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Systems of Differential Equations

Chapter 11. Systems of Differential Equations : Examples of Systems : Basic First-order system Methods : Structure of Linear Systems : Matrix Exponential : The Eigenanalysis Method for x = Ax : Jordan Form and Eigenanalysis : Nonhomogeneous Linear Systems : Second-order Systems : Numerical Methods for Systems Linear Systems . A linear system is a system of differential equa- tions of the form x 1 = a11 x1 + + a1n xn + f1 , x 2 = a21 x1 + + a2n xn + f2 , (1) .. x m = am1 x1 + + amn xn + fm , where = d/dt. Given are the functions aij (t) and fj (t) on some interval a < t < b. The unknowns are the functions x1 (t).

partment X is done by writing dX/dt for the left side of the differential equation and then algebraically adding the input and output rates to ob-tain the right side of the differential equation, according to the balance law dX dt = sum of input rates −sum of output rates By convention, a compartment with no arriving arrowhead has input

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Systems of Differential Equations

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partment X is done by writing dX/dt for the left side of the differential equation and then algebraically adding the input and output rates to ob-tain the right side of the differential equation, according to the balance law dX dt = sum of input rates −sum of output rates By convention, a compartment with no arriving arrowhead has input

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