musabe24/labor_mathematische_anwendungen
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Lösungen der Aufgaben rüberkopiert.

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Musab Erdem
2024-02-26 16:58:38 +01:00
parent be933b27d3
commit e81056717e
39 changed files with 449 additions and 0 deletions
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20
MATLAB/Uebungen/02 Symbolic Math Toolbox/Aufgabe 3/Aufgabe3.m Normal file
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syms t s;
sigma = heaviside(t);
SIGMA(s) = laplace(sigma,s);
syms s D w_0 w_e;
assume(w_0>0);
assumeAlso(0<D<1);
G(s) = 1/((1 / w_0^2)*s^2+(2*D/w_0)*s+1);
H(s) = SIGMA * G;
h(t) = ilaplace(H, t);
w_e = w_0*(1 - D^2)^(1/2);
disp(simplify(h,"Steps",100));

14
MATLAB/Uebungen/02 Symbolic Math Toolbox/Aufgabe 4/Aufgabe4_a.m Normal file
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syms x;
f(x) = x^x;
f_x = diff(f,x);
f_xx = diff(f_x,x);
f_xxx = diff(f_xx,x);
disp("f'(x):");
disp(simplify(f_x,100));
disp("f''(x):");
disp(simplify(f_xx,100));
disp("f'''(x):");
disp(simplify(f_xxx,100));

4
MATLAB/Uebungen/02 Symbolic Math Toolbox/Aufgabe 4/Aufgabe4_b.m Normal file
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syms x;
f(x) = tan(x);
f_x = diff(f,x);
disp(f_x);

5
MATLAB/Uebungen/02 Symbolic Math Toolbox/Aufgabe 4/Aufgabe4_c.m Normal file
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syms x;
f(x) = 1-x / sqrt(x)-x;
f_x = diff(f,x);
disp(f_x);

8
MATLAB/Uebungen/02 Symbolic Math Toolbox/Aufgabe 4/Aufgabe4_d.m Normal file
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syms x;
f(x) = x^2 * x^(3/4);
f_x = diff(f,x);
%simplify(f_x,Steps=100);
disp(f_x);

9
MATLAB/Uebungen/02 Symbolic Math Toolbox/Aufgabe 4/Aufgabe4_e.m Normal file
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syms t;
f(t) = (6*(1+2*t^2 )*(t^3 - t)^2) / (sqrt(t+5*t^2)*(4*t)) + (sqrt(1+2*t)) / (t + sqrt(1+t^2));
f_t = diff(f,t);
%simplify(f_t,Steps=100);
disp(f_t);

13
MATLAB/Uebungen/02 Symbolic Math Toolbox/Aufgabe 4/Aufgabe4_f.m Normal file
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syms x y;
f(x,y) = (sin(x-2)*exp(2*y)) / ((x-1)^3 * (y^2 +3)^5 );
f_x = diff(f,x);
f_y = diff(f,y);
f_xy = diff(f_x,y);
%simplify(f_t,Steps=100);
disp(f_x);
disp(f_y);
disp(f_xy);

5
MATLAB/Uebungen/02 Symbolic Math Toolbox/Aufgabe 4/Aufgabe4_g.m Normal file
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syms x y z;
f(x,y,z) = [x*y^3; x*y*z; y^2*z^4];
disp(jacobian(f));

10
MATLAB/Uebungen/02 Symbolic Math Toolbox/Aufgabe 5/Aufgabe5_a.m Normal file
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syms x;
x_0 = 0;
n=4;
f(x) = log(1+x);
T(x) = taylor(f,x,x_0);
disp(T);

10
MATLAB/Uebungen/02 Symbolic Math Toolbox/Aufgabe 5/Aufgabe5_b.m Normal file
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syms x;
x_0 = 1;
n=5;
f(x) = 3^x;
T(x) = taylor(f,x,x_0);
disp(T);

10
MATLAB/Uebungen/02 Symbolic Math Toolbox/Aufgabe 5/Aufgabe5_c.m Normal file
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syms x;
x_0 = 0;
n=4;
f(x) = 1 / (1-x)^3;
T(x) = taylor(f,x,x_0);
disp(T);

10
MATLAB/Uebungen/02 Symbolic Math Toolbox/Aufgabe 5/Aufgabe5_d.m Normal file
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syms x y;
x_0 = [13; -11];
n=3;
f(x,y) = exp(y/x-2);
T(x,y) = taylor(f,[x,y],x_0);
disp(T);

10
MATLAB/Uebungen/02 Symbolic Math Toolbox/Aufgabe 5/Aufgabe5_e.m Normal file
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syms x y z;
x_0 = [1,2,3];
n=3;
f(x,y,z) = sin(x*y*z)*sinh(x*y*z);
T(x,y,z) = taylor(f,[x,y,z],x_0);
disp(T);

5
MATLAB/Uebungen/02 Symbolic Math Toolbox/Aufgabe 6/Aufgabe6_a.m Normal file
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syms x;
f(x) = x^sin(x);
disp(limit(f,x,0));

5
MATLAB/Uebungen/02 Symbolic Math Toolbox/Aufgabe 6/Aufgabe6_b.m Normal file
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syms x;
f(x) = x+sin(x) / x;
disp(limit(f,x,inf()));

7
MATLAB/Uebungen/02 Symbolic Math Toolbox/Aufgabe 6/Aufgabe6_c.m Normal file
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syms x;
f(x) = 2 / 1+exp(-1/x);
disp(limit(f,x,"left"));
disp(limit(f,x,"right"));
disp(limit(f,x,0));

7
MATLAB/Uebungen/02 Symbolic Math Toolbox/Aufgabe 8/Aufgabe8_a1.m Normal file
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syms x
f(x) = log(x);
F(x) = int(f, x);
disp(F);

7
MATLAB/Uebungen/02 Symbolic Math Toolbox/Aufgabe 8/Aufgabe8_a2.m Normal file
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syms x a b n
f(x) = nthroot(a*x-b,n);
F(x) = int(f, x);
disp(F);

7
MATLAB/Uebungen/02 Symbolic Math Toolbox/Aufgabe 8/Aufgabe8_a3.m Normal file
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syms x a b n c
f(x) = x / sin(a * x)^2;
F(x) = int(f, x);
disp(F);

7
MATLAB/Uebungen/02 Symbolic Math Toolbox/Aufgabe 8/Aufgabe8_a4.m Normal file
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syms x a b n c
f(x) = 1 / (b + c * exp(a * x));
F(x) = int(f, x);
disp(F);

9
MATLAB/Uebungen/02 Symbolic Math Toolbox/Aufgabe 8/Aufgabe8_a5.m Normal file
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syms x a b n c
f(x) = tan(a * x) / (1 + tan(a * x));
F(x) = int(f, x);
F(x) = simplify(F, Steps=10000, Seconds=30);
disp(F);