Y
Ingenieurmathematik Prüfung 2
12.Mai2009
Zeit 90 Minuten, Reihenfolge beliebig, 8 Punkte pro Hauptaufgabe,
40 Pt. = N.6.
zsqr = exp(j*pi/4) tstsq = zsqr^2 dum = input('YL1a) weiter?');
M = [6 3 0; 0 3 0]; MM= [M M]; % Anfangspunkt muss nochmal vorkommen plot(MM(1,:),MM(2,:)); axis equal dum = input('YL1b) weiter?');
Oexa = [0 1; 1 0] Otst = Oexa'*Oexa dum = input('YL1c) weiter?');
disp('Diagonalelement in dieser Spalte k') disp('if abs(A(k,k)) > 0') dum = input('YL1d) weiter?');
w = 0:pi/40:4*2*pi; r = 3 h = 6/4 , x = w*h/(2*pi); z = r*cos(w) ; % z = r*cos(w) ; y = r*sin(w) ; % y = r*sin(w) ; figure(1); clf plot3(x,y,z); axis equal dum = input('YL2) weiter?');
figure(1); clf wnro = 0:5; wo = 2*pi*wnro/5 + pi/2; zo = exp(j*wo); wnrh = 0:10; wh = 2*pi*wnrh/10 + pi/2; zh = exp(j*wh); plot(zo,'k') ; hold on ; plot(zh, 'r');axis equal; hold off dum = input('YL3) weiter?');
figure(1); clf A = [ 0 0 0]'; B = [ 8 0 0]'; C = [ 8 3 0]'; D = [ 0 3 0]'; E = [ 0 0 6]'; F = [ 8 0 6]'; G = [ 8 3 6]'; H = [ 0 3 6]'; Mab = (A+B)/2; Mcd = (C+D)/2; Nf = cross(D-Mab,H-Mab), enf = Nf/norm(Nf) dkrf = enf'*Mab, dtD = enf'*D-dkrf, dtH = enf'*H-dkrf eng = enf % Parallele Ebenen dkrg = eng'*B, dtMcd = eng'*Mcd-dkrg, dtF = eng'*F-dkrg % en'*(Vg + lam*rg) - dkrit - 0 % lam = (dkrit - en'*Vg)/(en'*rg) laf = dkrf / (enf'*(G-A)) , DPtf = 0 + laf * G lag = dkrg / (enf'*(G-A)) , DPtg = 0 + lag * G dum = input('YL4) weiter?');
% function Apt = antsymmcop(M) M = rand(5) [nzei,nspa] = size(M); Apt = M; for zei = 2:nzei for spa = 1:zei-1 Apt(zei,spa) = -Apt(spa,zei); end end for k = 1:nzei Apt(k,k) = 0; end Apt, Tasym = Apt'+Apt dum = input('YL5) weiter?');
figure(1); clf Dori = [ 0 10 5 0; 0 0 5*sqrt(3) 0; 1 1 1 1] w = atand(sqrt(3)) Rot1 = [ cosd(-w) -sind(-w) 0; sind(-w) cosd(w) 0; 0 0 1] Mx = [1 0 0; 0 -1 0 ; 0 0 1] Rot2 = [ cosd(w) -sind(w) 0; sind(w) cosd(w) 0; 0 0 1] Ttot = Rot2*Mx*Rot1 Dtr = Ttot*Dori plot(Dori(1,:), Dori(2,:)) hold on axis([-12 12 -12 12]); axis square plot([0 0 ],[-12 12],'k') ; plot([-12 12 ],[0 0],'k') plot([-5 15],[-5*sqrt(3) 15*sqrt(3)],'k') plot(Dtr(1,:), Dtr(2,:),'r') hold off dum = input('YL6) weiter?');