1 1 Eng. Mohamed Eltaher Eng.Ahmed Ibrahim. 2 2 Exercise (1)  Solve the following set of equations using MATLAB x 1 + 2x 2 + 3x 3 + 5x 4 = 21 – 2x 1.

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Presentation transcript:

1 1 Eng. Mohamed Eltaher Eng.Ahmed Ibrahim

2 2 Exercise (1)  Solve the following set of equations using MATLAB x 1 + 2x 2 + 3x 3 + 5x 4 = 21 – 2x 1 + 5x 2 + 7x 3 – 9x 4 = 18 5x 1 + 7x 2 + 2x 3 – 5x 4 = 25 – x 1 + 3x 2 – 7x 3 + 7x 4 = 30 Solution x 1 = – , x 2 = , x 3 = – , x 4 =

3 3 Eng. Mohamed Eltaher Eng.Ahmed Ibrahim Exercise (2)  Differentiation of the following functions: (a)S 1 = exp(x 8 ) (b) S 2 = 3x 3 exp(x 5 ) (c) S 3 = 5x 3 – 7x 2 + 3x + 6

4 4 Eng. Mohamed Eltaher Eng.Ahmed Ibrahim Exercise (3)  Use MATLAB’s symbolic commands to find the values of the following integrals: (a) (9/40) (b) (7/3*pi^3) (c) (d)7x 5 – 6x x 3 + 4x 2 + 8x + 9

5 5 Eng. Mohamed Eltaher Eng.Ahmed Ibrahim Exercise (4)  Obtain the general solution of the following first order differential equations: (a) ans =(5*t)/6 + C6/(36*exp(6*t)) - 5/36 (b) (c) ans =A*t*x^3 + C11 (d) ans =(a^2*x^3)/2 + C15

6 6 Eng. Mohamed Eltaher Eng.Ahmed Ibrahim Exercise (5)  Obtain the general solution of the following: Using MATLAB program, find (a)General solution. (b)x(t) when all the initial conditions are zero. (c)x(t) when x(0) = 1 and Dx(0) = 2.

7 7 Eng. Mohamed Eltaher Eng.Ahmed Ibrahim Exercise (6) (a) Expand the following function F(s) into partial fractions using MATLAB. (b) Determine the inverse Laplace transform of F(s) :

8 8 Eng. Mohamed Eltaher Eng.Ahmed Ibrahim Exercise (7)  Find the Laplace transform of the following function using MATLAB. (a) (b) (c) (d)