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symbolick\[AAcute] line\[AAcute]rn\[IAcute] algebra, symbolick\[EAcute] \
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Tato \[CHacek]\[AAcute]st p\[RHacek]edstavuje operace na polynomech a racion\
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V podstat\[EHacek] v\[SHacek]echny symbolick\[EAcute] funkce jsou zalo\
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\[CapitalRHacek]e\[SHacek]te kvadratickou rovnici s nezn\[AAcute]mou x.\
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\[CapitalRHacek]e\[SHacek]te rovnici s omezen\[IAcute]mi \
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N\[EHacek]kter\[EAcute] transcendent\[AAcute]ln\[IAcute] rovnice mohou b\
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Cell["\<\
Mnoho nepolynomi\[AAcute]ln\[IAcute]ch rovnic je trnascendent\[AAcute]ln\
\[IAcute]ch a nemohou b\[YAcute]t \[RHacek]e\[SHacek]eny \
algebraick\[YAcute]mi metodami. \
\>", "MathCaption",
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Cell[TextData[{
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 " nalezne ko\[RHacek]eny t\[EHacek]chto transcendent\[AAcute]ln\[IAcute]ch \
rovnic a\[CHacek]koliv jsou repreznetov\[AAcute]ny jako ",
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Cell["\<\
N\[AAcute]sleduj\[IAcute]c\[IAcute] konvertuje ko\[RHacek]eny na explicitn\
\[IAcute] \[CHacek]\[IAcute]sla.\
\>", "MathCaption",
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 "RSolve"
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Cell[TextData[{
 "Rekurentn\[IAcute] rovnice (diferen\[CHacek]n\[IAcute] rovnice 1. \[RHacek]\
\[AAcute]du) mohou b\[YAcute]t \[RHacek]e\[SHacek]eny s pou\[ZHacek]it\
\[IAcute]m ",
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  ButtonBox["RSolve",
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 ". N\[AAcute]sleduj\[IAcute]c\[IAcute], nap\[RHacek]\[IAcute]klad \[RHacek]e\
\[SHacek]\[IAcute] logistick\[EAcute] rovnice pomoc\[IAcute] trigonometrick\
\[YAcute]ch funkc\[IAcute]."
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Cell["\<\
N\[AAcute]sleduj\[IAcute]c\[IAcute] \[RHacek]e\[SHacek]en\[IAcute] rekurentn\
\[IAcute]ch rovnic vede na Fibonacciho posloupnost. \
\>", "MathCaption",
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Cell[TextData[{
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 "Pou\[ZHacek]it\[IAcute] seznamu pravidel"
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Cell[TextData[{
 "Mnoho funkc\[IAcute] v ",
 StyleBox["Mathematica",
  FontSlant->"Italic"],
 " generuje v\[YAcute]stup ve form\[EHacek] seznamu pravidel. Nap\[RHacek]\
\[IAcute]klad v\[YAcute]stup funkce ",
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 " je seznam \[RHacek]e\[SHacek]en\[IAcute], kter\[EAcute] ka\[ZHacek]d\
\[EAcute] je reprezentov\[AAcute]no jako pravidlo ve tvaru ",
 StyleBox["var\[ThinSpace]",
  FontSlant->"Italic"],
 "\[Rule]\[ThinSpace]",
 StyleBox["expr",
  FontSlant->"Italic"],
 ". \[CapitalCHacek]asto je t\[RHacek]eba z\[IAcute]skat samostatn\[EAcute] v\
\[YAcute]razy na prav\[EAcute] stran\[EHacek] t\[EHacek]chto pravidel a pou\
\[ZHacek]\[IAcute]t je v dal\[SHacek]\[IAcute]ch v\[YAcute]po\[CHacek]tech. "
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Cell["\<\
Zde je soustava rovnic, kter\[AAcute] m\[AAcute] 4 \[RHacek]e\[SHacek]en\
\[IAcute] dan\[YAcute]ch pravidly.\
\>", "MathCaption",
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Cell["\<\
N\[AAcute]sleduj\[IAcute]c\[IAcute] p\[RHacek]\[IAcute]kaz vykresl\[IAcute] \
ob\[EHacek] k\[RHacek]ivky dan\[EAcute] rovnicemi.\
\>", "MathCaption",
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Cell["\<\
P\[RHacek]edpokl\[AAcute]dejme, \[ZHacek]e chceme vykreslit tato 4 \[RHacek]e\
\[SHacek]en\[IAcute] spolu s grafy obou k\[RHacek]ivek. Nejprve z\[IAcute]sk\
\[AAcute]me hodnoty \[RHacek]e\[SHacek]en\[IAcute] na prav\[YAcute]ch stran\
\[AAcute]ch pravidel.\
\>", "MathCaption",
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Cell[TextData[{
 "Pomoc\[IAcute] takto z\[IAcute]skan\[YAcute]ch sou\[RHacek]adnic \[RHacek]e\
\[SHacek]en\[IAcute] a grafick\[EAcute]ho primitivu ",
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   BaseStyle->"Link",
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 " vykresl\[IAcute]me po\[ZHacek]adovan\[EAcute] body \[RHacek]e\[SHacek]en\
\[IAcute] do grafu."
}], "MathCaption",
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Cell["\<\
Uvoln\[IAcute]me v\[SHacek]echny pou\[ZHacek]it\[EAcute] symboly.\
\>", "MathCaption",
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Cell[CellGroupData[{

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Cell[CellGroupData[{

Cell[TextData[{
 "integr\[AAcute]l, ur\[CHacek]it\[YAcute] a neur\[CHacek]it\[YAcute]\
\[LongDash]",
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Cell["\<\
vlo\[ZHacek]en\[IAcute] znaku integr\[AAcute]lu z palety nebo z \
kl\[AAcute]vesnice\
\>", "Item",
 CellChangeTimes->{{3.579348021296875*^9, 3.5793480420625*^9}},
 CellTags->"Calculus"],

Cell[TextData[{
 "derivace\[LongDash]",
 Cell[BoxData[
  ButtonBox["D",
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   ButtonData->"paclet:ref/D"]], "InlineFormula"]
}], "Item",
 CellChangeTimes->{{3.579348045296875*^9, 3.57934804684375*^9}},
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Cell[TextData[{
 "diferenci\[AAcute]ln\[IAcute] rovnice\[LongDash]",
 Cell[BoxData[
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   ButtonData->"paclet:ref/DSolve"]]]
}], "Item",
 CellChangeTimes->{{3.579348051984375*^9, 3.579348057875*^9}},
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Cell[TextData[{
 "limity a \[RHacek]ady\[LongDash]",
 Cell[BoxData[
  ButtonBox["Limit",
   BaseStyle->"Link",
   ButtonData->"paclet:ref/Limit"]], "InlineFormula"],
 " a ",
 Cell[BoxData[
  ButtonBox["Series",
   BaseStyle->"Link",
   ButtonData->"paclet:ref/Series"]]]
}], "Item",
 CellChangeTimes->{{3.579348060609375*^9, 3.579348070078125*^9}},
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Cell[CellGroupData[{

Cell["", "SlideShowNavigationBar",
 CellTags->"SlideShowHeader"],

Cell[CellGroupData[{

Cell[TextData[{
 StyleBox["Kalkulus: ", "Color7",
  FontSlant->"Plain"],
 "Symbolick\[YAcute] integr\[AAcute]l"
}], "Subsection",
 CellChangeTimes->{{3.579348073171875*^9, 3.5793480885*^9}},
 CellTags->"Calculus"],

Cell[TextData[{
 "Symbolick\[YAcute] integr\[AAcute]l je ur\[CHacek]en \
pou\[ZHacek]it\[IAcute]m funkce ",
 Cell[BoxData[
  ButtonBox["Integrate",
   BaseStyle->"Link",
   ButtonData->"paclet:ref/Integrate"]], "InlineFormula"],
 "."
}], "Text",
 CellChangeTimes->{{3.57934809153125*^9, 3.57934811271875*^9}},
 CellTags->"Calculus"],

Cell["\<\
N\[AAcute]sleduj\[IAcute]c\[IAcute] vypo\[CHacek]te neur\[CHacek]it\[YAcute] \
integral.\
\>", "MathCaption",
 CellChangeTimes->{{3.57934811640625*^9, 3.57934813665625*^9}},
 CellTags->"Calculus"],

Cell[BoxData[
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    RowBox[{"Cos", "[", "x", "]"}]}], ",", "x"}], "]"}]], "Input",
 CellTags->"Calculus"],

Cell[TextData[{
 "Pokud druh\[YAcute] argument obsahuje meze integr\[AAcute]lu, potom funkce ",
 Cell[BoxData[
  ButtonBox["Integrate",
   BaseStyle->"Link",
   ButtonData->"paclet:ref/Integrate"]], "InlineFormula"],
 " vrac\[IAcute] ur\[CHacek]it\[YAcute] integr\[AAcute]l."
}], "MathCaption",
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Cell[BoxData[
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 CellTags->"Calculus"],

Cell["\<\
V\[SHacek]imn\[EHacek]me si, \[ZHacek]e integr\[AAcute]l je mo\[ZHacek]n\
\[EAcute] vlo\[ZHacek]it pomoc\[IAcute] tradi\[CHacek]n\[IAcute] notace. \
Tento vstup je ekvivalentn\[IAcute] p\[RHacek]\[IAcute]kazu z p\[RHacek]edch\
\[AAcute]zej\[IAcute]c\[IAcute]ho p\[RHacek]\[IAcute]kladu.\
\>", "MathCaption",
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Cell[BoxData[
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 CellTags->"Calculus"],

Cell[TextData[{
 "Mnoho symbolick\[YAcute]ch integr\[AAcute]l\[URing] s parametry \
nen\[IAcute] mo\[ZHacek]n\[EAcute] symbolicky ur\[CHacek]it bez \
dopl\[NHacek]uj\[IAcute]c\[IAcute] informace o t\[EHacek]chto parametrech. \
Nastaven\[IAcute] ",
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 " je pou\[ZHacek]ito ve funkci ",
 Cell[BoxData[
  ButtonBox["Integrate",
   BaseStyle->"Link",
   ButtonData->"paclet:ref/Integrate"]], "InlineFormula"],
 " ke specifikaci informace o dom\[EAcute]n\[EHacek] parametr\[URing] v \
integrandu."
}], "Text",
 CellChangeTimes->{{3.57934826065625*^9, 3.579348397546875*^9}},
 CellTags->"Calculus"],

Cell["\<\
Nap\[RHacek]\[IAcute]klad n\[AAcute]sleduj\[IAcute]c\[IAcute] \
integr\[AAcute]l nelze ur\[CHacek]it bez dodate\[CHacek]n\[EAcute]m \
p\[RHacek]edpokladu o parametru c.\
\>", "MathCaption",
 CellChangeTimes->{{3.579348401984375*^9, 3.579348447859375*^9}},
 CellTags->"Calculus"],

Cell[BoxData[
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  RowBox[{
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     SuperscriptBox["x", "2"]}], "]"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", ",", "0", ",", "\[Infinity]"}], "}"}]}], "]"}]], "Input",
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Cell[TextData[{
 "Ale s p\[RHacek]edpokladem ",
 Cell[BoxData[
  FormBox[
   RowBox[{"a", "<", "0"}], TraditionalForm]]],
 " tje mo\[ZHacek]n\[EAcute] integr\[AAcute]l kompletn\[EHacek] ur\[CHacek]it."
}], "MathCaption",
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Cell[BoxData[
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  RowBox[{
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    RowBox[{"a", " ", 
     SuperscriptBox["x", "2"]}], "]"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", ",", "0", ",", "\[Infinity]"}], "}"}], ",", 
   RowBox[{"Assumptions", "\[Rule]", 
    RowBox[{"a", "<", "0"}]}]}], "]"}]], "Input",
 CellTags->"Calculus"],

Cell["\<\
M\[URing]\[ZHacek]eme integrovat multidimenzion\[AAcute]ln\[IAcute] integr\
\[AAcute]ly specifikac\[IAcute] hranic pro ka\[ZHacek]dou prom\[EHacek]nnou.\
\>", "Text",
 CellChangeTimes->{{3.579348563015625*^9, 3.57934860959375*^9}},
 CellTags->"Calculus"],

Cell[TextData[{
 "N\[AAcute]sleduj\[IAcute]c\[IAcute] ur\[CHacek]\[IAcute] multiple integr\
\[AAcute]l ",
 Cell[BoxData[
  FormBox[
   RowBox[{
    SubsuperscriptBox["\[Integral]", "0", "1"], 
    RowBox[{
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     RowBox[{
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       StyleBox["x", "TI"]], 
      RowBox[{
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       RowBox[{"(", 
        RowBox[{
         SuperscriptBox["x", "2"], "+", 
         SuperscriptBox[
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  "InlineFormula"],
 ". Rozsah vn\[EHacek]j\[SHacek]\[IAcute] prom\[EHacek]nn\[EAcute] se uv\
\[AAcute]d\[IAcute] jako prvn\[IAcute]. "
}], "MathCaption",
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Cell[BoxData[
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   RowBox[{"{", 
    RowBox[{"y", ",", "0", ",", "x"}], "}"}]}], "]"}]], "Input",
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Cell[TextData[{
 "Tento p\[RHacek]\[IAcute]kaz integruje ",
 Cell[BoxData[
  FormBox[
   SuperscriptBox["x", "2"], TraditionalForm]]],
 " na oblasti jednotkov\[EAcute]ho kruhu s vyu\[ZHacek]it\[IAcute]m funkce \
Boolean k definici t\[EAcute]to oblasti. ",
 StyleBox["Boole[", "MR"],
 StyleBox["expr", "IT"],
 StyleBox["]", "MR"],
 " vrac\[IAcute] 1 kdykoliv je ",
 StyleBox["expr",
  FontSlant->"Italic"],
 "  ",
 Cell[BoxData[
  ButtonBox["True",
   BaseStyle->"Link",
   ButtonData->"paclet:ref/True"]], "InlineFormula"],
 " a vrac\[IAcute] 0 pokud je ",
 StyleBox["expr",
  FontSlant->"Italic"],
 " ",
 Cell[BoxData[
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\[SHacek]\[IAcute]ch \[RHacek]\[AAcute]d\[URing] s pou\[ZHacek]it\[IAcute]m \
formy ",
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M\[URing]\[ZHacek]eme po\[CHacek]\[IAcute]tat i parci\[AAcute]ln\[IAcute] \
derivace.\
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Cell["\<\
Nebo je mo\[ZHacek]n\[EAcute] pou\[ZHacek]\[IAcute]t trad\[CHacek]n\[IAcute] \
notaci (snadno dostupnou z palet).\
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Cell["\<\
Lze pou\[ZHacek]\[IAcute]t tak\[EAcute] tradi\[CHacek]n\[IAcute] notaci k v\
\[YAcute]po\[CHacek]tu derivace funkce.\
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Cell[TextData[{
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Cell[TextData[{
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\[IAcute]ch rovnic je mo\[ZHacek]n\[EAcute] vypo\[CHacek]\[IAcute]tat pomoc\
\[IAcute] funkce ",
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Cell[TextData[{
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\[AAcute]ln\[IAcute] rovnici ",
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hledanou funkci, t\[RHacek]et\[IAcute] argument ur\[CHacek]uje \
prom\[EHacek]nou. V\[YAcute]sledek je d\[AAcute]n pravidly stejn\[EHacek] tak \
jako v\[YAcute]sledek z funkce ",
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Omezen\[IAcute] a po\[CAcute]\[AAcute]te\[CHacek]n\[IAcute] podm\[IAcute]nky \
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Zde je neline\[AAcute]rn\[IAcute] diferenci\[AAcute]ln\[IAcute] rovnice 1. \
\[RHacek]\[AAcute]du. V t\[EHacek]chto p\[RHacek]\[IAcute]padech je nalezen\
\[IAcute] \[RHacek]e\[SHacek]en\[IAcute] snadn\[EAcute].\
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P\[RHacek]\[IAcute]kaz vykresl\[IAcute] graf prvn\[IAcute]ho \[RHacek]e\
\[SHacek]en\[IAcute] v ur\[CHacek]en\[EAcute]m rozsahu.\
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Cell[TextData[{
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Cell[TextData[{
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rozvoj p\[RHacek]\[IAcute]slu\[SHacek]n\[EAcute] funkce a stupe\[NHacek] \
rozvoje."
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Cell[TextData[{
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\[IAcute] funkce ",
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optimalizov\[AAcute]n pro pr\[AAcute]ci s ostatn\[IAcute]m v\[YAcute]sledky \
funkce. Pokud pot\[RHacek]ebujeme pracovat s polynomem, je nutn\[EAcute] \
konvertovat datov\[YAcute] objekt na regul\[AAcute]rn\[IAcute] polynom pomoc\
\[IAcute] funkce ",
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aproximaci funkce na polynom a pot\[EAcute] je tento rozvoj vykreslen spolu s \
aproximovanou funkc\[IAcute] ",
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Cell["\<\
Existuje velmi m\[AAcute]lo obecn\[YAcute]ch algoritm\[URing], kter\[EAcute] \
um\[IAcute] ur\[CHacek]it limity nebo rozvoj funkc\[IAcute], pro \
kter\[EAcute] neexistuje mocninn\[YAcute] rozvoj. Pou\[ZHacek]it\[YAcute] \
odpov\[IAcute]daj\[IAcute]c\[IAcute] v\[YAcute]po\[CHacek]et \[CHacek]asto \
sel\[ZHacek]e.\
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Cell["\<\
zjednodu\[SHacek]en\[IAcute] s pou\[ZHacek]it\[IAcute] p\[RHacek]edpoklad\
\[URing]\
\>", "Item",
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Cell["\<\
doporu\[CHacek]en\[IAcute] pro zjednodu\[SHacek]en\[IAcute] v\[YAcute]raz\
\[URing]\
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\[IAcute] operace a dal\[SHacek]\[IAcute] transformace a vrac\[IAcute] \
nejjednodu\[SHacek]\[SHacek]\[IAcute] formu, kterou nalezne."
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\[YAcute]po\[CHacek]et v\[EHacek]t\[SHacek]inou trv\[AAcute] d\[EAcute]le, \
ale vede k jednodu\[SHacek]\[SHacek]\[IAcute]mu v\[YAcute]sledku."
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Cell["\<\
Ve v\[EHacek]t\[SHacek]in\[EHacek] p\[RHacek]\[IAcute]pad\[URing] existuj\
\[IAcute] dal\[SHacek]\[IAcute] funkce a jejich kombinace, kter\[EAcute] \
vedou p\[RHacek]\[IAcute]mo a efektivn\[EHacek] k jednoduch\[EAcute]mu v\
\[YAcute]sledku.\
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