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> restart;
<Text-field style="Heading 2" layout="Heading 2">3.114. Banach-f<Font encoding="UTF-8">\303\251</Font>le fixpontt<Font encoding="UTF-8">\303\251</Font>tel.</Text-field>
<Text-field style="Heading 2" layout="Heading 2">3.115. Megjegyz<Font encoding="UTF-8">\303\251</Font>s.</Text-field>
<Text-field style="Heading 2" layout="Heading 2">3.116. Feladat.</Text-field> T:=x->(cos(x/2)-abs(x-0.5))/2; Zio2I0kieEc2IkYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLCYqJiMiIiIiIiNGLC1JJGNvc0dGJTYjLCQqJkYrRixGJEYsRixGLEYsKiZGK0YsLUkkYWJzRyUqcHJvdGVjdGVkRzYjLCZGJEYsJCIiJiEiIkY7RixGO0YlRiVGJQ== 0.6;T(%);T(%);T(%);T(%);T(%);T(%);T(%);T(%);T(%);T(%);T(%);T(%);T(%);T(%);T(%);T(%);T(%);T(%);T(%);T(%);T(%);T(%);T(%);T(%);T(%);T(%);T(%);T(%);T(%);T(%); JCIiJyEiIg== JCIrWUNvd1UhIzU= JCIrZk5ZQ1ghIzU= JCIrd1QkW2olISM1 JCIrR2p2JG8lISM1 JCIrQlFSMFohIzU= JCIra1cmXHIlISM1 JCIrcHE8PlohIzU= JCIrJXBUNXMlISM1 JCIrNV0nPXMlISM1 JCIrRiZHQXMlISM1 JCIrRyEqUUFaISM1 JCIrIyopZkNzJSEjNQ== JCIrIT0iXEFaISM1 JCIrJSpcXUFaISM1 JCIrJDQ2RHMlISM1 JCIrJ3k4RHMlISM1 JCIrdlxeQVohIzU= JCIrK2JeQVohIzU= JCIrS2ReQVohIzU= JCIrTWVeQVohIzU= JCIremVeQVohIzU= JCIrK2ZeQVohIzU= JCIrM2ZeQVohIzU= JCIrN2ZeQVohIzU= JCIrOWZeQVohIzU= JCIrOmZeQVohIzU= JCIrOWZeQVohIzU= JCIrOmZeQVohIzU= JCIrOWZeQVohIzU= JCIrOmZeQVohIzU=
<Text-field style="Heading 2" layout="Heading 2">3.117. Feladat.</Text-field>
<Text-field style="Heading 2" layout="Heading 2">3.118. Feladat.</Text-field>
<Text-field style="Heading 2" layout="Heading 2">Feladat.</Text-field> solve([x1^2+x2^2=1,2*x1+x2=1],[x1,x2]); NyQ3JC9JI3gxRzYiIiIhL0kjeDJHRiYiIiI3JC9GJSMiIiUiIiYvRikjISIkRi8= T1:=x->[(1-x[2])/2,sqrt(1-x[1]^2)]; Zio2I0kieEc2IkYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlNyQsJiMiIiIiIiNGLComRitGLCZGJDYjRi1GLCEiIi1JJXNxcnRHRiU2IywmRixGLCokKSZGJDYjRixGLUYsRjFGJUYlRiU= x:=[-0.9,0.9];T1(%);T1(%);T1(%);T1(%);T1(%);T1(%);T1(%);T1(%);T1(%);T1(%);T1(%); NyQkISIqISIiJCIiKkYl NyQkIiorKysrJiEjNSQiK1cqKSopZVZGJQ== NyQkIitHMGI/RyEjNSQiK3lAXCgpKipGJQ== NyQkIig2UkQnISM1JCIrOUEpUmYqRiU= NyQkIiokKikzST8hIzUkIitXISkqKioqKipGJQ== NyQkIiR5KiEjNSQiK2QiUnoqKipGJQ== NyQkIihBLy4iISM1JCIiIiIiIQ== NyQkIiIhRiQkIitaKioqKioqKiohIzU= NyQkIiNFISM1JCIiIiIiIQ== NyQkIiIhRiQkIiIiRiQ= NyQkIiIhRiQkIiIiRiQ= NyQkIiIhRiQkIiIiRiQ= T2:=x->[(1-x[2])/2,-sqrt(1-x[1]^2)]; Zio2I0kieEc2IkYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlNyQsJiMiIiIiIiNGLComRitGLCZGJDYjRi1GLCEiIiwkLUklc3FydEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYjLCZGLEYsKiQpJkYkNiNGLEYtRixGMUYxRiVGJUYl x:=[0.9,0.9];T2(%);T2(%);T2(%);(%);T2(%);T2(%);T2(%);T2(%);T2(%);T2(%);T2(%);T2(%);T2(%);T2(%);T2(%);T2(%);T2(%);T2(%);T2(%);T2(%);T2(%);T2(%);T2(%);T2(%);T2(%);T2(%);T2(%);T2(%);T2(%);T2(%);T2(%);T2(%);T2(%);T2(%);T2(%);T2(%);T2(%);T2(%);T2(%);T2(%);T2(%);T2(%);(%);T2(%);T2(%);T2(%);T2(%);T2(%);T2(%); NyQkIiIqISIiRiM= NyQkIiorKysrJiEjNSQhK1cqKSopZVZGJQ== NyQkIitzJVwlenIhIzUkISt5QFwoKSoqRiU= NyQkIisqM1lQKioqISM1JCErcikpKjQncEYl NyQkIisqM1lQKioqISM1JCErcikpKjQncEYl NyQkIitPJSpcIVspISM1JCEraXAzT04hIzY= NyQkIitbViFvPCYhIzUkISt4STsqSCZGJQ== NyQkIitROmVcdyEjNSQhK3MwdWImKUYl NyQkIisnR3F5RiohIzUkISs9KSp6U2tGJQ== NyQkIis0KipSPyMpISM1JCErNkA1SlBGJQ== NyQkIitjNWJsbyEjNSQhKzt3SCVwJkYl NyQkIiszKVtyJXkhIzUkIStCeHhxc0Yl NyQkIitpKSlRTicpISM1JCErTSlvJik+J0Yl NyQkIis8V0cqNCkhIzUkIStWRCNHLyZGJQ== NyQkIitzN1RAdiEjNSQhK0hxR2xlRiU= NyQkIis5TmtLeiEjNSQhK3UxLSFmJ0Yl NyQkIitQLiwmSCkhIzUkIStTUXgpMydGJQ== NyQkIis/cFFXISkhIzUkISsiel5dZSZGJQ== NyQkIisnKmVfI3ooISM1JCErOW9OU2ZGJQ== NyQkIisyJXksKHohIzUkISs/KSo0bmlGJQ== NyQkIis1KlxOOCkhIzUkISs4d2JSZ0Yl NyQkIisxKXkoPiEpISM1JCErO3FuPGVGJQ== NyQkIiszJlEpM3ohIzUkISstdGB0ZkYl NyQkIiteJ29uKXohIzUkISthR20+aEYl NyQkIitGOSQpZiEpISM1JCErJFIsdywnRiU= NyQkIisncCspMyEpISM1JCErIilbUT5mRiU= NyQkIitTQ3BmeiEjNSQhK3Z4QykpZkYl NyQkIispKVE3JSp6ISM1JCErYDFQYGdGJQ== NyQkIitFYG9FISkhIzUkIStMbyN5KydGJQ== NyQkIis7TSJSKykhIzUkIStTUERrZkYl NyQkIitxbzcjKXohIzUkIStrJnlaKmZGJQ== NyQkIisjRypRKCp6ISM1JCErJz1kUC0nRiU= NyQkIiskZnk9LCkhIzUkISshUXpNKydGJQ== NyQkIishcFI8KykhIzUkIStGIkhUKWZGJQ== NyQkIitrWDEjKnohIzUkISs3KHp3KmZGJQ== NyQkIitjKVIpKSp6ISM1JCErSWdjNWdGJQ== NyQkIis6SUcwISkhIzUkIStabGEsZ0Yl NyQkIit1S3grISkhIzUkISs3JlxIKmZGJQ== NyQkIitjWlonKnohIzUkIStJKW8qKSpmRiU= NyQkIis6V1sqKnohIzUkIStedXAvZ0Yl NyQkIitFKFtCKykhIzUkISsmUShvK2dGJQ== NyQkIisjcFYuKykhIzUkISspM25vKmZGJQ== NyQkIitXTlYpKnohIzUkISs8PGEqKmZGJQ== NyQkIitXTlYpKnohIzUkISs8PGEqKmZGJQ== NyQkIitlM3gqKnohIzUkIStTISkzLWdGJQ== NyQkIis/Uy8sISkhIzUkISs2YkkrZ0Yl NyQkIitjRjorISkhIzUkIStAeGcpKmZGJQ== NyQkIitnUUkqKnohIzUkISs/anoqKmZGJQ== NyQkIitnIikqKSoqeiEjNSQhK3YhRzQrJ0Yl NyQkIitRU1krISkhIzUkISsleU4sKydGJQ== with(LinearAlgebra); with(VectorCalculus); 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 x:='x';T1:=<(1-y)/2,sqrt(1-x^2)>; SSJ4RzYi LSZJJ1ZlY3Rvckc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSdjb2x1bW5HRig2Iy9JJCVpZEdGKCIqXz4nRzk= Jacobian(T1,[x,y]); LUknTWF0cml4RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMvSSQlaWRHRiciKlsmKVJWIg== a:=subs(x=0,y=1,%); LUknTWF0cml4RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMvSSQlaWRHRiciKltSU1Yi MatrixNorm(a); IyIiIiIiIw== T2:=<(1-y)/2,-sqrt(1-x^2)>; LSZJJ1ZlY3Rvckc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSdjb2x1bW5HRig2Iy9JJCVpZEdGKCIqU0RLViI= Jacobian(T2,[x,y]); LUknTWF0cml4RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMvSSQlaWRHRiciKksmKltWIg== a:=subs(x=4/5,y=-3/5,%); LUknTWF0cml4RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMvSSQlaWRHRiciKjsuXVYi MatrixNorm(a); evalf(%); LCQqKCMiIiUiI1giIiIpIiIqI0YnIiIjRicpIiNERipGJ0Yn JCIrTExMTDghIio= Eigenvalues(a); evalf(%); LSZJJ1ZlY3Rvckc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSdjb2x1bW5HRig2Iy9JJCVpZEdGKCIqMydcUzk= LSZJJ1ZlY3Rvckc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSdjb2x1bW5HRig2Iy9JJCVpZEdGKCIqP2ouVyI=
<Text-field style="Heading 2" layout="Heading 2">3.119. Feladat.</Text-field>
<Text-field style="Heading 2" layout="Heading 2">3.120. Feladat: a fixpont folytonos f<Font encoding="UTF-8">\303\274</Font>gg<Font encoding="UTF-8">\303\251</Font>se a param<Font encoding="UTF-8">\303\251</Font>terekt<Font encoding="UTF-8">\305\221</Font>l.</Text-field>
<Text-field style="Heading 2" layout="Heading 2">->3.121. Feladat.</Text-field>
<Text-field style="Heading 2" layout="Heading 2">Fixpont tulajdons<Font encoding="UTF-8">\303\241</Font>g.</Text-field>
<Text-field style="Heading 2" layout="Heading 2">Retraktum.</Text-field>
<Text-field style="Heading 2" layout="Heading 2">T<Font encoding="UTF-8">\303\251</Font>tel.</Text-field>
<Text-field style="Heading 2" layout="Heading 2"><Font encoding="UTF-8">\303\226</Font>sszeh<Font encoding="UTF-8">\303\272</Font>zhat<Font encoding="UTF-8">\303\263</Font>s<Font encoding="UTF-8">\303\241</Font>g.</Text-field>
<Text-field style="Heading 2" layout="Heading 2">T<Font encoding="UTF-8">\303\251</Font>tel.</Text-field>
<Text-field style="Heading 2" layout="Heading 2">T<Font encoding="UTF-8">\303\251</Font>tel.</Text-field>
<Text-field style="Heading 2" layout="Heading 2">T<Font encoding="UTF-8">\303\251</Font>tel.</Text-field>
<Text-field style="Heading 2" layout="Heading 2">Megjegyz<Font encoding="UTF-8">\303\251</Font>s.</Text-field>
<Text-field style="Heading 2" layout="Heading 2">*3.122. Egyenletek megold<Font encoding="UTF-8">\303\241</Font>sa <Font encoding="UTF-8">\303\251</Font>s fixpontt<Font encoding="UTF-8">\303\251</Font>telek.</Text-field> v:='v'; f:=Vector(2,[v[1]^2+v[2]^2-1,2*v[1]+v[2]-1]); SSJ2RzYi LSZJJ1ZlY3Rvckc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSdjb2x1bW5HRig2Iy9JJCVpZEdGKCIqY1dSVSI= J:=Jacobian(f,[v[1],v[2]]); LUknTWF0cml4RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMvSSQlaWRHRiciKk9ENlci Jinv:=MatrixInverse(J); LUknTWF0cml4RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMvSSQlaWRHRiciKl89PFci Jinv0:=subs(v[1]=-2.,v[2]=2.,Jinv); v:=Vector(2,[-2.,2.]); LUknTWF0cml4RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMvSSQlaWRHRiciKmcvPVci LSZJJ1ZlY3Rvckc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSdjb2x1bW5HRig2Iy9JJCVpZEdGKCIqR3ciUjk= v:=v-Jinv0.f;v:=v-Jinv0.f;v:=v-Jinv0.f;v:=v-Jinv0.f;v:=v-Jinv0.f;v:=v-Jinv0.f;v:=v-Jinv0.f;v:=v-Jinv0.f;v:=v-Jinv0.f;v:=v-Jinv0.f;v:=v-Jinv0.f; LSZJJ1ZlY3Rvckc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSdjb2x1bW5HRig2Iy9JJCVpZEdGKCIqQyQqZVci LSZJJ1ZlY3Rvckc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSdjb2x1bW5HRig2Iy9JJCVpZEdGKCIqO2B5VyI= LSZJJ1ZlY3Rvckc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSdjb2x1bW5HRig2Iy9JJCVpZEdGKCIqP3QmXDk= LSZJJ1ZlY3Rvckc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSdjb2x1bW5HRig2Iy9JJCVpZEdGKCIqISkzPVUi LSZJJ1ZlY3Rvckc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSdjb2x1bW5HRig2Iy9JJCVpZEdGKCIqd1JQVSI= LSZJJ1ZlY3Rvckc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSdjb2x1bW5HRig2Iy9JJCVpZEdGKCIqNyxgVSI= LSZJJ1ZlY3Rvckc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSdjb2x1bW5HRig2Iy9JJCVpZEdGKCIqS3dcViI= LSZJJ1ZlY3Rvckc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSdjb2x1bW5HRig2Iy9JJCVpZEdGKCIqQ1Z5VSI= LSZJJ1ZlY3Rvckc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSdjb2x1bW5HRig2Iy9JJCVpZEdGKCIqNy11VyI= LSZJJ1ZlY3Rvckc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSdjb2x1bW5HRig2Iy9JJCVpZEdGKCIqK2tjVyI= LSZJJ1ZlY3Rvckc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSdjb2x1bW5HRig2Iy9JJCVpZEdGKCIqM0QnWzk= v:=Vector(2,[-0.9,0.9]); v:=v-Jinv.f;v:=v-Jinv.f;v:=v-Jinv.f;v:=v-Jinv.f;v:=v-Jinv.f;v:=v-Jinv.f;v:=v-Jinv.f; LSZJJ1ZlY3Rvckc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSdjb2x1bW5HRig2Iy9JJCVpZEdGKCIqa09GViI= LSZJJ1ZlY3Rvckc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSdjb2x1bW5HRig2Iy9JJCVpZEdGKCIqQ2xBViI= LSZJJ1ZlY3Rvckc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSdjb2x1bW5HRig2Iy9JJCVpZEdGKCIqX3lIWCI= LSZJJ1ZlY3Rvckc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSdjb2x1bW5HRig2Iy9JJCVpZEdGKCIqY1pkViI= LSZJJ1ZlY3Rvckc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSdjb2x1bW5HRig2Iy9JJCVpZEdGKCIqayZRYzk= LSZJJ1ZlY3Rvckc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSdjb2x1bW5HRig2Iy9JJCVpZEdGKCIqXygzZTk= LSZJJ1ZlY3Rvckc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSdjb2x1bW5HRig2Iy9JJCVpZEdGKCIqVyV6Zjk= LSZJJ1ZlY3Rvckc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSdjb2x1bW5HRig2Iy9JJCVpZEdGKCIqRyFbaDk=
<Text-field style="Heading 2" layout="Heading 2"><Font encoding="UTF-8">3.123. Aitken \316\224^2-m\303\263</Font>dszere.</Text-field> Aitken:=proc(x1,x2,x3) x1-(x2-x1)^2/((x3-x2)-(x2-x1)) end; Zio2JUkjeDFHNiJJI3gyR0YlSSN4M0dGJUYlRiVGJS1fSS9WZWN0b3JDYWxjdWx1c0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJUkiK0dGLDYkRiQtX0YqSSItR0YlNiMtX0YqSSIqR0YsNiQqJCktRik2JEYmLUYxNiNGJCIiIyIiIiokLUYpNiQtRik2JEYnLUYxNiNGJi1GMTYjRjohIiJGJUYlRiU=
<Text-field style="Heading 2" layout="Heading 2">*3.124. Feladat.</Text-field> fsolve(x=cos(x)); JCIrSzgmM1IoISM1 x:=1.5;cos(%);cos(%);cos(%);cos(%);cos(%);cos(%);cos(%);cos(%);cos(%);cos(%);cos(%);cos(%);cos(%);cos(%);cos(%);cos(%);cos(%);cos(%);cos(%);cos(%);cos(%);cos(%);cos(%);cos(%);cos(%);cos(%);cos(%);cos(%);cos(%);cos(%);cos(%); JCIjOiEiIg== JCIrbixzdHEhIzY= JCIrczsqXCgqKiEjNQ== JCIrQipcU1UmISM1 JCIrITQocGsmKSEjNQ== JCIrPCEpM15sISM1 JCIrZWsiKUh6ISM1 JCIrJG9UcywoISM1 JCIrOEpJUHchIzU= JCIrQDNoQXMhIzU= JCIrZClHSl0oISM1 JCIrIWViWkooISM1 JCIrbmUqPVcoISM1 JCIrJCk0UGN0ISM1 JCIrSFAuOXUhIzU= JCIrWGJAdnQhIzU= JCIrW1pQLHUhIzU= JCIrVSZlUFEoISM1 JCIraHNpJlIoISM1 JCIrbUxqKFEoISM1 JCIrNSc9SVIoISM1 JCIrYTdSKlEoISM1 JCIrIXlNPVIoISM1 JCIrTSkpPSFSKCEjNQ== JCIrJGUoSCJSKCEjNQ== JCIrRDJiIVIoISM1 JCIrQFEwIlIoISM1 JCIrS1xyIVIoISM1 JCIrN0slNFIoISM1 JCIrUyUqeSFSKCEjNQ== JCIrQkkqM1IoISM1 JCIrXEsjM1IoISM1 x:=0.;cos(%);cos(%);Aitken(%%%,%%,%);cos(%);cos(%);Aitken(%%%,%%,%);cos(%);cos(%);Aitken(%%%,%%,%);cos(%);cos(%);Aitken(%%%,%%,%); JCIiIUYj JCIiIiIiIQ== JCIrZkktLmEhIzU= JCIrdU50XW8hIzU= JCIrUWpzVnghIzU= JCIrOygpZltyISM1 JCIraTpnJ1EoISM1 JCIraExyJFIoISM1 JCIrS0ojKilRKCEjNQ== JCIrajUmM1IoISM1 JCIrODomM1IoISM1 JCIrNTcmM1IoISM1 JCIrSzgmM1IoISM1
<Text-field style="Heading 2" layout="Heading 2">*3.125. Feladat.</Text-field> x:=1.;2/%;2/%;2/%;2/%;2/%;2/%;2/%;2/%;2/%;2/%;2/%;2/%;2/%;2/%;2/%;2/%;2/%; JCIiIiIiIQ== JCIiIyIiIQ== JCIrKysrKzUhIio= JCIrKysrKz8hIio= JCIrKysrKzUhIio= JCIrKysrKz8hIio= JCIrKysrKzUhIio= JCIrKysrKz8hIio= JCIrKysrKzUhIio= JCIrKysrKz8hIio= JCIrKysrKzUhIio= JCIrKysrKz8hIio= JCIrKysrKzUhIio= JCIrKysrKz8hIio= JCIrKysrKzUhIio= JCIrKysrKz8hIio= JCIrKysrKzUhIio= JCIrKysrKz8hIio= x:=1.;2/%;2/%;Aitken(%%%,%%,%);2/%;2/%;Aitken(%%%,%%,%);2/%;2/%;Aitken(%%%,%%,%);2/%;2/%;Aitken(%%%,%%,%);2/%;2/%;Aitken(%%%,%%,%);2/%;2/%;Aitken(%%%,%%,%);2/%;2/%;Aitken(%%%,%%,%); JCIiIiIiIQ== JCIiIyIiIQ== JCIrKysrKzUhIio= JCIrKysrKzohIio= JCIrTExMTDghIio= JCIrKysrKzohIio= JCIrbW1tOzkhIio= JCIrMlp3NjkhIio= JCIrbW1tOzkhIio= JCIrJ286VVQiISIq JCIrUjlAOTkhIio= JCIrJ286VVQiISIq JCIraU5AOTkhIio= JCIrak5AOTkhIio= JCIraU5AOTkhIio= JCIraU5AOTkhIio= JCIrak5AOTkhIio= JCIraU5AOTkhIio= JCIraU5AOTkhIio= JCIrak5AOTkhIio= JCIraU5AOTkhIio= JCIraU5AOTkhIio=
<Text-field style="Heading 2" layout="Heading 2">*3.126. Feladat.</Text-field>
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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn
<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 1" layout="Heading 1">18. Fourier-transzform<Font encoding="UTF-8">\303\241</Font>ci<Font encoding="UTF-8">\303\263</Font></Text-field>
VI. Vari\303\241ci\303\263sz\303\241m\303\255t\303\241s
<Text-field style="Heading 1" layout="Heading 1">19. Az Euler-Lagrange-egyenletek</Text-field>
VII. K\303\266z\303\266ns\303\251ges differenci\303\241legyenletek
<Text-field style="Heading 1" layout="Heading 1">20. Alapfogalmak</Text-field>
<Text-field style="Heading 1" layout="Heading 1">21. Elemi megold<Font encoding="UTF-8">\303\241</Font>si m<Font encoding="UTF-8">\303\263</Font>dszerek</Text-field>
<Text-field style="Heading 1" layout="Heading 1">22. <Font encoding="UTF-8">\303\201</Font>ltal<Font encoding="UTF-8">\303\241</Font>nos eredm<Font encoding="UTF-8">\303\251</Font>nyek</Text-field>
<Text-field style="Heading 1" layout="Heading 1">23. Line<Font encoding="UTF-8">\303\241</Font>ris egyenletek</Text-field>
<Text-field style="Heading 1" layout="Heading 1">24. Stabilit<Font encoding="UTF-8">\303\241</Font>s</Text-field>
VIII. Parci\303\241lis differenci\303\241legyenletek
<Text-field style="Heading 1" layout="Heading 1">25. Alapfogalmak</Text-field>
<Text-field style="Heading 1" layout="Heading 1">26. Disztrib<Font encoding="UTF-8">\303\272</Font>ci<Font encoding="UTF-8">\303\263</Font>k</Text-field>
<Text-field style="Heading 1" layout="Heading 1">27. Cauchy-feladatok</Text-field>
<Text-field style="Heading 1" layout="Heading 1">28. Perem<Font encoding="UTF-8">\303\251</Font>rt<Font encoding="UTF-8">\303\251</Font>k probl<Font encoding="UTF-8">\303\251</Font>m<Font encoding="UTF-8">\303\241</Font>k</Text-field>
<Text-field style="Heading 1" layout="Heading 1">29. Vegyes feladatok</Text-field>
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn