Skillfully organized introductory text examines origin of differential equations, then defines basic terms and outlines the general solution of a differential equation. Subsequent sections deal with integrating factors; dilution and accretion problems; linearization of first order systems; Laplace Transforms; Newton's Interpolation Formulas, more.

Fourteen unforgettable short stories provoke, illuminate, and startle as they explore our perception of nature and the conflict between wildness and civilization within each of us. As we are recognizing the consequences of the destruction of forests and wetlands, the pillaging of the seas, and the toxicity of industry, we are experiencing profound uncertainty about our relationship with the earth. These stellar short stories by writers such as Barry Lopez, Rick Bass, Margaret Atwood, E. L. Doctorow, Chris Offutt, and others plumb the mystery--as only fiction can--of nature within us and the world of nature that surrounds us. We are nature, in spite of our machines, our plastics, and our artificial ingredients. Yet what do we make of our own nature? Our own wildness? And how do we explain the paradox of our urge to both exploit and protect wilderness? From E. L. Doctorow's shattering tale, "Willi," in which a young boy witnesses adults transformed into animals by the frenzy of sexual lust, to Rick Bass's "Swamp Boy," whose young hero is hounded by a pack of boys incensed by his solitary communion with the wild, to Margaret Atwood's wickedly funny story, "My Life as a Bat," or Kent Meyers's soulful ballad of love regained, "The Heart of the Sky," these memorable stories articulate our deep need for wilderness and the indelible role nature plays in our psychological and spiritual well-being.

This traditional text is intended for mainstream one- or two-semester differential equations courses taken by undergraduates majoring in engineering, mathematics, and the sciences. Written by two of the world's leading authorities on differential equations, Simmons/Krantz provides a cogent and accessible introduction to ordinary differential equations written in classical style. Its rich variety of modern applications in engineering, physics, and the applied sciences illuminate the concepts and techniques that students will use through practice to solve real-life problems in their careers. This text is part of the Walter Rudin Student Series in Advanced Mathematics.

Unlike most texts in differential equations, this textbook gives an early presentation of the Laplace transform, which is then used to motivate and develop many of the remaining differential equation concepts for which it is particularly well suited. For example, the standard solution methods for constant coefficient linear differential equations are immediate and simplified, and solution methods for constant coefficient systems are streamlined. By introducing the Laplace transform early in the text, students become proficient in its use while at the same time learning the standard topics in differential equations. The text also includes proofs of several important theorems that are not usually given in introductory texts. These include a proof of the injectivity of the Laplace transform and a proof of the existence and uniqueness theorem for linear constant coefficient differential equations. Along with its unique traits, this text contains all the topics needed for a standard three- or four-hour, sophomore-level differential equations course for students majoring in science or engineering. These topics include: first order differential equations, general linear differential equations with constant coefficients, second order linear differential equations with variable coefficients, power series methods, and linear systems of differential equations. It is assumed that the reader has had the equivalent of a one-year course in college calculus.

This brief modern introduction to the subject of ordinary differential equations emphasizes stability theory. Concisely and lucidly expressed, it is intended as a supplementary text for advanced undergraduates or beginning graduate students who have completed a first course in ordinary differential equations. The author begins by developing the notions of a fundamental system of solutions, the Wronskian, and the corresponding fundamental matrix. Subsequent chapters explore the linear equation with constant coefficients, stability theory for autonomous and nonautonomous systems, and the problems of the existence and uniqueness of solutions and related topics. Problems at the end of each chapter and two Appendixes on special topics enrich the text.