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Elementary differential equations and boundary value problems
This edition, like its predecessors, is written from the viewpoint of the applied mathematician, whose interest in differential equations may be sometimes quite theoretical, sometimes intensely practical, and often somewhere in between. We have sought to combine a sound and accurate (but not abstract) exposition of the elementary theory of differential equations with considerable material on methods of solution, analysis, and approximation that have proved useful in a wide variety of applications. The book is written primarily for undergraduate students of mathematics, science, or engineering, who typically take a course on differential equations during their first or second year of study. The main prerequisite for reading the book is a working knowledge of calculus, gained from a normal two- or three-semester course sequence or its equivalent. Some familiarity with matrices will also be helpful in the chapters on systems of differential equations. To be widely useful, a textbook must be adaptable to a variety of instructional strategies. This implies at least two things. First, instructors should have maximum flexibility to choose both the particular topics they wish to cover and the order in which they want to cover them. Second, the book should be useful to students who have access to a wide range of technological capability. With respect to content, we provide this flexibility by making sure that, so far as possible, individual chapters are independent of each other. Thus, after the basic parts of the first three chapters are completed (roughly Sections 1.1 through 1.3,2.1 through 2.5, and 3.1 through 3.5), the selection of additional topics, and the order and depth in which they are covered, are at the discretion of the instructor. Chapters 4 through 11 are essentially independent of each other, except that Chapter 7 should precede Chapter 9 and that Chapter 10 should precede Chapter 11. This means that there are multiple pathways through the book, and many different combinations have been used effectively with earlier editions.
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