Differential equations are of fundamental importance in the applications of mathematics to the physical and biological sciences. This text provides an elementary but cohesive development of the topic. The primary goal of the book is to teach students how to use differential equations in applied areas. To this end, the book includes more than 400 worked examples and 2500 exercises, chapter summaries than include a review of the important concepts, chapter review exercises, self-quiz problems, numerous applications in various fields, a section in each chapter on solving problems using symbolic manipulators such as Mathematica, MAPLE, and DERIVE, and a manual for such solutions. *The First Chapter is motivated by first order linear methods. *Separation of Variables discussion has been moved from Chapter 1 to 2. *Early Introduction to Numerical Methods - Euler's method isdiscussed in Section 1.4, giving the student an early look at approximationfollowed by a thorough treatment of this topic in Chapter 8. *This edition has a great deal of coverage and attention to computeralgebra systems and how they can be used in differential equations to help solveproblems.
"Generic" CAS code is found at the ends of many chapters along with amanual providing specific Mathematica, Maple, and Derive coverage. *Self-tests, chapter summaries, and titled examples. *Three sections of the book, 1.1, 2.3, and 4.3 are devoted tomathematical modeling where students are asked to question the reasonableness ofmodels. *More illustrations, many of which are graphs of solutions to examples. *Outstanding Applications - diverse, interesting, and referenced.Theory is secondary to the goal of applying the mathematics to problems thatstudents who take the course will be solving. *Historical Notes and biographical sketches of some of themathematicians who have made significant contributions to calculus anddifferential equations add a human dimension often lacking in such books. *Perspectives explore topics from a different point of view and in moredepth.