An introduction to difference equations. 2nd ed. (English) Zbl 0930.39001

Elaydi, Saber N.

Undergraduate Texts in Mathematics. New York, NY: Springer. xviii, 427 p. (1999).

The first edition of the book (1996; Zbl 0840.39002) is extended by new sections on global stability, periodic solutions, conjugacy maps, new applications to mathematical biology, Birkhoff’s theory on asymptotic power series as solutions of linear difference equations, continued fractions and orthogonal polynomials. A list of symbols and some Maple programs are added, and the bibliography is enlarged and collected at the end of the book.
Reviewer’s remark: Not all errors and misprints, pointed out in the above quoted review, are corrected, and there are further ones: On p. 44 Figure 1.18 is absent, on p. 76 the Exercises 16-18 to the solutions on p. 397 are absent, on p. 219 the final value theorem is wrong for Example 5.6 on p. 224, \(\varphi_1\) and \(\varphi_2\) on p. 331 (2 times) and on p. 337 are no fundamental matrices, the asymptotic relations for vectors on pp. 336, 340, 362 are not defined, \(u=u_1\) on p. 357 is only valid up to a constant factor, on p. 359 frac is not clear comparing with Frac(.) on p. 376, on pp. 365, 367 the statement concerning every second-order difference equation is only valid for homogeneous linear ones, the simple closed curve on p. 392 (2 times) must be positively directed, on p. 398 the solutions 1, 2 and 7 of Exercise 2.6 are wrong, on p. 401 it is not clear, which problems of Exercise 4.1.1 are answered. Moreover, there are misprints on pp. \(45^1\), \(45_6\), \(90^2\), \(208_3\), \(209^1\), \(211^{2,3,6,15,19}\), \(231_{5,7}\), \(301_{10}\), \(324_7\), \(325^3\), \(329^9\), \(329_6\), \(330^3\), \(331^5\), \(336_4\), \(356_{10}\), \(366_{10}\), \(397_{10,13}\), \(398_6\), \(405^8\), \(405_{6,7}\) and \(406^2\).

Reviewer: Lothar Berg (Rostock)

MSC:

39Axx	Difference equations
93-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to systems and control theory
37Jxx	Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
00A06	Mathematics for nonmathematicians (engineering, social sciences, etc.)
39-04	Software, source code, etc. for problems pertaining to difference and functional equations
39-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to difference and functional equations

Keywords:

nonlinear equations; method of Lyapunov; observability; dynamical systems; power series; \(Z\)-transform; Riccati equation; Volterra equation; heat equation; textbook; linear equations; systems; feedback; iteration; chaos; perturbations; oscillations; stability; control theory; bifurcations; asymptotics; periodic solutions; conjugacy maps; mathematical biology; asymptotic power series; continued fractions; orthogonal polynomials; Maple programs; bibliography

Citations:

Zbl 0840.39002

Software:

Maple