Introduction to differential equations with dynamical systems

"This textbook addresses the challenges that undergraduate mathematics, engineering, and science students experience during a first course on differential equations. While covering all the standard parts of the subject, the book emphasizes linear constant coefficient equations and applications including the topics essential to engineering students."--Jacket

Includes index.

First-Order Differential Equations and Their Applications -- Introduction to ordinary differential equations -- The definite integral and the initial value problem -- The initial value problem and the indefinite integral -- The initial value problem and the definite integral -- Mechanics I: elementary motion of a particle with gravity only -- First-order separable differential equations -- Using definite integrals for separable differential equations -- Direction fields -- Existence and uniqueness -- Euler's numerical method (optional) -- First-order linear differential equations -- Form of the general solution -- Solutions of homogeneous first-order linear differential equations -- Integrating factors for first-order linear differential equations -- Linear first-order differential equations with constant coefficients and constant input -- Homogeneous linear differential equations with constant coefficients -- Constant coefficient linear differential equations with constant input -- Constant coefficient differential equations with exponential input -- Constant coefficient differential equations with discontinuous input -- Growth and decay rroblems -- A first model of population gr…