Modern alkalmazott anal\303\255zis J\303\241rai Antal Ezek a programok csak szeml\303\251ltet\303\251sre szolg\303\241lnak LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn Bevezet\303\251s I. M\303\251rt\303\251k \303\251s integr\303\241l LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn
<Text-field style="Heading 1" layout="Heading 1">1. M<Font encoding="UTF-8">\303\251</Font>rt<Font encoding="UTF-8">\303\251</Font>kelm<Font encoding="UTF-8">\303\251let</Font></Text-field>
<Text-field style="Heading 1" layout="Heading 1">2. Integr<Font encoding="UTF-8">\303\241</Font>l<Font encoding="UTF-8">\303\241</Font>s</Text-field>
II. Funkcion\303\241lanal\303\255zis
<Text-field style="Heading 1" layout="Heading 1">3. Metrikus terek</Text-field>
<Text-field style="Heading 1" layout="Heading 1">4. Norm<Font encoding="UTF-8">\303\241</Font>lt terek</Text-field>
<Text-field style="Heading 1" layout="Heading 1">5. Line<Font encoding="UTF-8">\303\241</Font>ris oper<Font encoding="UTF-8">\303\241</Font>torok</Text-field>
<Text-field style="Heading 1" layout="Heading 1">6. Hilbert-terek</Text-field>
<Text-field style="Heading 1" layout="Heading 1">7. Spektr<Font encoding="UTF-8">\303\241</Font>lelm<Font encoding="UTF-8">\303\251</Font>let</Text-field>
<Text-field style="Heading 1" layout="Heading 1">8. Kompakt oper<Font encoding="UTF-8">\303\241</Font>torok</Text-field>
<Text-field style="Heading 1" layout="Heading 1">9. Differenci<Font encoding="UTF-8">\303\241</Font>lsz<Font encoding="UTF-8">\303\241</Font>m<Font encoding="UTF-8">\303\255</Font>t<Font encoding="UTF-8">\303\241</Font>s</Text-field>
III. Vektoranal\303\255zis
<Text-field style="Heading 1" layout="Heading 1">10. A differenci<Font encoding="UTF-8">\303\241</Font>lgeometria alapjai</Text-field>
<Text-field style="Heading 1" layout="Heading 1">11. Stieltjes-integr<Font encoding="UTF-8">\303\241</Font>l <Font encoding="UTF-8">\303\251</Font>s g<Font encoding="UTF-8">\303\266</Font>rbe menti integr<Font encoding="UTF-8">\303\241</Font>l</Text-field>
<Text-field style="Heading 1" layout="Heading 1">12. Differenci<Font encoding="UTF-8">\303\241</Font>lform<Font encoding="UTF-8">\303\241</Font>k integr<Font encoding="UTF-8">\303\241</Font>l<Font encoding="UTF-8">\303\241</Font>sa</Text-field>
IV. Komplex f\303\274ggv\303\251nytan
<Text-field style="Heading 1" layout="Heading 1">13. Analitikus <Font encoding="UTF-8">f\303\274ggv\303\251nyek</Font></Text-field>
<Text-field style="Heading 1" layout="Heading 1">14. Holomorf <Font encoding="UTF-8">f\303\274ggv\303\251nyek</Font></Text-field>
<Text-field style="Heading 1" layout="Heading 1">15. Meromorf <Font encoding="UTF-8">f\303\274ggv\303\251nyek</Font></Text-field>
V. Fourier-elm\303\251let
<Text-field style="Heading 1" layout="Heading 1">16. Klasszikus Fourier-sorok</Text-field>
<Text-field style="Heading 1" layout="Heading 1">17. Ortogon<Font encoding="UTF-8">\303\241</Font>lis polinomok</Text-field>
<Text-field style="Heading 2" layout="Heading 2">*17.26. Inverz interpol<Font encoding="UTF-8">\303\241</Font>ci<Font encoding="UTF-8">\303\263</Font>.</Text-field> 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(%); JCIiIiIiIQ== JCIrcT4lSG8iISIq JCIrSWxWKCk+ISIq JCIrYHYhKkc9ISIq JCIrVXd1TD4hIio= JCIrYWhxcD0hIio= JCIremhKNj4hIio= JCIrW0I7Jik9ISIq JCIrNV8pPiE+ISIq JCIrXkdKIio9ISIq JCIrP2M5KSo9ISIq JCIrQ2Z6JCo9ISIq JCIrX15kJyo9ISIq JCIrMk4hWyo9ISIq JCIrXlgkZio9ISIq JCIraUpAJio9ISIq JCIrXU5uJio9ISIq JCIrWSl6YCo9ISIq JCIrZ3NjJio9ISIq JCIrKm9aYSo9ISIq JCIrJSlSXyYqPSEiKg== JCIrMGBaJio9ISIq JCIrbGpdJio9ISIq JCIrW2xbJio9ISIq JCIrIz4qXCYqPSEiKg== JCIrRDZcJio9ISIq JCIrc2lcJio9ISIq JCIrKSlIXCYqPSEiKg== JCIrJDMmXCYqPSEiKg== JCIrWVBcJio9ISIq JCIrKmYlXCYqPSEiKg== JCIrYlNcJio9ISIq JCIrLVdcJio9ISIq JCIrIj0lXCYqPSEiKg== JCIrQVZcJio9ISIq JCIrS1VcJio9ISIq JCIrKkclXCYqPSEiKg== JCIrYFVcJio9ISIq JCIrd1VcJio9ISIq JCIraFVcJio9ISIq JCIrclVcJio9ISIq JCIrbFVcJio9ISIq JCIrb1VcJio9ISIq JCIrbVVcJio9ISIq JCIrb1VcJio9ISIq JCIrbVVcJio9ISIq JCIrb1VcJio9ISIq JCIrbVVcJio9ISIq 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 JCIiIyIiIQ== JCIiIiIiIQ== JCIiIiIiIQ== JCIrKysrKzohIio= JCIrKysrK10hIzU= JCIqdCoqKVxcISIq JCIrKysrKzohIio= JCIrKysrXTwhIio= JCIrKysrK0QhIzU= JCIqJSo9KHpAISIq JCIrKysrXTwhIio= JCIrKysrdj0hIio= JCIrKysrXTchIzU= JCIpajo8TCEiKg== JCIrKysrdj0hIio= JCIrKytdUD4hIio= JCIrKysrXWkhIzY= JCEpUTlacSEiKg== JCIrKytdUD4hIio= JCIrKytEMT4hIio= JCIrKysrREohIzY= JCEpJCl5czwhIio= JCIrKytEMT4hIio= JCIrK11pISo9ISIq JCIrKytdaTohIzY= JCIoJ2ZgeiEiKg== JCIrK11pISo9ISIq JCIrK3ZWKSo9ISIq JCIrKytdN3khIzc= JCEoYiRIWyEiKg== JCIrK3ZWKSo9ISIq JCIrXTdgJSo9ISIq JCIrKytEMVIhIzc= JCIoJ2V3OiEiKg== JCIrXTdgJSo9ISIq JCIrdlZbJyo9ISIq JCIrK103YD4hIzc= JCEocUZpIiEiKg== JCIrdlZbJyo9ISIq JCIrN3ldJio9ISIq JCIrK11pbCgqISM4 JCEmKD1BISIq JCIrN3ldJio9ISIq JCIrSiY+XSo9ISIq JCIrK0QiRylbISM4 JCInRHV4ISIq JCIrSiY+XSo9ISIq JCIrc09FJio9ISIq JCIrXWlTVEMhIzg= JCIndndQISIq JCIrc09FJio9ISIq JCIrVWRRJio9ISIq JCIrREpxPzchIzg= JCInZXg8ISIq JCIrVWRRJio9ISIq JCIreG5XJio9ISIq JCIrRGNeLmghIzk= JCImKnl4ISIq JCIreG5XJio9ISIq JCIrJUh4YSo9ISIq JCIrN3l2XkkhIzk= JCImLXkjISIq JCIrJUh4YSo9ISIq JCIrYERcJio9ISIq JCIrMSp5ZV8iISM5 JCIlM0chIio= JCIrYERcJio9ISIq JCIrIz0rYio9ISIq JCIrSVhSSHchIzo= JCElKm8qISIq JCIrIz0rYio9ISIq JCIrb2pcJio9ISIq JCIrbHNwOVEhIzo= JCElVE0hIio= JCIrb2pcJio9ISIq JCIrZ1dcJio9ISIq JCIrSydbdCE+ISM6 JCEkOyQhIio= JCIrZ1dcJio9ISIq JCIrMU5cJio9ISIq JCIrZ0p1TyYqISM7 JCIlWjchIio= <-- exit halfing (now at top level) = 1.895493506} JCIrMU5cJio9ISIq 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 JCEiIiIiIQ== JCIiIiIiIQ== JCIiIiIiIQ== JCIiIiIiIQ== JCIiIyIiIQ== JCEiIkkpaW5maW5pdHlHJSpwcm90ZWN0ZWRH JCIiIkkpaW5maW5pdHlHJSpwcm90ZWN0ZWRH JCIiIiIiIQ== JCIiIiIiIQ== JCEiIkkpaW5maW5pdHlHJSpwcm90ZWN0ZWRH JCIiIkkpaW5maW5pdHlHJSpwcm90ZWN0ZWRH JCIiIkkpaW5maW5pdHlHJSpwcm90ZWN0ZWRH JCIiIkkqdW5kZWZpbmVkRyUqcHJvdGVjdGVkRw== JCIiIkkqdW5kZWZpbmVkRyUqcHJvdGVjdGVkRw== JCEiIkkpaW5maW5pdHlHJSpwcm90ZWN0ZWRH JCIiIkkpaW5maW5pdHlHJSpwcm90ZWN0ZWRH JCIiIkkqdW5kZWZpbmVkRyUqcHJvdGVjdGVkRw== JCIiIkkqdW5kZWZpbmVkRyUqcHJvdGVjdGVkRw== JCIiIkkqdW5kZWZpbmVkRyUqcHJvdGVjdGVkRw== SSVGQUlMRyUqcHJvdGVjdGVkRw== <-- 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 JCEiIiIiIQ== JCIiJiEiIg== JCIiIiIiIQ== JCIjRCEiIw== JCIjOiEiIg== JCIrKysrKzUhIio= JCIrKysrKzUhIio= JCIiJiEiIg== JCIjRCEiIw== JCIrKysrKzUhIio= JCIrKysrKzUhIio= JCIqKysrKyYhIio= JCIrTUxMTEwhIzU= JCIrNzY2NjYhIzU= JCIrKysrKzUhIio= JCIrKysrKzUhIio= JCIrTUxMTEwhIzU= JCIrNzY2NjYhIzU= JCIrbW1tbW0hIzU= JCIrLCsrK0QhIzU= JCIrMCsrXWkhIzY= JCIrTUxMTEwhIzU= JCIrNzY2NjYhIzU= JCIrLCsrK0QhIzU= JCIrMCsrXWkhIzY= JCIqTExMTCkhIzU= JCIrSTlkRzkhIzU= JCIrSmoiMy8jISM2 JCIrLCsrK0QhIzU= JCIrMCsrXWkhIzY= JCIrSTlkRzkhIzU= JCIrSmoiMy8jISM2 JCIrciZHOTIiISM1 JCIqNDQ0NCohIzU= JCIrM0dZayMpISM3 JCIrSTlkRzkhIzU= JCIrSmoiMy8jISM2 JCIqNDQ0NCohIzU= JCIrM0dZayMpISM3 JCIqQDBbPiYhIzU= JCIrZWJiYmIhIzY= JCIrYyg+azMkISM3 JCIqNDQ0NCohIzU= JCIrM0dZayMpISM3 JCIrZWJiYmIhIzY= JCIrYyg+azMkISM3 JCIrS05OTk4hIzY= JCIra2VGW00hIzY= JCIrVjExKj0iISM3 JCIrZWJiYmIhIzY= JCIrYyg+azMkISM3 JCIra2VGW00hIzY= JCIrVjExKj0iISM3 JCIrJXB6czUjISM2 JCIreCZmdzcjISM2 JCIrd18kcF8lISM4 JCIra2VGW00hIzY= JCIrVjExKj0iISM3 JCIreCZmdzcjISM2 JCIrd18kcF8lISM4 JCIrKEc7MUsiISM2 JCIrdSUqeTo4ISM2 JCIrUz5JSjwhIzg= JCIreCZmdzcjISM2 JCIrd18kcF8lISM4 JCIrdSUqeTo4ISM2 JCIrUz5JSjwhIzg= JCIqLiwoPSIpISM2 <-- exit secant (now at top level) = 0.1315789474e-1} JCIrdSUqeTo4ISM2 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 JCIiIiIiIQ== JCIiIyIiIQ== JCIqcT4lSG8hIio= JCEqWV5TIj0hIio= JCIiIiIiIQ== JCIrZlk3IXoiISIq JCIqYkgnPjshIio= JCIiIyIiIQ== JCEqWV5TIj0hIio= JCIrZlk3IXoiISIq JCIqYkgnPjshIio= JCIqVGAoKTQjISIq JCIrWzA3Kik9ISIq JCIpNT5TNSEiKg== JCIrZlk3IXoiISIq JCIqYkgnPjshIio= JCIrWzA3Kik9ISIq JCIpNT5TNSEiKg== JCIpKillKiopKiEiKg== JCIrO1siZio9ISIq JCEnWSEqbyEiKg== JCIrWzA3Kik9ISIq JCIpNT5TNSEiKg== JCIrO1siZio9ISIq JCEnWSEqbyEiKg== JCIob1V6JyEiKg== JCIrNUZcJio9ISIq JCIlXUQhIio= JCIrO1siZio9ISIq JCEnWSEqbyEiKg== JCIrNUZcJio9ISIq JCIlXUQhIio= JCInMUBVISIq JCIrbVVcJio9ISIq JCIiIyEiKg== JCIrNUZcJio9ISIq JCIlXUQhIio= JCIrbVVcJio9ISIq JCIiIyEiKg== JCIlYzohIio= JCIrblVcJio9ISIq JCIiIUYj JCIrbVVcJio9ISIq JCIiIyEiKg== JCIrblVcJio9ISIq JCIiIUYj JCIiIiEiKg== <-- exit secant (now at top level) = 1.895494267} JCIrblVcJio9ISIq 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 JCIiIiIiIQ== JCIiIyIiIQ== JCIqcT4lSG8hIio= JCEqWV5TIj0hIio= JCIiIiIiIQ== JCIrZlk3IXoiISIq JCIqYkgnPjshIio= JCIiIyIiIQ== JCEqWV5TIj0hIio= JCIrZlk3IXoiISIq JCIqYkgnPjshIio= JCIqVGAoKTQjISIq JCIrWzA3Kik9ISIq JCIpNT5TNSEiKg== JCIrZlk3IXoiISIq JCIqYkgnPjshIio= JCIrWzA3Kik9ISIq JCIpNT5TNSEiKg== JCIpKillKiopKiEiKg== JCIrO1siZio9ISIq JCEnWSEqbyEiKg== JCIrWzA3Kik9ISIq JCIpNT5TNSEiKg== JCIrO1siZio9ISIq JCEnWSEqbyEiKg== JCIob1V6JyEiKg== JCIrNUZcJio9ISIq JCIlXUQhIio= JCIrO1siZio9ISIq JCEnWSEqbyEiKg== JCIrNUZcJio9ISIq JCIlXUQhIio= JCInMUBVISIq JCIrbVVcJio9ISIq JCIiIyEiKg== JCIrNUZcJio9ISIq JCIlXUQhIio= JCIrbVVcJio9ISIq JCIiIyEiKg== JCIlYzohIio= JCIrblVcJio9ISIq JCIiIUYj JCIrbVVcJio9ISIq JCIiIyEiKg== JCIrblVcJio9ISIq JCIiIUYj JCIiIiEiKg== <-- 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 JCIqdlAjM1EhIio= 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==
<Text-field style="Heading 2" layout="Heading 2">*17.27. Egy p<Font encoding="UTF-8">\303\251</Font>lda: a konvergencia rendje.</Text-field> 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
<Text-field style="Heading 2" layout="Heading 2">*17.28. Feladat.</Text-field>
<Text-field style="Heading 2" layout="Heading 2">*17.29. Feladat.</Text-field>
<Text-field style="Heading 2" layout="Heading 2">*17.30. Feladat.</Text-field>
<Text-field style="Heading 2" layout="Heading 2">*17.31. Feladat.</Text-field>
<Text-field style="Heading 2" layout="Heading 2">*Feladat.</Text-field>
<Text-field style="Heading 2" layout="Heading 2">*Feladat.</Text-field>
<Text-field style="Heading 2" layout="Heading 2">*Feladat.</Text-field> 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); NiUtSSdDVVJWRVNHNiI2JDdgbzckJCIiIUYqRik3JCQiM2ApKioqKlxQPigzKSohIz8kIjNibGtuYXNGRlEhI0I3JCQiMyMqKipcaWxMS009ISM+JCIzJHAnZk9DLiMzKyhGMTckJCIzMysrRGMoPVR6I0Y1JCIzNSIpXC03bmRSNSEjQTckJCIzIioqKipcUEh3LXckRjUkIjNGQTpZKjM5Rk8iRj03JCQiM04qKlw3YD0lPXMlRjUkIjMlKW8+XChSemRtIkY9NyQkIjMjKSoqXGk6aUw4Y0Y1JCIzWzA0ImYqKVItJD5GPTckJCIzVioqXGkhKnBVT2xGNSQiM3hddU0lR0J0PSNGPTckJCIzNStdaSF6KTMiXChGNSQiMyFScW1cSXRfViNGPTckJCIzLStdN3kqKW9VJSlGNSQiM0Q0cCR6VylHa0VGPTckJCIzJzMrK3Z0RTpVKkY1JCIzcXgmSGpFajQpR0Y9NyQkIjMnKioqXChvdm8kRzUhIz0kIjNNODZGVihRZjAkRj03JCQiMysrK0RZd1VENkZebyQiMzIibyE9OkA4TktGPTckJCIzJSoqKipcKG9dKUdBIkZebyQiM1MpKSp6JSpmMGhSJEY9NyQkIjM4Kyt2YEwhb0oiRl5vJCIzJEd0WytqaEtgJEY9NyQkIjMpKipcaVM6ITQtOUZebyQiMzJMRSJlKTRgVU9GPTckJCIzIioqKipcKDNXXS46Rl5vJCIzIz1gVS0lSGBgUEY9NyQkIjMoKioqKioqXGU6JSplIkZebyQiM14/I3l4LXk5JFFGPTckJCIzIyoqXGlscV0kKm8iRl5vJCIzNyV5YHAmSGUuUkY9NyQkIjN3KioqKlxBLSJ5eCJGXm8kIjNWJVxFJnBUdl1SRj03JCQiMyQqKlxpOkxrWyg9Rl5vJCIzVz5banE7XyUpUkY9NyQkIjM8K3ZvJXojR24+Rl5vJCIzJ2Y2OVAsIj4qKlJGPTckJCIzMytdaWw8cmo/Rl5vJCIzNysuR0xgSycqUkY9NyQkIjMpKipcN0dtakE6I0ZebyQiM15WclgkeWp0KFJGPTckJCIzJSkqKlwobyUpeXhDI0ZebyQiM2FWTy8lbzMlUlJGPTckJCIzdipcaSF6QSpwTSNGXm8kIjNrVnAzUzF6ISlRRj03JCQiM3MqXFBNJ3lOTENGXm8kIjN2Okc8KDQpKVEiUUY9NyQkIjMoKSoqXGlnXWpFREZebyQiM3ZsVSZwbzBecyRGPTckJCIzJioqKioqXEsmKipIaSNGXm8kIjNoUHJfKjN1YWgkRj03JCQiMykqKipcN29MRjxGRl5vJCIzKW9Fb0NkcjJcJEY9NyQkIjMoKSpcaTo6KVszR0ZebyQiM0FcI1FKVDdSTiRGPTckJCIzcioqXChvaG0oNEhGXm8kIjMhZW1mUi1wTz0kRj03JCQiM2QqKioqXEEpcDIrJEZebyQiMztCUWtOYHk5SUY9NyQkIjMzKyt2b14kejQkRl5vJCIzIlJLX11yPSc9R0Y9NyQkIjMhKSpcaVNUIilmPSRGXm8kIjMoNFJYbl4lcEZFRj03JCQiM0UrK0Q7I1JBRyRGXm8kIjNNL00jZUQkPjFDRj03JCQiMyIpKlxpbEk1R1AkRl5vJCIzYFMjcCU0dHAoPSNGPTckJCIzJioqXDdHPiRbbk1GXm8kIjNgd0E6N2czXz5GPTckJCIzZSoqKlxQQ1YrYyRGXm8kIjMhcGd3OlJzIj48Rj03JCQiM28qXGkhUl0lcGwkRl5vJCIzNTNUJSkqZk0pejlGPTckJCIzJioqKioqKlwpSEZdUEZebyQiMy1YIlJrRS5RRSJGPTckJCIzOitdUCpHOWQlUUZebyQiMzdUcld1KEhGMiJGPTckJCIzR10oby96UkkqUUZebyQiM2RFLS5BRipwJioqRjE3JCQiM1ArRGMiSGwuJVJGXm8kIjNrVWFxYXY1XSQqRjE3JCQiM0R2b3osKjNAJ1JGXm8kIjN2J0hRXjR3dzgqRjE3JCQiMzhdNy43RCZRKVJGXm8kIjN0YU44XjdmdCopRjE3JCQiMytEY0VBaGYwU0ZebyQiM3kiKj0nKVthNWopKUYxNyQkIjMpKSoqKipcSyhSdC0lRl5vJCIzRVZhOSdSWz4iKSlGMTckJCIzKFsoby9bKyEpUlNGXm8kIjMhcFxKKSkpb3c2KSlGMTckJCIzJylcUGZqLkVfU0ZebyQiMzlrQ2BTJXBWJCkpRjE3JCQiMyZbaVMiejFza1NGXm8kIjMoPVJHOTV6NSkpKUYxNyQkIjMlKSpcKG8lKjQ9eFNGXm8kIjM9JUhrXmAnR2AqKUYxNyQkIjMjKVw3eUQ7NS1URl5vJCIzYjwiWztOOyw9KkYxNyQkIjMhKSoqXChvREFxNyVGXm8kIjMmNEhfJGVBWkYmKkYxNyQkIjMyK3YkZigzZ3JURl5vJCIzJDNQKjRXcFVcNUY9NyQkIjN5KioqKipcXHpoQCVGXm8kIjMlM1pgJiopKTQlKT4iRj03JCQiM0ZdN3krJzRQRSVGXm8kIjMpenA/ZkF2c1UiRj03JCQiM0ErRGMxKFI3SiVGXm8kIjMhZU1hQjRLVHUiRj03JCQiM1FdN2AlKmUpUkwlRl5vJCIzO3IicDckZVRLPkY9NyQkIjMqKioqKipcIzNLbk4lRl5vJCIzV25qW0FQbVpARj03JCQiM2dcKG8vRnklelZGXm8kIjNNPmJsR0ZhI1IjRj03JCQiM3gqXFAlZVdBLVdGXm8kIjNzLlt3WVEoKnBFRj03JCQiMzhEIkdRTW9tVSVGXm8kIjNZI3BTdi5nITNJRj03JCQiMyUqXCg9I0hBNl5XRl5vJCIzI2ZcWGUsLT1SJEY9NyQkIjNOaVMiPjxNTFklRl5vJCIzNnAtX0chekFnJEY9NyQkIjN2dSQ0WTZjYlolRl5vJCIzLGd1WHM/LEVRRj03JCQiM3Eoby90MHl4WyVGXm8kIjMhZltrZ0Yhb2pTRj03JCQiMzcrKysrKysrWEZebyQiM0VjVXgkeicqZkolRj0tSSdDT0xPVVJHRiU2JkkkUkdCR0YlJCIjNSEiIkYpRiktSStBWEVTTEFCRUxTRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YlNiRRIlVGJVEhRiUtSSVWSUVXR0ZiYWw2JDtGKSQiI1ghIiNJKERFRkFVTFRHRiU= 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=
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<Text-field style="Heading 1" layout="Heading 1">18. Fourier-transzform<Font encoding="UTF-8">\303\241</Font>ci<Font encoding="UTF-8">\303\263</Font></Text-field>
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<Text-field style="Heading 1" layout="Heading 1">19. Az Euler-Lagrange-egyenletek</Text-field>
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<Text-field style="Heading 1" layout="Heading 1">20. Alapfogalmak</Text-field>
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<Text-field style="Heading 1" layout="Heading 1">23. Line<Font encoding="UTF-8">\303\241</Font>ris egyenletek</Text-field>
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<Text-field style="Heading 1" layout="Heading 1">29. Vegyes feladatok</Text-field>
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