This introductory equations book is one of the first to integrate technology throughout the text. Using a computer algebra system (CAS) helps students to solve problems (both specific and general cases), to reason spatially through visualisation, to compare changing variables and parameters, to make inferences, and to evaluate outcomes. Students learn how and when to use technology tools by examples, in exercises, and in applications. Features: * Numerous graphs and figures help students visualize and interpret differential equations and their solutions. * "In Touch with Technology" exercises in almost every section require students to use graphing software or a computer algebra system to solve more advanced problems, study concepts, and experiment with technology. * "Think About It" questions follow many examples and are marked with an icon. They encourage students to draw inferences from the examples, explore additional cases, and experiment with technology. * "Differential Equations at Work" sections at the end of most chapters are ideal for group work or discussion. They pose real problems, documented by references, from such fields as economics, biology, physics, chemistry, and engineering. Students use technology to analyze the problems and suggest ways to solve them. * Numerous examples throughout the text are explained in detail. Solutions to more difficult examples are constructed with the help of graphing software or a CAS, so students learn how and when to use technology. * The exercise sets at the end of each section include a wide range of problems from very easy to difficult. Routine problems are included so students master basic techniques. The many interesting applied problems and conceptual problems test students' comprehension. Answers to selected exercises are at the back of the text. The Student Resource Manual includes CAS output for selected exercises. * Summary and Review Exercises are at the end of each chapter.

Table of Contents:
Part I: Introduction to Differential Equations. Definitions and Concepts. Solutions of Differential Equations. Initial and Boundary Value Problems. Direction Fields. The Origin of Differential Equations. Part II: First-Order Ordinary Differential Equations. Separation of Variables. Homogeneous Equations. Exact Equations. Linear Equations. Theory of First-Order Equations: A Brief Discussion. Numerical Approximations of Solutions of First-Order Equations. Differential Equations at Work: Modeling the Spread of a Disease. Part III: Applications of First-Order Differential Equations. Orthogonal Trajectories. Population Growth and Decay. Newton's Law of Cooling. Free-Falling Bodies Differential Equations at Work: Mathematics of Finance. Part IV: Higher-Order Differential Equations. Introduction. Fundamental Set of Solutions. Solutions of Linear Homogeneous Equations with Constant Coeffiecients. Introduction to Solving Nonhomogeneous Equations with Constant Coefficients: Using the Annihilator Method. Nonhomogeneous Equations with Constant Coefficients: The Method of Undetermined Coefficients. Nonhomogeneous Equations with Constant Coefficients: Variation of Parameters. Differential Equations at Work: Modeling the Motion of a Skier. Part V: Applications of Higher-Order Differential Equations. Simple Harmonic Motion. Damped Motion. Forced Motion. Other Applications. The Pendulum Problem. Differential Equations at Work: Rack-And-Gear Systems. Part VI: Ordinary Differential Equations with Nonconstant Coefficients. Cauchy-Euler Equations. Power Series Review. Power Series Solutions About Ordinary Points. Power Series Solutions About Regular Singular Points. Some Special Equations. Differential Equations at Work: The Schrodinger Equation. Part VII: Introduction to the Laplace Transform. The Laplace Transform: Preliminary Definitions and Notation. Properties of the Laplace Transform. The Inverse Laplace Transform. Solving Initial-Value Problems with the Laplace Transform. Laplace Transforms of Several Important Functions. The Convolution Theorem. Applications of Laplace Transforms. Differential Equations at Work: The Tautochrone. Part VIII: Systems of Ordinary Differential Equations. Systems of Equations: Preliminary Theory and Methods: Review of Matrix Algebra and Calculus. Preliminary Definitions and Notation. Homogeneous Linear Systems with Constant Coefficients. Nonhomogeneous First-Order Systems: Undetermined Coefficients and Variation of Parameters. Laplace Transfroms. Nonlinear Systems, Linearization, And Classification of Equilibrium Points. Numerical Methods. Differential Equations at Work: Controlling the Spread of a Disease. Part IX: Applications of Systems of Ordinary Differential Equations. Mechanical and Electrical Problems with First-Order Linear Systems. Diffusion and Population Problems with First-Order Linear Systems. Applications Using Laplace Transforms. Nonlinear Systems of Equations. Differential Equations at Work: Free Vibration of a Three-Storey Building.