wake up

大家直接忽略这一篇阿，我拿blog当个中转站而已...顺便抒发下，忙活了一个晚上就为了这些，唉，好累好累的一天。

$\star$\textbf{pdf/jpg-Bild}:$\backslash$usepackage\{graphicx\}…$\backslash$includegraphics[width=0.5$\backslash$textwidth]\{bild.jpg\}\

$\star$\textbf{eps-Bild}:$\backslash$usepackage\{epsf\}…$\backslash$epsfx(y)size 10cm…$\backslash$epsfbox\{bild.eps\} \

$\backslash$left$\backslash$\{$\backslash$begin\{array\}\{cl\}\

1\& $\backslash$mbox\{für \} i=k$\backslash$$\backslash#CONTENT#\& \mbox\{für \} i$\backslash$neq k   $\backslash$end\{array\} $\backslash$right.\

f(i)

\quad (i,k=0,1,$\backslash$ldots,m)$\star$ Leere Zeichen: $\backslash$, \hspace{0.1cm} $\backslash$: \hspace{0.1cm} $\backslash$; \hspace{0.1cm} $\backslash$! \

{\Large\textbf{Matlabteil:}} \

$\star$ A=[1 2 3;4,5,6]; A(2,3)=$a_23$,A(2:4)=(2. bis 4. Elemente);A(2,:)=(2. Zeile);

A(1:2,1:2)=(1.bis2. Zeilen bzw. Spalten);B=(2*)ones(zeros,eye)(4,4); E(1,:)=[] (1.Zeile streichen);

x=1:2:7(=1,3,5,7), D=[A(1:3,1:2) A(1:3,3:4)] (qianhou$A^{3*2}$)\C=[A(1,:); 0 0 0 2; A(2,:); A(3,:)](HuanHang); D=zeros(ones,eye)(4,4) [m,n]=size(A)\

Sei A gegeben:diag(A)(als Spaltenvektor);diag(diag(A))(Matrix); A./B; a=ones(19,1),v=1:1:20,

b=2*a,A=diag(v)+diag(a,1)(ober)+diag(b,-1)(unter)\

\quad $[x,y]$=meshgrid(-1:1:1,-2:1:0)(2 Matr.);\

$\star$\textit{Operationen mit Matrizen:}A’,A+B,A*B,A\^{}3,A/B,A.*(/,\^{})B(elementweise Mult.) \

a=input('a='); disp('show text');

$\star$\textbf{Graphik:} a=input('a=');x=0:0,1:10;y=x./(1+a.*x+x.\^{}2);figure(1);subplot(2,2,1);plot(x,y,'r-','MarkerEdge(Face)color','k'(hei)('g'),'MarkerSize',15,'LineWidth,2) \hspace{0.2cm}\textit{3D:}t=0:0.01:1;x=x(t);y=y(t);z=z(t);plot3(x,y,z);grid on

\hspace{0.2cm}\textit{Höhenkarte:}$[x,y]$=meshgrid(-1:1:1,-2:1:0);z=x.*y.*(x.^2+y.^2-1);(surf,surfl)mesh(x,y,z); [c,h]=contour(x,y,z,150);clabel(c,h,'manual')-(Höhe markieren)\

axis equal,off,on \hspace{0.2cm}hold on;\

legend('f(x)','g(x)','h(x)'); title('...')\quad mesh(x,y,z);surf(x,y,z);surfl(x,y,z);

$\star$\textbf{Balken- und Kuchendiagramme:}\quad A=[1,2,;3,4;5,6];(barh,bar3)bar(A).

B=[0.2,0.5,0.3];figure(1);pie(A,{'SPD','CDU','CSU'})(bing); saveas(figure(1),'2005.eps','eps');\

bar(C)(zhu)\quad[c,h]=contour(x,y,z,150);clabel(c,h,'manual');(DengGao)\

$\star$\textbf{Logische Ausdrücke:}\<,\>,\<=,\>=,==,\~{}=,\&,$\mid$(oder),\~{}\

$\star$\textbf{Ein- und Ausgabe:}

fid=fopen(’datei’);Zeile1=fgetl(fid)...Z=fscanf(fid,’\%g’,[2,7]);title(Zeile1);fclose(fid).

(oderA=load('aufgabe16.ein'),n=length(A););\quadfid=fopen('aufgabe16.aus','w');fprintf(fid,'\%4.3f \%11.6f$\backslash$n', [A';B']); fclose(fid); open aufgabe16.aus;\quad Ausgabe auf dem Bildschirm:text=sprintf’(A(2,3)=\%6.2f’,A(2,3));disp(text)\

$\star$\textbf{Verzweigungen:}

p=input('p=');$\backslash$$\backslash$switch p$\backslash$$\backslash$

case\{…\}$\backslash$$\backslash$disp('…')$\backslash$$\backslash$...otherwise$\backslash$$\backslash$disp('…')$\backslash$$\backslash$end\

if…$\backslash$$\backslash$Anweisungen;elseif…else…end\

function li=l(x,t,i) $\backslash$$\backslash$y = 1;i=i+1;m=length(t);for j=1:m

$\backslash$$\backslash$if j~=i $\backslash$$\backslash$ y=y.*(x-t(j))./(t(i)-t(j));end

$\backslash$$\backslash$end$\backslash$$\backslash$li=y\

$\star$\textbf{Rechn:} log2(7);abs();

round()(4,5);floor();ceil();sum(A) (Spalten aufsummieren,ergibt als Zeilenvektor);\~{}=; sqrt(x);

prod(x,1)(1:i); rand(m,n)\

$\star$Pixelbilder:colormap(colorcube(12));image(A)\

{\Large\textbf{Numerisches Rechnen:}}\

$\star$

\begin{eqnarry*}

x=3.1415...=10^1(3*10^{-1}+1*10^{-2}+4*10^{-3}+5*10^{-4}+...)\

x=11.1875 \hspace{0.2cm}Dezimal(10):0.111875*10^2\hspace{0.2cm}Dual(2):0.10110011*2^4=2^4*(1*2^{-1}+0*2^{-2}+1*2^{-3}+...)\hspace{0.2cm}Hexadezimal(16):0.B3*16^1=16*(11*16^{-1}+3*16^{-2})(1,0,1,1=[1*2^3+0*2^2+1*2^1+1*2^0]=11)

\end{eqnarry*}

$\star$\textbf{Hornerschema:}

\begin{eqnarry*}

a_{n}^{(1)}=a_{n}^{(0)} \hspace{0.2cm} a_{n-i}^{(1)}=a_{n-1}^{(0)}+a_{n-i+1}^{(1)}*t_0

\hspace{0.2cm} a_{0}^{(1)}=p(t_0)

\end{eqnarry*}

Taylor-Entwicklung:

\begin{equation*}

p(t)= \sum\limits_{i=0}^{n}\frac{p^{(i)}(t_0)}{i!}*(t-t_0)^i

\end{equation*}

{\Large\textbf{Mapleteil:}}\

$\star$ \#(Kommentar); x:=10(+,-,*,/,\^{});pi; 30!\

Digits:=40;evalf()(Kommadars. Hier 40 Dezimalstellen);

binomial(43, 3)($C_{43}^3$); sqrt();sin(1.0); log[2](16);

(sin@exp)(z);:($sin(e^z)$); (ln@@2)(z;):($ln^{(2)}(z)$);D(cos);:-sin;

c:= expand(d)(zhankai); factor(c)(Helong);simplify(z):(huajian)\

$\star$ $f := x \rightarrow exp(sqrt(2*x^2+10)+5*x^3)$; f(2); diff(f(z),z)(f'(z)) oder D(f)(f’(x)); diff(f(z), z,z)(f''(x)); diff(f(z),z$3)(3mal); diff(h(u,v),u)($h_u$);diff(h(u,v),u,v)($h_{uv}$) oder D[1,2](h)($h_{xy}$); \

$\star$ int(f(w),w)(integal); int(exp(-t\^{}2),t=-infinity..infinity);\quad int(x\^{}3*cos(10*x), x = 0..2*pi);\

$\star$ sum(f(i), i = 1..10)(Reihe:infinity);\quad limit((sin(x)-x)/x\^{}3, x = 0):($lim_

{x\rightarrow0}$);\quad taylor(ln(1+z),z = 0,10):($x_0$=0,grad=10); \

$\star$solve(2*x\^{}5-3*x\^{}4+38*x\^{}3-57*x\^{}2-300*x = -450, x); \quad

evalf(allvalues(solve(\{16*x\^{}4+16*y\^{}4+z\^{}4 = 16,x\^{}2+y\^{}2+z\^{}2 = 3, x\^{}3-y = 0\}, [x, y, z])))

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