Singular Systems of Differential Equations
Singular Systems of Differential Equations, Pitman, 1980, 176
pages. This book is no longer in print and the copyright has been returned to the author. A scanned copy may be downloaded and used for research and educational purposes. The file is 24 mb and somewhat discolored due to age but it is readable.
Some errata from Alexander Gouberman.
LaTeX notation is used.
- p. 6: "Jordon" -> "Jordan"
- p. 10: Proof 1.4.2: p(A) E_i = \sum ... * (A-\lambda_i) E ... -> the expression (A-\lambda_i) must be (A-\lambda_i)^k
- p. 12, above Eq. (4): m_i -> m_1 in r(\lambda).
- p. 34: close to the end: in B\hat_\lambda = ... = I - \lambda A\hat" -> must be "A\hat_\lambda"
- p. 35, top: must be "T\inv A\hat_\lambda T" instead of "T\inv A T" (?), etc.
- p. 39, 2nd paragraph: "But then ... x(t_0) for all t" -> must be x(t)
- p. 81, top: compute -> commute
- p. 81, mid page: "Hence taking ..." in (I - \lambda\inv A\hat B\hat^D)\inv the "-" must be "+"
- p. 88: Theorem 5.2.1: limit does not hold for t=0 (case B = 0 is considered special in the proof)
at p. 97 below X_0(0) = I - BB^D assumes that the limit holds at t=0, i.e. X(t) is continuous
- p. 90, bottom: "r_0 = ||A_12|| + ||A_22|| + 1" -> A_12 must be A_21
- p. 92: "Thus F_0(\eps) = 1/(2pi*i) \int (\zeta - B)\inv ..." -> in the integral there is a \zeta factor missing