Transcription of Systems of Differential Equations
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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), .. , xn (t).
Pond Pollution Consider three ponds connected by streams, as in Figure 4. The first pond has a pollution source, which spreads via the connecting streams to the other ponds. The plan is to determine the amount of pollutant in each pond. 1 3 2 f(t) Figure 4. Three ponds 1, 2, 3 of volumes V1, V2, V3 connected by streams. The pollution source f ...
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