Fundamentals of Differential Equations and Boundary Value Problems, Pearson New International Edition, 6th edition

Fundamentals of Differential Equations presents the basic theory of differential equations and offers a variety of modern applications in science and engineering. Available in two versions, these flexible texts offer the instructor many choices in syllabus design, course emphasis (theory, methodology, applications, and numerical methods), and in using commercially available computer software.

Fundamentals of Differential Equations, Eighth Edition is suitable for a one-semester sophomore- or junior-level course. Fundamentals of Differential Equations with Boundary Value Problems,¿Sixth Edition, contains enough material for a two-semester course that covers and builds on boundary value problems. The Boundary Value Problems version consists of the main text plus three additional chapters (Eigenvalue Problems and Sturm-Liouville Equations; Stability of Autonomous Systems; and Existence and Uniqueness Theory).

• Applications-driven sections are included in the chapter on linear second-order equations.
• Modernized treatment of the chapter on the introduction to systems and phase plane analysis increases student comprehension of the material.
• Group Projects relating to the material covered appear at the end of each chapter. They may involve more challenging applications, delve deeper into theory, or introduce more advanced topics.
• The expanded coverage of dynamical systems is consistent with the level of the text.
• The phase line is covered at the beginning of the text.
• Updated Instructor Manuals for MAPLE/Matlab/Mathematica , tied to the development of the text, Included are suggestions on incorporating these technologies into the courses, along with sample worksheets for labs.

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 Figures By including five new sketches of the various eigenfunctions arising from separating variables in our chapter on partial differential equations (Chapter 10), we are able to visualize and anticipate the qualitative features mandated by Sturm's Comparison and Oscillation theorems in the subsequent chapter (Chapter 11).
• 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.