Tartalomjegyzék

Script segedszamitasok_2017_09_13_gyak1

TELJES MATLAB SCRIPT KIEGÉSZÍTŐ FÜGGVÉNYEKKEL

file:   segedszamitasok_2017_09_13_gyak1.m
author: Peter Polcz <ppolcz@gmail.com>

Created on 2017. September 13.

Output:

┌segedszamitasok_2017_09_13_gyak1
│   - Persistence for `segedszamitasok_2017_09_13_gyak1` reused (inherited) [run ID: 4434, 2017.09.16. Saturday, 15:34:36]
│   - Script `segedszamitasok_2017_09_13_gyak1` backuped

Vonalintegrál kiszámítása - ellipszis mentén

syms a b x y t real
r = [x;y];

F = [
    x^2
    y^2
    ];

gamma = [
    a*cos(t)
    b*sin(t)
    ];

Dgamma = diff(gamma,t);

Dgamma = subs(F,r,gamma);

Integrand = Dgamma' * Dgamma;

Vonalintegral_erteke = int(Integrand, t, 0, pi/2)

Output:

Vonalintegral_erteke =
(3*pi*(a^4 + b^4))/16

Vonalintegrál kiszámítása - egyenes mentén

syms x y z t real
r = [x;y;z];

F = [
    3*x^2*y^2*z
    2*x^3*y*z
    x^3*y^2
    ];

A = [0;0;0];
B = [1;2;3];
gamma(t) = (B-A)*t + A;

Dgamma = diff(gamma,t);

Fgamma = subs(F,r,gamma);

Integrand = Fgamma' * Dgamma;

Vonalintegral_erteke = int(Integrand, t, 0, 1)

f = potential(F,r)

Vonalintegral_erteke_potenciallal = subs(f,r,B) - subs(f,r,A)

Output:

Vonalintegral_erteke =
12
f =
x^3*y^2*z
Vonalintegral_erteke_potenciallal =
12

Vonalintegrál kiszámítása - egyenes mentén

syms x y z t real
r = [x;y;z];

F = [
    y*z
    x*z
    x*y
    ];

A = [-1;2;0];
B = [5;5;9];
gamma(t) = (B-A)*t + A;
gamma(t) = [
    2*t^2
    3*t-5
    t
    ];

A = gamma(0);
B = gamma(3);


Dgamma = diff(gamma,t);

Fgamma = subs(F,r,gamma);

Integrand = Fgamma' * Dgamma;

Vonalintegral_erteke = int(Integrand, t, 0, 3)

f = potential(F,r)

Vonalintegral_erteke_potenciallal = subs(f,r,B) - subs(f,r,A)

Output:

Vonalintegral_erteke =
216
f =
x*y*z
Vonalintegral_erteke_potenciallal =
216

End of the script.

Output:

└ 2.7535 [sec]

Published with MATLAB® R2015a, and sanitarized by BeautifulSoup (Python script using BSoup is written by Polcz).