With this edition we are pleased to feature some new projects and discussions that bear upon current issues in the news and in academia. In brief:

• Review of Integration Techniques In response to our colleagues' perception that many of today's students' skills in integration have gotten rusty by the time they enter the differential equations course, we have included a new appendix offering a quick review of the methods for integrating functions analytically. We trust that our light overview will prove refreshing (Appendix A).
• New Projects The projects in the text have been well received by its users. We have built upon the options available to instructors and students by adding the following:
  • A project that models spread of staph infections in a hospital setting (an ongoing problem in the health community's battle to contain and confine dangerous infectious strains in the population) (Project B, Chapter 5).
  • A project presenting a cursory analysis of oil dispersion after a spill, based roughly on an incident that occurred in the Mississippi River (Project A, Chapter 4).
  • A project involving an application of the grande dame of differential equations techniques--power series--to predict the performance of Quicksort, a machine algorithm that alphabetizes large lists (Project A, Chapter 8).
  • Closely related to the current interest in hydroponics is our project describing the growth of phytoplankton by controlling the supply of the necessary nutrients in a chemostat tank (Project F, Chapter 5).
  • The basic theorems on linear difference equationsclosely resemble those for differential equations (but are easier to prove), so we have includeda project exploring this kinship (Project D, Chapter 6).
• New Exercises We have added dozens of new problems on such topics as barometric pressure, compound interest, the mathematical equivalence of an impulse force and a velocity boost, and the systems description of the method of undetermined coefficents, when the nonhomogeneity is related to the associated homogeneous solutions.
• New Computing Technique We finesse the abstruseness of generalized eigenvector chain theory with a novel technique for computing the matrix exponential for defective matrices (Section 8, Chapter 9).
• “Boxcar Function” The rectangular window (or "boxcar function") has become a standard mathematical tool in communications industry, the backbone of such schemes as pulse code modulation, etc. Our revised chapter on Laplace transforms incorporates it to facilitate the analysis of switching functions for differential equations (Section 6, Chapter 7).
• Power Series Expansions We conclude our chapter on power series expansions with a tabulation of the historically significant second-order differential equations, the practical considerations that inspired them, the mathematicians who analyzed them, and the standard notations for their solutions (Chapter 8).
• Updated References Finally, we have updated the references to relevant literature and websites, especially those facilitating the online implemention of numerical methods.