Elements of Ordinary Differential Equations

This text is intended for use in a first course in ordinary differential equations and is written for students who have had but a year's course in elementary calculus. It is designed to appeal to students majoring in engineering, science, or mathematics. The result of the authors' combined efforts is a book which mixes in an admirable fashion the demands for logic and rigor of a mathematician and the practical ideas of an engineer.The reader is introduced to the concepts of differential equations by means of geometric interpretations. Various types of differential equations are solved by methods suggestive of general procedures. The use of special rules and formulas is avoided. Operator notation is introduced and the operational methods are discussed in a logical fashion. Later, various special equations are discussed. The authors are to be commended for the introduction of a chapter devoted to the discussion of Bessel functions, Legendre polynomials, hypergeometric functions, and various other related subjects not usually discussed in such a book.The procedures are well illustrated by the inclusion of many examples. These examples are well chosen as problems which are often met in theoretical physics and related fields. The examples themselves will form a useful reference collection for the student. Many problems for the reader, with answers, are provided.* Some Basic Facts and Techniques* Techniques for Solving First-Order Equations* Existence, Uniqueness, and Geometry of Solutions* Applications of First-Order Equations* Second-Order Differential Equations* Linear Differential Equations of Higher Order; Constant Coefficients* Laplace Transforms and Operator Methods* Systems of Differential Equations* Linear Equations with Variable Coefficients* Solution in Power Series; Some Classical Equations* Clairaut's Equation; Envelopes* Successive Integrations