
JCIrKysrXUshIzU=
JCIrKysrK0QhIzY=
JCIqKFsqM0cjISM1
JCIrKysrXUshIzU=
JCIrKysrdkwhIzU=
JCIrKysrXTchIzY=
JCEoYyxBJyEjNQ==
JCIrKysrdkwhIzU=
JCIrKytdN0whIzU=
JCIrKysrXWkhIzc=
JCIqJnkhWzgiISM1
JCIrKytdN0whIzU=
JCIrKyt2VkwhIzU=
JCIrKysrREohIzc=
JCIpR3o+YSEjNQ==
JCIrKyt2VkwhIzU=
JCIrK11QZkwhIzU=
JCIrKytdaTohIzc=
JCIpLjc3QyEjNQ==
JCIrK11QZkwhIzU=
JCIrK3Y9bkwhIzU=
JCIrKytdN3khIzg=
JCIoUUIpKikhIzU=
JCIrK3Y9bkwhIzU=
JCIrXVA0ckwhIzU=
JCIrKytEMVIhIzg=
JCIoJCkpKVEiISM1
JCIrXVA0ckwhIzU=
JCIrdm8vdEwhIzU=
JCIrK103YD4hIzg=
JCEoNFBUIyEjNQ==
JCIrdm8vdEwhIzU=
JCIrNy4yc0whIzU=
JCIrK11pbCgqISM5
JCEnRz5eISM1
<-- exit halfing (now at top level) = .3372070312}
JCIrNy4yc0whIzU=
halfing(0.1,0.2,ff,0.0001,1,30);
{--> enter halfing, args = .1, .2, ff, 0.1e-3, 1, 30
JCIiIiEiIg==
JCIiIyEiIg==
JCIiIiEiIg==
JCIrKysrKzohIzU=
JCIrKysrK10hIzY=
JCImIkhbISM1
JCIrKysrKzohIzU=
JCIrKysrXTchIzU=
JCIrKysrK0QhIzY=
JCEqNUIpXGkhIzU=
JCIrKysrXTchIzU=
JCIrKysrdjghIzU=
JCIrKysrXTchIzY=
JCEqZDJzJEghIzU=
JCIrKysrdjghIzU=
JCIrKytdUDkhIzU=
JCIrKysrXWkhIzc=
JCEqPCpcQDkhIzU=
JCIrKytdUDkhIzU=
JCIrKyt2bzkhIzU=
JCIrKysrREohIzc=
JCEpciN6KXAhIzU=
JCIrKyt2bzkhIzU=
JCIrK11QJVsiISM1
JCIrKytdaTohIzc=
JCEpNkVpTSEjNQ==
JCIrK11QJVsiISM1
JCIrK3Y9I1wiISM1
JCIrKytdN3khIzg=
JCEpU1JAPCEjNQ==
JCIrK3Y9I1wiISM1
JCIrXVA0J1wiISM1
JCIrKytEMVIhIzg=
JCEoP1hjKSEjNQ==
JCIrXVA0J1wiISM1
JCIrdm8vKVwiISM1
JCIrK103YD4hIzg=
JCEoUU5EJSEjNQ==
JCIrdm8vKVwiISM1
JCIrUU0tKlwiISM1
JCIrK11pbCgqISM5
JCEoeTk1IyEjNQ==
<-- exit halfing (now at top level) = .1499023438}
JCIrUU0tKlwiISM1
halfing(0.4,0.5,ff,0.0001,1,30);
{--> enter halfing, args = .4, .5, ff, 0.1e-3, 1, 30
JCIiJSEiIg==
JCIiJiEiIg==
JCIiIiEiIg==
JCIrKysrK1ghIzU=
JCIrKysrK10hIzY=
JCIrYGg+ek8hIzU=
JCIrKysrK1ghIzU=
JCIrKysrXVUhIzU=
JCIrKysrK0QhIzY=
JCEqKXowazchIzU=
JCIrKysrXVUhIzU=
JCIrKysrdlYhIzU=
JCIrKysrXTchIzY=
JCIrJSpSQSY9IiEjNQ==
JCIrKysrdlYhIzU=
JCIrKytdN1YhIzU=
JCIrKysrXWkhIzc=
JCIqaTY9PCUhIzU=
JCIrKytdN1YhIzU=
JCIrKytEIkclISM1
JCIrKysrREohIzc=
JCIqeWMnMzchIzU=
JCIrKytEIkclISM1
JCIrK11pbFUhIzU=
JCIrKytdaTohIzc=
JCEoJVwwJikhIzU=
JCIrK11pbFUhIzU=
JCIrK3ZWdFUhIzU=
JCIrKytdN3khIzg=
JCIpdCgpcGEhIzU=
JCIrK3ZWdFUhIzU=
JCIrXTdgcFUhIzU=
JCIrKytEMVIhIzg=
JCIpZUJ0QSEjNQ==
JCIrXTdgcFUhIzU=
JCIrRCJ5dkUlISM1
JCIrK103YD4hIzg=
JCIoMkotKCEjNQ==
JCIrRCJ5dkUlISM1
JCIraTpnbVUhIzU=
JCIrK11pbCgqISM5
JCEnIW9qKCEjNQ==
<-- exit halfing (now at top level) = .4266601562}
JCIraTpnbVUhIzU=
*17.32. A legkisebb n\303\251 gyzetek m\303\263 dszere.
*17.33. Sim\303\255 t\303\241 s.
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn
18. Fourier-transzform\303\241 ci\303\263
VI. Vari\303\241ci\303\263 sz\303\241m\303\255 t\303\241s
19. Az Euler-Lagrange-egyenletek
VII. K\303\266 z\303\266 ns\303\251 ges differenci\303\241legyenletek
21. Elemi megold\303\241 si m\303\263 dszerek
22. \303\201 ltal\303\241 nos eredm\303\251 nyek
23. Line\303\241 ris egyenletek
VIII. Parci\303\241 lis differenci\303\241 legyenletek
26. Disztrib\303\272 ci\303\263 k
28. Perem\303\251 rt\303\251 k probl\303\251 m\303\241 k
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn