MATLAB6 - MATLAB#6 Systems of ODEs Jillian Peacock A06402794 Math 20D Professor Stevens Section B01 9 November 2006 MATLAB#6 Exercise 6.1 a >

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MATLAB #6: Systems of ODEs Jillian Peacock A06402794 Math 20D Professor Stevens Section B01 9 November 2006
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MATLAB #6 Exercise 6.1: a. >> B=[1.2, 2.5; 4, 0.7] B = 1.2000 2.5000 4.0000 0.7000 b. >> [eigvec, eigval]=eig(B) eigvec = 0.6501 -0.5899 0.7599 0.8075 eigval = 4.1221 0 0 -2.2221 Exercise 6.2: a. b. >> A=[1,-2;-1,-4] A = 1 -2 -1 -4 >> [eigvec, eigval]=eig(A) eigvec = 0.9831 0.3489 -0.1830 0.9372 eigval = 1.3723 0 0 -4.3723 c. Exercise 6.3: a. Depending on the sign of x’ and y’ the direction changes. The direction changes to that of the sign of the value, meaning that with a positive x’ value and a negative y’ value, the direction field will be in the direction of a positive x and down towards negative y, in turn
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making the solutions have a negative slope. This is true for all combinations of x’ and y’ in that they will go in the direction of their sign. Exercise 6.4: x ' = y y ' = - x -10 -8 -6 -4 -2 0 2 4 6 8 10 -10 -8 -6 -4 -2 0 2 4 6 8 10 x y Exercise 6.5: x ' = x - 2 y y ' = - x - 4 y -10 -8 -6 -4 -2 0 2 4 6 8 10 -10 -8 -6 -4 -2 0 2 4 6 8 10 x
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As t gets larger, the solutions either approach infinity or zero. Based on the exponential
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This note was uploaded on 04/19/2008 for the course MATH 20D taught by Professor Mohanty during the Winter '06 term at UCSD.

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MATLAB6 - MATLAB#6 Systems of ODEs Jillian Peacock A06402794 Math 20D Professor Stevens Section B01 9 November 2006 MATLAB#6 Exercise 6.1 a >

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