1. Abramowitz, M. and I. A. Stegun, Handbook of Mathematical Functions. New York: Dover, 1965. The comprehensive collection of tables to which frequent reference is made in the text.

2. Birkhoff, G. and G.-C. Rota, Ordinary Differential Equations (4th ed.). New York: John Wiley, 1989. An intermediate-level text that includes a more complete treatment of existence and uniqueness theorems, Sturm-Liouville problems, and eigenfunction expansions.

3. Braun, M., Differential Equations and Their Applications (3rd ed.). New York: Springer-Verlag, 1983. An introductory text at a slightly higher level than this book; it includes several interesting ''case study'' applications.

4. Churchill, R. V., Operational Mathematics (3rd ed.). New York: McGraw-Hill, 1972. The standard reference for theory and applications of Laplace transforms, starting at about the same level as Chapter 10 of this book.

5. Coddington, E. A., An Introduction to Ordinary Differential Equations. Hoboken, NJ: Pearson, 1961. An intermediate-level introduction; Chapters 3 and 4 include proofs of the theorems on power series and Frobenius series solutions stated in Chapter 11 of this book.

6. Coddington, E. A. and N. Levinson, Theory of Ordinary Differential Equations. New York: McGraw-Hill, 1955. An advanced theoretical text; Chapter 5 discusses solutions near an irregular singular point.

7. Dormand, J. R., Numerical Methods for Differential Equations. Boca Raton: CRC Press, 1996. More complete coverage of modern computational methods for approximate solution of differential equations.

8. Hubbard, J. H. and B. H. West, Differential Equations: A Dynamical Systems Approach. New York: Springer-Verlag, 1992 (part I) and 1995 (Higher-Dimensional Systems). Detailed treatment of qualitative phenomena, with a balanced combination of computational and theoretical viewpoints.

9. Ince, E. L., Ordinary Differential Equations. New York: Dover, 1956. First published in 1926, this is the classic older reference work on the subject.

10. McLachlan, N. W., Ordinary Non-Linear Differential Equations in Engineering and Physical Sciences. London: Oxford University Press, 1956. A concrete introduction to the effects of nonlinearity in physical systems.

11. Noble, B. and J.W. Daniel, Applied Linear Algebra (3rd ed.). Hoboken, NJ: Pearson, 1988. An especially concrete introduction to linear algebra, with significant applications included.

12. Polking, J. C. and D. Arnold, Ordinary Differential Equations Using MATLAB (3rd ed.). Hoboken, NJ: Pearson, 2003. A manual for using Matlab in an elementary differential equations course; based on the Matlab programs dfield and pplane that are used and referenced in this text.

13. Press, W. H., B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes: The Art of Scientific Computing, 3rd ed. Cambridge: Cambridge University Press, 2007. Chapter 17 discusses modern techniques for the numerical solution of ordinary differential equations. Programs in C⁺⁺, as well as C, Fortran, Pascal, and other languages can be downloaded from the accompanying web site numerical.recipes.

14. Simmons, G. F., Differential Equations (2nd ed.). New York: McGraw-Hill, 1991. An introductory text with interesting historical notes and fascinating applications and with the most eloquent preface in any mathematics book currently in print.

15. Strang, W. G., Linear Algebra and Its Applications. (4th ed.). New York: Brooks Cole, 2006. An introductory treatment of linear algebra with motivating applications. Appendix B contains a concrete derivation of the Jordan normal form for square matrices.