Author’s Foreword This textbook reflects my personal views on how an introductory course in ordinary differential equations really should be taught, tempered by the constraints of time, the level and interests of the students, and other practical concerns. It also reflects my beliefs that a good text should be a useful resource beyond the course, and that it should back up its claims with solid and clear proofs (even if those proofs are ignored by most readers). It also, I hope, reflects the fact that such a book should be written for those normally taking such a course; namely, students who are reasonably acquainted with the differentiation and integration of functions of one variable, but who might not yet be experts and may, on occasion, need to return to their elementary calculus texts for review. These students are reasonably intelligent, but are not mathematicians and may have no desire to be mathematicians. Still, most are interested in fields of study for which a fundamental understanding of the mathematics and applications of ordinary differential equations is extremely
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