\documentclass[a4paper, 10pt, leqno]{article}

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%% Created with wxMaxima 18.02.0

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                      % "Export animations to TeX" was enabled when this file was generated.

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\begin{document}

\pagebreak{}
{\Huge {\sc wxMaxima, predavanja}}
\setcounter{section}{0}
\setcounter{subsection}{0}
\setcounter{figure}{0}

slajd 8, maxima, komandna linija 


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i1) 
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
\%pi;
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o1} 
\ensuremath{\pi} \mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i2)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
float(\%pi);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o2} 
3.141592653589793\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i3)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
ev(\%pi, numer);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o3} 
3.141592653589793\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i4)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
\%e;
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o4} 
\% e\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i5)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
float(\%e);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o5} 
2.718281828459045\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i6)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
float(\%i);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o6} 
\% i\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i7)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
\%i\^{}2;
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o7} 
-1\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i8)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
sqrt(-1);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o8} 
\% i\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i9)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
sin(\%pi/4);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o9} 
\frac{1}{\sqrt{2}}\mbox{}
\]
%%%%%%%%%%%%%%%
slajd 9, simboli, brojevi, razlomci 


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i10)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
3/4;
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o10} 
\frac{3}{4}\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i11)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
3.0/4;
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o11} 
0.75\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i12)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
3/4.;
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o12} 
\frac{3}{4}\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i13)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
3/4.0;
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o13} 
0.75\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i14)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
float(3/4);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o14} 
0.75\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i15)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
ev(3/4, numer);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o15} 
0.75\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i16)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
1/2-1/3;
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o16} 
\frac{1}{6}\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i17)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
float(\%);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o17} 
0.1666666666666666\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i18)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
sin(2);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o18} 
\sin{(2)}\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i19)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
sin(2.0);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o19} 
0.9092974268256817\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i20)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
63\^{}3;
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o20} 
250047\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i21)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
3\^{}63;
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o21} 
1144561273430837494885949696427\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i22)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
10!;
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o22} 
3628800\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i23)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
100!;
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o23} 
933262154439441526816992388562[98 digits]916864000000000000000000000000\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i24)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
1000!;
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o24} 
402387260077093773543702433923[2508 digits]000000000000000000000000000000\mbox{}
\]
%%%%%%%%%%%%%%%
slajd 10, problemi sa =, osnovna prepreka primeni 


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i25)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
solve(2*x-8 = 2, x);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o25} 
[x=5]\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i26)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
solve(x\^{}2-5*x=-6, x);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o26} 
[x=3,x=2]\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i27)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
solve(x\^{}2-2, x);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o27} 
[x=-\sqrt{2},x=\sqrt{2}]\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i28)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
a;
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o28} 
a\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i29)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
a: 4;
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{a}
4\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i30)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
a;
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o30} 
4\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i31)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
a\$
\end{minipage}


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i32)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
a\^{}3;
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o32} 
64\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i33)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
sqrt(a);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o33} 
2\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i34)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
f(x):=x\^{}2;
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o34} 
\operatorname{f}(x):={{x}^{2}}\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i35)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
f(3);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o35} 
9\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i36)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
f(a);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o36} 
16\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i37)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
f(b);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o37} 
{{b}^{2}}\mbox{}
\]
%%%%%%%%%%%%%%%
slajd 11, =, \% i solve 


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i38)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
\%;
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o38} 
{{b}^{2}}\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i39)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
\%i245;
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o39} 
\mathit{\% i245}\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i40)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
\%o245;
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o40} 
\mathit{\% o245}\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i41)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
3*x+2=8;
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o41} 
3 x+2=8\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i42)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
solve(\%, x);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o42} 
[x=2]\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i43)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
solve(y\^{}3=27, y);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o43} 
[y=\frac{{{3}^{\frac{3}{2}}} \% i-3}{2},y=-\frac{{{3}^{\frac{3}{2}}} \% i+3}{2},y=3]\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i44)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
solve(f(t)=64, t);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o44} 
[t=-8,t=8]\mbox{}
\]
%%%%%%%%%%%%%%%
slajd 12, undefinisanje 


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i45)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
fundef(f);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o45} 
\operatorname{f}(x):={{x}^{2}}\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i46)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
remfunction(f);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o46} 
[f]\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i47)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
remfunction(all);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o47} 
[]\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i48)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
values;
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o48} 
[a]\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i49)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
remvalue(a);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o49} 
[a]\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i50)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
a;
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o50} 
a\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i51)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
a: 2;
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{a}
2\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i52)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
b: 3;
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{b}
3\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i53)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
values;
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o53} 
[a,b]\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i54)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
remvalue(all);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o54} 
[a,b]\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i55)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
values;
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o55} 
[]\mbox{}
\]
%%%%%%%%%%%%%%%
slajd 13, kill 


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i56)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
a: 4;
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{a}
4\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i57)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
b: 5;
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{b}
5\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i58)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
f(x):=x\^{}2;
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o58} 
\operatorname{f}(x):={{x}^{2}}\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i59)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
values;
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o59} 
[a,b]\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i60)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
kill(b);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o60} 
\mathit{done}\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i61)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
values;
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o61} 
[a]\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i62)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
fundef(f);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o62} 
\operatorname{f}(x):={{x}^{2}}\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i63)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
kill(f);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o63} 
\mathit{done}\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i64)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
b: 7;
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{b}
7\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i65)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
values;
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o65} 
[a,b]\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i66)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
kill(all);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o0} 
\mathit{done}\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i1)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
values;
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o1} 
[]\mbox{}
\]
%%%%%%%%%%%%%%%
slajd 14, jos o funkcijama i ev 


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i2)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
f(x):=x\^{}2;
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o2} 
\operatorname{f}(x):={{x}^{2}}\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i3)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
a: x\^{}2;
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{a}
{{x}^{2}}\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i4)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
f(y);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o4} 
{{y}^{2}}\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i5)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
ev(a, x=y);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o5} 
{{y}^{2}}\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i6)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
f(4);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o6} 
16\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i7)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
ev(a, x=4);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o7} 
16\mbox{}
\]
%%%%%%%%%%%%%%%
slajd 15, fpprec i bfloat 


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i8)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
fpprec;
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o8} 
16\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i9)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
float(\%pi);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o9} 
3.141592653589793\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i10)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
bfloat(\%pi);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o10} 
3.141592653589793b0\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i11)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
fpprec: 50;
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{fpprec}
50\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i12)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
bfloat(\%pi);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o12} 
3.1415926535897932384626433832795028841971693993751b0\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i13)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
float(\%pi);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o13} 
3.141592653589793\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i14)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
fpprec: 3;
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{fpprec}
3\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i15)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
bfloat(\%pi);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o15} 
3.14b0\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i16)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
float(\%pi);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o16} 
3.141592653589793\mbox{}
\]
%%%%%%%%%%%%%%%
slajd 16, fpprintprec 


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i17)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
fpprintprec;
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o17} 
0\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i18)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
float(\%pi);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o18} 
3.141592653589793\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i19)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
float(\%e);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o19} 
2.718281828459045\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i20)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
fpprintprec: 3;
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{fpprintprec}
3\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i21)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
float(\%pi);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o21} 
3.14\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i22)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
float(\%e);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o22} 
2.71\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i23)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
fpprintprec: 5;
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{fpprintprec}
5\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i24)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
float(\%pi);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o24} 
3.1415\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i25)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
float(\%e);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o25} 
2.7182\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i26)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
fpprintprec: 0;
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{fpprintprec}
0\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i27)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
float(\%pi);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o27} 
3.141592653589793\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i28)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
float(\%e);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o28} 
2.718281828459045\mbox{}
\]
%%%%%%%%%%%%%%%
slajd 17, expand i factor 


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i29)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
expand((x+1)\^{}2);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o29} 
{{x}^{2}}+2 x+1\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i30)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
expand((x+1)*(x-1));
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o30} 
{{x}^{2}}-1\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i31)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
expand((x-3)\^{}7);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o31} 
{{x}^{7}}-21 {{x}^{6}}+189 {{x}^{5}}-945 {{x}^{4}}+2835 {{x}^{3}}-5103 {{x}^{2}}+5103 x-2187\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i32)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
factor(\%);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o32} 
{{\left( x-3\right) }^{7}}\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i33)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
eq: expand((x-4)*(x-5)*(x-6));
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{eq}
{{x}^{3}}-15 {{x}^{2}}+74 x-120\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i34)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
solve(eq, x);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o34} 
[x=4,x=5,x=6]\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i35)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
factor(eq);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o35} 
\left( x-6\right) \, \left( x-5\right) \, \left( x-4\right) \mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i36)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
factor(4*x\^{}5-4*x\^{}4-13*x\^{}3+x\^{}2-17*x+5);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o36} 
\left( 2 x-5\right) \, \left( {{x}^{2}}+1\right) \, \left( 2 {{x}^{2}}+3 x-1\right) \mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i37)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
factor(1001);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o37} 
7 11 13\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i38)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
factor(123412341234);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o38} 
2 3 7 13 37 617 9901\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i39)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
factor(2048);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o39} 
{{2}^{11}}\mbox{}
\]
%%%%%%%%%%%%%%%
slajd 18, parcijalni razlomci, partfrac(expression, variable) 


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i40)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
ex: (s\^{}3+4*s\^{}2+6*s+4)/(s\^{}3+3*s\^{}2+3*s+1);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{ex}
\frac{{{s}^{3}}+4 {{s}^{2}}+6 s+4}{{{s}^{3}}+3 {{s}^{2}}+3 s+1}\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i41)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
factor(ex);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o41} 
\frac{\left( s+2\right) \, \left( {{s}^{2}}+2 s+2\right) }{{{\left( s+1\right) }^{3}}}\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i42)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
partfrac(ex, s);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o42} 
\frac{1}{s+1}+\frac{1}{{{\left( s+1\right) }^{2}}}+\frac{1}{{{\left( s+1\right) }^{3}}}+1\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i43)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
expand(\%);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o43} 
\frac{1}{{{s}^{3}}+3 {{s}^{2}}+3 s+1}+\frac{1}{{{s}^{2}}+2 s+1}+\frac{1}{s+1}+1\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i44)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
ratsimp(\%);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o44} 
\frac{{{s}^{3}}+4 {{s}^{2}}+6 s+4}{{{s}^{3}}+3 {{s}^{2}}+3 s+1}\mbox{}
\]
%%%%%%%%%%%%%%%
slajd 19, ratsimp i fullratsimp 


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i45)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
kill(all);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o0} 
\mathit{done}\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i1)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
eq: sin(x/(x\^{}2+x))=exp((log(x)+1)\^{}2-log(x)\^{}2);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{eq}
\sin{\left( \frac{x}{{{x}^{2}}+x}\right) }={{\% e}^{{{\left( \log{(x)}+1\right) }^{2}}-{{\log{(x)}}^{2}}}}\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i2)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
ratsimp(eq);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o2} 
\sin{\left( \frac{1}{x+1}\right) }=\% e {{x}^{2}}\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i3)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
((x-1)\^{}(3/2)-(x+1)*sqrt(x-1))/sqrt((x-1)*(x+1));
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o3} 
\frac{{{\left( x-1\right) }^{\frac{3}{2}}}-\sqrt{x-1}\, \left( x+1\right) }{\sqrt{\left( x-1\right) \, \left( x+1\right) }}\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i4)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
ratsimp(\%);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o4} 
-\frac{2 \sqrt{x-1}}{\sqrt{{{x}^{2}}-1}}\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i5)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
expr: (x\^{}(a/2)+1)\^{}2*(x\^{}(a/2)-1)\^{}2/(x\^{}a-1);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{expr}
\frac{{{\left( {{x}^{\frac{a}{2}}}-1\right) }^{2}}\, {{\left( {{x}^{\frac{a}{2}}}+1\right) }^{2}}}{{{x}^{a}}-1}\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i6)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
ratsimp(\%);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o6} 
\frac{{{x}^{2 a}}-2 {{x}^{a}}+1}{{{x}^{a}}-1}\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i7)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
fullratsimp(\%);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o7} 
{{x}^{a}}-1\mbox{}
\]
%%%%%%%%%%%%%%%
slajd 20, trigonometrija 


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i8)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
cos(\%pi/3);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o8} 
\frac{1}{2}\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i9)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
sin(\%pi/3);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o9} 
\frac{\sqrt{3}}{2}\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i10)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
ev(sin(\%pi/3), numer);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o10} 
0.8660254037844386\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i11)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
float(sin(\%pi/3));
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o11} 
0.8660254037844386\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i12)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
csc(45*\%pi/180);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o12} 
\sqrt{2}\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i13)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
tan(\%pi/4);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o13} 
1\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i14)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
tan(\%pi/8);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o14} 
\tan{\left( \frac{\ensuremath{\pi} }{8}\right) }\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i15)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
acos(1/2);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o15} 
\frac{\ensuremath{\pi} }{3}\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i16)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
180/\%pi*asin(sqrt(3)/2);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o16} 
60\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i17)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
acsc(1);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o17} 
\frac{\ensuremath{\pi} }{2}\mbox{}
\]
%%%%%%%%%%%%%%%
slajd 21, trigonometrija, izrazi 


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i18)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
ex: sin(x)\^{}2+cos(x)\^{}2;
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{ex}
{{\sin{(x)}}^{2}}+{{\cos{(x)}}^{2}}\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i19)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
trigsimp(ex);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o19} 
1\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i20)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
kill(all);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o0} 
\mathit{done}\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i1)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
ex: sin(a+b);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{ex}
\sin{\left( b+a\right) }\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i2)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
trigexpand(ex);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o2} 
\cos{(a)} \sin{(b)}+\sin{(a)} \cos{(b)}\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i3)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
trigrat(\%);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o3} 
\sin{\left( b+a\right) }\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i4)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
ex: sin(x)\^{}2;
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{ex}
{{\sin{(x)}}^{2}}\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i5)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
trigsimp(ex);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o5} 
{{\sin{(x)}}^{2}}\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i6)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
trigreduce(ex);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o6} 
\frac{1-\cos{\left( 2 x\right) }}{2}\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i7)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
trigrat(ex);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o7} 
-\frac{\cos{\left( 2 x\right) }-1}{2}\mbox{}
\]
%%%%%%%%%%%%%%%
slajd 22, linearni sistemi jednacina 1 


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i8)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
3*x+2*y=7;
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o8} 
2 y+3 x=7\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i9)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
lhs(\%);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o9} 
2 y+3 x\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i10)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
rhs(\%);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o10} 
0\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i11)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
rhs(\%o253);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o11} 
0\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i12)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
e1: 3*x+2*y=7;
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{e1}
2 y+3 x=7\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i13)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
lhs(e1);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o13} 
2 y+3 x\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i14)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
rhs(e1);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o14} 
7\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i15)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
e2: 5*x-y=3;
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{e2}
5 x-y=3\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i16)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
linsolve([e1,e2], [x,y]);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o16} 
[x=1,y=2]\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i17)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
r: \%;
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{r}
[x=1,y=2]\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i18)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
r[1];
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o18} 
x=1\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i19)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
r[2];
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o19} 
y=2\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i20)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
rhs(r[1]);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o20} 
1\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i21)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
rhs(r[2]);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o21} 
2\mbox{}
\]
%%%%%%%%%%%%%%%
slajd 23, linearni sistemi jednacina 2 


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i22)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
e1;
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o22} 
2 y+3 x=7\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i23)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
e1: 10*x-2*y=6;
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{e1}
10 x-2 y=6\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i24)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
e2;
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o24} 
5 x-y=3\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i25)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
linsolve([e1,e2], [x,y]);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\mbox{}\\\mbox{solve: dependent equations eliminated: (2)}\mbox{}\]
\[\displaystyle
\]
\[\tag{\% o25} 
[x=\frac{\mathit{\% r1}+3}{5},y=\mathit{\% r1}]\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i26)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
e1: 10*x-2*y=5;
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{e1}
10 x-2 y=5\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i27)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
linsolve([e1,e2], [x,y]);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o27} 
[]\mbox{}
\]
%%%%%%%%%%%%%%%
slajd 24, eliminacija 


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i28)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
remvalue(all);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o28} 
[\mathit{ex},\mathit{bestlength},\mathit{trylength},\mathit{e1},\mathit{e2},r]\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i29)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
a1: x+y+2*t=7;
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{a1}
y+x+2 t=7\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i30)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
a2: x-y-t=2;
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{a2}
-y+x-t=2\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i31)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
eliminate([a1,a2], [t]);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o31} 
[-y+3 x-11]\mbox{}
\]
%%%%%%%%%%%%%%%
slajd 25, matrice 


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i32)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
A: matrix([1,2],[2,1]);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{A}
\begin{pmatrix}1 & 2\\
2 & 1\end{pmatrix}\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i33)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
B: invert(A);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{B}
\begin{pmatrix}-\frac{1}{3} & \frac{2}{3}\\
\frac{2}{3} & -\frac{1}{3}\end{pmatrix}\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i34)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
A*B;
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o34} 
\begin{pmatrix}-\frac{1}{3} & \frac{4}{3}\\
\frac{4}{3} & -\frac{1}{3}\end{pmatrix}\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i35)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
a*B;
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o35} 
\begin{pmatrix}-\frac{a}{3} & \frac{2 a}{3}\\
\frac{2 a}{3} & -\frac{a}{3}\end{pmatrix}\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i36)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
A.B;
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o36} 
\begin{pmatrix}1 & 0\\
0 & 1\end{pmatrix}\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i37)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
determinant(A);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o37} 
-3\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i38)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
determinant(B);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o38} 
-\frac{1}{3}\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i39)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
b: matrix([3],[3]);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{b}
\begin{pmatrix}3\\
3\end{pmatrix}\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i40)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
x: B.b;
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{x}
\begin{pmatrix}1\\
1\end{pmatrix}\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i41)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
A.x;
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o41} 
\begin{pmatrix}3\\
3\end{pmatrix}\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i42)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
A.x-b;
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o42} 
\begin{pmatrix}0\\
0\end{pmatrix}\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i43)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
kill(all);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o0} 
\mathit{done}\mbox{}
\]
%%%%%%%%%%%%%%%
slajd 26, Kronecker-Capelli 


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i1)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
A: matrix([5,-1, 3],[10,-2,6]);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{A}
\begin{pmatrix}5 & -1 & 3\\
10 & -2 & 6\end{pmatrix}\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i2)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
echelon(A);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o2} 
\begin{pmatrix}1 & -\frac{1}{5} & \frac{3}{5}\\
0 & 0 & 0\end{pmatrix}\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i3)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
A[2][3]: 5;
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o3} 
5\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i4)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
A;
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o4} 
\begin{pmatrix}5 & -1 & 3\\
10 & -2 & 5\end{pmatrix}\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i5)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
echelon(A);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o5} 
\begin{pmatrix}1 & -\frac{1}{5} & \frac{3}{5}\\
0 & 0 & 1\end{pmatrix}\mbox{}
\]
%%%%%%%%%%%%%%%
slajd 27, nelinearni sistemi 


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i6)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
remvalue(all);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o6} 
[A]\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i7)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
a1: x\^{}2+y\^{}2=41;
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{a1}
{{y}^{2}}+{{x}^{2}}=41\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i8)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
a2: y=x+1;
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{a2}
y=x+1\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i9)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
algsys([a1,a2],[x,y]);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o9} 
[[x=4,y=5],[x=-5,y=-4]]\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i10)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
t: solve(a1, y);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{t}
[y=-\sqrt{41-{{x}^{2}}},y=\sqrt{41-{{x}^{2}}}]\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i11)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
y1: rhs(t[1]);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{y1}
-\sqrt{41-{{x}^{2}}}\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i12)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
y2: rhs(t[2]);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{y2}
\sqrt{41-{{x}^{2}}}\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i13)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
solve(a2, y);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o13} 
[y=x+1]\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i14)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
y3: rhs(solve(a2, y)[1]);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{y3}
x+1\mbox{}
\]
%%%%%%%%%%%%%%%
slajd 28, plotovanje 


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i15)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
plot2d([y1,y2,y3],[x,-10,10],[y,-15,15]);
\end{minipage}
%%% OUTPUT:
%\[\displaystyle
%\mbox{}\\\mbox{plot2d: expression evaluates to non-numeric value somewhere in plotting range.}\mbox{}\\\mbox{plot2d: expression evaluates to non-numeric value somewhere in plotting range.}\mbox{}\]
\[\displaystyle
\]
\[\tag{\% o15} 
[\mbox{}
\]/tmp/maxout11052.gnuplot\_ pipes
\[\displaystyle
]\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i16)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
wxplot2d([y1,y2,y3],[x,-10,10],[y,-15,15]);
\end{minipage}
%%% OUTPUT:
%\[\displaystyle
%\mbox{}\\\mbox{plot2d: expression evaluates to non-numeric value somewhere in plotting range.}\mbox{}\\\mbox{plot2d: expression evaluates to non-numeric value somewhere in plotting range.}\mbox{}\]
\[\displaystyle
\]
\[\tag{\% t16} 
\includegraphics[width=.95\linewidth,height=.80\textheight,keepaspectratio]{wxMaxima-2018_img/wxMaxima-2018_1}\mbox{}\]
\[\displaystyle
\]
\[\tag{\% o16} 
\mbox{}
\]
%%%%%%%%%%%%%%%
slajd 29, limesi 


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i17)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
limit((1+1/x)\^{}(2*x), x, inf);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o17} 
{{\% e}^{2}}\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i18)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
float(\%);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o18} 
7.38905609893065\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i19)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
(x-2)/(x\^{}2-4);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o19} 
\frac{x-2}{{{x}^{2}}-4}\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i20)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
limit(\%, x, 2);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o20} 
\frac{1}{4}\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i21)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
f(x):=atan(x);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o21} 
\operatorname{f}(x):=\operatorname{atan}(x)\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i22)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
limit(f(x), x, inf);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o22} 
\frac{\ensuremath{\pi} }{2}\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i23)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
limit(f(x), x, minf);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o23} 
-\frac{\ensuremath{\pi} }{2}\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i24)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
limit(x\^{}3, x, inf);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o24} 
\infty \mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i25)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
limit(x\^{}3, x, minf);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o25} 
-\infty \mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i26)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
limit(sin(3*x)/x, x, 0);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o26} 
3\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i27)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
limit(sin(3*x)/x, x, inf);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o27} 
0\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i28)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
limit(sin(3*x)/x, x, minf);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o28} 
0\mbox{}
\]
%%%%%%%%%%%%%%%
slajd 30, kombinacije . . . 


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i29)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
f(x):=x\^{}3*tan(x);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o29} 
\operatorname{f}(x):={{x}^{3}} \tan{(x)}\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i30)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
rd: (f(x+h)-f(x))/h;
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{rd}
\frac{{{\left( x+h\right) }^{3}} \tan{\left( x+h\right) }-{{x}^{3}} \tan{(x)}}{h}\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i31)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
limit(rd, h, 0);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o31} 
3 {{x}^{2}} \tan{(x)}+\frac{{{x}^{3}}}{{{\cos{(x)}}^{2}}}\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i32)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
trigsimp(\%);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o32} 
\frac{3 {{x}^{2}} \cos{(x)} \sin{(x)}+{{x}^{3}}}{{{\cos{(x)}}^{2}}}\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i33)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
trigrat(\%);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o33} 
\frac{3 {{x}^{2}} \sin{\left( 2 x\right) }+2 {{x}^{3}}}{\cos{\left( 2 x\right) }+1}\mbox{}
\]
%%%%%%%%%%%%%%%
slajd 31, 0, 0- i 0+ 


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i34)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
limit(1/x, x, 0);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o34} 
\mathit{infinity}\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i35)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
limit(1/x, x, 0, plus);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o35} 
\infty \mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i36)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
limit(1/x, x, 0, minus);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o36} 
-\infty \mbox{}
\]
%%%%%%%%%%%%%%%
slajd 32, izvodi 


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i37)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
remvalue(all);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o37} 
[\mathit{a1},\mathit{a2},t,\mathit{y1},\mathit{y2},\mathit{y3},\mathit{rd},\mathit{bestlength},\mathit{trylength}]\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i38)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
diff(x\^{}2, x);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o38} 
2 x\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i39)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
diff(sin(x), x);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o39} 
\cos{(x)}\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i40)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
diff(sin(x), x, 2);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o40} 
-\sin{(x)}\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i41)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
diff(sin(x), x, 3);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o41} 
-\cos{(x)}\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i42)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
diff(sin(x), x, 4);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o42} 
\sin{(x)}\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i43)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
diff(sin(x*y), x);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o43} 
y \cos{\left( x y\right) }\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i44)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
diff(sin(w*t), t);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o44} 
w \cos{\left( t w\right) }\mbox{}
\]
%%%%%%%%%%%%%%%
slajd 33, razvoj u red 


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i45)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
taylor(sin(x), x, 0, 5);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o45)/T} 
x-\frac{{{x}^{3}}}{6}+\frac{{{x}^{5}}}{120}+\mbox{...}\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i46)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
taylor(cos(x), x, 0, 7);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o46)/T} 
1-\frac{{{x}^{2}}}{2}+\frac{{{x}^{4}}}{24}-\frac{{{x}^{6}}}{720}+\mbox{...}\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i47)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
f(x):=\%e\^{}x-cos(x);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o47} 
\operatorname{f}(x):={{\% e}^{x}}-\cos{(x)}\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i48)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
taylor(f(x), x, 0, 7);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o48)/T} 
x+{{x}^{2}}+\frac{{{x}^{3}}}{6}+\frac{{{x}^{5}}}{120}+\frac{{{x}^{6}}}{360}+\frac{{{x}^{7}}}{5040}+\mbox{...}\mbox{}
\]
%%%%%%%%%%%%%%%
slajd 34, integrali 


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i49)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
integrate(x\^{}2, x);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o49} 
\frac{{{x}^{3}}}{3}\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i50)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
integrate(sin(x), x);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o50} 
-\cos{(x)}\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i51)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
integrate(x\^{}2, x, 1, 2);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o51} 
\frac{7}{3}\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i52)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
integrate(sin(x), x, 0, \%pi);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o52} 
2\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i53)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
integrate(1/(1+x\^{}2), x, 0, 1);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o53} 
\frac{\ensuremath{\pi} }{4}\mbox{}
\]
%%%%%%%%%%%%%%%
slajd 35, operator ' 


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i54)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
kill(all);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o0} 
\mathit{done}\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i1)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
a: 4;
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{a}
4\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i2)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
a;
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o2} 
4\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i3)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
'a;
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o3} 
a\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i4)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
'diff(x\^{}2, x);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o4} 
\frac{d}{d x} {{x}^{2}}\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i5)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
'integrate(x\^{}2, x);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o5} 
\int {\left. {{x}^{2}}dx\right.}\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i6)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
ev(\%, integrate);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o6} 
\frac{{{x}^{3}}}{3}\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i7)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
'integrate(x\^{}2, x, 0, 1);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o7} 
\int_{0}^{1}{\left. {{x}^{2}}dx\right.}\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i8)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
ev(\%, integrate);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o8} 
\frac{1}{3}\mbox{}
\]
%%%%%%%%%%%%%%%
slajd 36, uvod u diferencijalne jednacine 


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i9)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
eq1: 'diff(y, t, 2) + 4 * y = 0;
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{eq1}
\frac{{{d}^{2}}}{d {{t}^{2}}} y+4 y=0\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i10)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
ode2(eq1, y, t);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o10} 
y=\mathit{\% k1} \sin{\left( 2 t\right) }+\mathit{\% k2} \cos{\left( 2 t\right) }\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i11)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
eq2: 'diff(y, t, 2) - 4 * y = 0;
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{eq2}
\frac{{{d}^{2}}}{d {{t}^{2}}} y-4 y=0\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i12)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
ode2(eq2, y, t);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o12} 
y=\mathit{\% k1}\, {{\% e}^{2 t}}+\mathit{\% k2}\, {{\% e}^{-2 t}}\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i13)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
eq3: 'diff(y, t, 2) - 2 * 'diff(y, t) + y = 0;
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{eq3}
\frac{{{d}^{2}}}{d {{t}^{2}}} y-2 \left( \frac{d}{d t} y\right) +y=0\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i14)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
ode2(eq3, y, t);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o14} 
y=\left( \mathit{\% k2} t+\mathit{\% k1}\right) \, {{\% e}^{t}}\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i15)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
eq4: 'diff(y,t,2)+2*'diff(y,t)+4*y=8*sin(4*t);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{eq4}
\frac{{{d}^{2}}}{d {{t}^{2}}} y+2 \left( \frac{d}{d t} y\right) +4 y=8 \sin{\left( 4 t\right) }\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i16)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
ode2(eq4, y, t);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o16} 
y={{\% e}^{-t}}\, \left( \mathit{\% k1} \sin{\left( \sqrt{3} t\right) }+\mathit{\% k2} \cos{\left( \sqrt{3} t\right) }\right) -\frac{6 \sin{\left( 4 t\right) }+4 \cos{\left( 4 t\right) }}{13}\mbox{}
\]
%%%%%%%%%%%%%%%
slajd 37, provera resenja, substitute 


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i17)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
eq: 'diff(y, t, 2) + y = 0;
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{eq}
\frac{{{d}^{2}}}{d {{t}^{2}}} y+y=0\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i18)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
s: ode2(eq, y, t);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{s}
y=\mathit{\% k1} \sin{(t)}+\mathit{\% k2} \cos{(t)}\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i19)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
s: rhs(s);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{s}
\mathit{\% k1} \sin{(t)}+\mathit{\% k2} \cos{(t)}\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i20)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
p: subst(s, y, eq);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{p}
\frac{{{d}^{2}}}{d {{t}^{2}}} \left( \mathit{\% k1} \sin{(t)}+\mathit{\% k2} \cos{(t)}\right) +\mathit{\% k1} \sin{(t)}+\mathit{\% k2} \cos{(t)}=0\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i21)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
ev(p, diff);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o21} 
0=0\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i22)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
is(\%);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o22} 
\mbox{true}\mbox{}
\]
%%%%%%%%%%%%%%%
slajd 38, scripting 

%
%
\noindent
%%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i23)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
batch("dj.mac");
\end{minipage}

%%%% OUTPUT:
%\[\displaystyle
%\mbox{}\\\mbox{read and interpret file: \neq p/home/peja/Desktop/skloni/PSAE-sve/PSAE-sources-2018/11-2018/primeri-11-2017/wxMaxima/dj.mac}\mbox{}\\\mbox{(\% i24) eq1:'diff(y,t,2)+4\cdot y = 0}\mbox{}\]
%\[\displaystyle
%\]
%\[\tag{\% o24} 
%\frac{{{d}^{2}}}{d {{t}^{2}}} y+4 y=0\mbox{}\\\mbox{(\% i25) ode2(eq1,y,t)}\mbox{}\]
%\[\displaystyle
%\]
%\[\tag{\% o25} 
%y=\mathit{\% k1} \sin{\left( 2 t\right) }+\mathit{\% k2} \cos{\left( 2 t\right) }\mbox{}\\\mbox{(\% i26) eq2:'diff(y,t,2)-4\cdot y = 0}\mbox{}\]
%\[\displaystyle
%\]
%\[\tag{\% o26} 
%\frac{{{d}^{2}}}{d {{t}^{2}}} y-4 y=0\mbox{}\\\mbox{(\% i27) ode2(eq2,y,t)}\mbox{}\]
%\[\displaystyle
%\]
%\[\tag{\% o27} 
%y=\mathit{\% k1}\, {{\% e}^{2 t}}+\mathit{\% k2}\, {{\% e}^{-2 t}}\mbox{}\\\mbox{(\% i28) eq3:'diff(y,t,2)-2\cdot 'diff(y,t)+y = 0}\mbox{}\]
%\[\displaystyle
%\]
%\[\tag{\% o28} 
%\frac{{{d}^{2}}}{d {{t}^{2}}} y-2 \left( \frac{d}{d t} y\right) +y=0\mbox{}\\\mbox{(\% i29) ode2(eq3,y,t)}\mbox{}\]
%\[\displaystyle
%\]
%\[\tag{\% o29} 
%y=\left( \mathit{\% k2} t+\mathit{\% k1}\right) \, {{\% e}^{t}}\mbox{}\\\mbox{(\% i30) eq4:'diff(y,t,2)+2\cdot 'diff(y,t)+4\cdot y = 8\cdot sin(4\cdot t)}\mbox{}\]
%\[\displaystyle
%\]
%\[\tag{\% o30} 
%\frac{{{d}^{2}}}{d {{t}^{2}}} y+2 \left( \frac{d}{d t} y\right) +4 y=8 \sin{\left( 4 t\right) }\mbox{}\\\mbox{(\% i31) ode2(eq4,y,t)}\mbox{}\]
%\[\displaystyle
%\]
%\[\tag{\% o31} 
%y={{\% e}^{-t}}\, \left( \mathit{\% k1} \sin{\left( \sqrt{3} t\right) }+\mathit{\% k2} \cos{\left( \sqrt{3} t\right) }\right) -\frac{6 \sin{\left( 4 t\right) }+4 \cos{\left( 4 t\right) }}{13}\mbox{}\]
%\[\displaystyle
%\]
%\[\tag{\% o31} 
%\mbox{}
%\]dj.mac
%(i23)	batch("dj.mac");
\begin{verbatim}
read and interpret file: dj.mac
(%i24) eq1:'diff(y,t,2)+4*y = 0
(%o24)	'diff(y,t,2)+4*y=0
(%i25) ode2(eq1,y,t)
(%o25)	y=%k1*sin(2*t)+%k2*cos(2*t)
(%i26) eq2:'diff(y,t,2)-4*y = 0
(%o26)	'diff(y,t,2)-4*y=0
(%i27) ode2(eq2,y,t)
(%o27)	y=%k1*%e^(2*t)+%k2*%e^(-2*t)
(%i28) eq3:'diff(y,t,2)-2*'diff(y,t)+y = 0
(%o28)	'diff(y,t,2)-2*('diff(y,t,1))+y=0
(%i29) ode2(eq3,y,t)
(%o29)	y=(%k2*t+%k1)*%e^t
(%i30) eq4:'diff(y,t,2)+2*'diff(y,t)+4*y = 8*sin(4*t)
(%o30)	'diff(y,t,2)+2*('diff(y,t,1))+4*y=8*sin(4*t)
(%i31) ode2(eq4,y,t)
(%o31)	y=%e^(-t)*(%k1*sin(sqrt(3)*t)+%k2*cos(sqrt(3)*t))-(6*sin(4*t)+4*cos(4*t))/13
(%o31)	"dj.mac"
\end{verbatim}

slajd 39, Laplasova transformacija 


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i32)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
kill(all);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o0} 
\mathit{done}\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i1)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
laplace(1, t, s);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o1} 
\frac{1}{s}\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i2)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
laplace(sin(w*t), t, s);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o2} 
\frac{w}{{{w}^{2}}+{{s}^{2}}}\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i3)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
laplace(cos(w*t), t, s);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o3} 
\frac{s}{{{w}^{2}}+{{s}^{2}}}\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i4)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
laplace(exp(a*t), t, s);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o4} 
\frac{1}{s-a}\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i5)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
laplace(exp(a*t)*sin(w*t), t, s);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o5} 
\frac{w}{{{w}^{2}}+{{s}^{2}}-2 a s+{{a}^{2}}}\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i6)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
laplace(exp(a*t)*cos(w*t), t, s);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o6} 
\frac{s-a}{{{w}^{2}}+{{s}^{2}}-2 a s+{{a}^{2}}}\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i7)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
laplace(exp(t-T), t, s);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o7} 
\frac{{{\% e}^{-T}}}{s-1}\mbox{}
\]
%%%%%%%%%%%%%%%
slajd 40, inverzna Laplasova transformacija 


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i8)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
ilt(1/(s+2), s, t);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o8} 
{{\% e}^{-2 t}}\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i9)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
ilt(2/(s\^{}2+4), s, t);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o9} 
\sin{\left( 2 t\right) }\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i10)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
ilt((s\^{}2+3*s+3)/(s\^{}3+3*s\^{}2+3*s+1), s, t);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o10} 
\frac{{{t}^{2}}\, {{\% e}^{-t}}}{2}+t\, {{\% e}^{-t}}+{{\% e}^{-t}}\mbox{}
\]
%%%%%%%%%%%%%%%
slajd 40, wxMaxima 


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i11)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
plot3d(x\^{}2-y\^{}2, [x,-1,1], [y,-1,1]);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% o11} 
[\mbox{}
\]/tmp/maxout11052.gnuplot\_ pipes
\[\displaystyle
]\mbox{}
\]
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{12ex}\color{red}\bf
(\% i12)
\end{minipage}
\begin{minipage}[t]{\textwidth}\color{blue}
wxplot3d(x\^{}2-y\^{}2, [x,-1,1], [y,-1,1]);
\end{minipage}
%%% OUTPUT:
\[\displaystyle
\tag{\% t12} 
\includegraphics[width=.95\linewidth,height=.80\textheight,keepaspectratio]{wxMaxima-2018_img/wxMaxima-2018_2}\mbox{}\]
\[\displaystyle
\]
\[\tag{\% o12} 
\mbox{}
\]
%%%%%%%%%%%%%%%
\end{document}
