906 pages | 131 B/W Illus.
The Second Edition of this successful text builds upon over ten years of in-class use. The text is unique in its approach to motivation, precision, explanations and methods. A layered approach offers an opportunity for flexible coverage and depth. Topics are introduced in a more accessfible way before subsequent sections develop these further. Motivating and giving reasons for the concepts and computations is an important part of the text. The author offers an emphasis on modeling and technology use. Guides for carrying out some of the lengthier computational procedures are given with illustrative examples integrated into the discussion. An engaging writing style appeals to students.
The Basics. The Starting Point: Basic Concepts and Terminology. Integration and Differential Equations. First-Order Equations. Some Basics about First-Order Equations.Separable First-Order Equations. Linear First-Order Equations. Simplifying Through Substitution. The Exact Form and General Integrating Factors. Slope Fields: Graphing Solutions Without the Solutions. Euler’s Numerical Method. The Art and Science of Modeling with First-Order Equations. Second- and Higher-Order Equations. Higher-Order Equations: Extending First-Order Concepts. Higher-Order Linear Equations and the Reduction of Order Method. General Solutions to Homogeneous Linear Differential Equations. Verifying the Big Theorems and an Introduction to Differential Operators. Second-Order Homogeneous Linear Equations with Constant Coefficients. Springs: Part I. Arbitrary Homogeneous Linear Equations with Constant Coefficients. Euler Equations. Nonhomogeneous Equations in General. Method of Undetermined Coefficients. Springs: Part II. Variation of Parameters.The Laplace Transform. The Laplace Transfrom (Intro). Differentiation and the Laplace Transform. The Inverse Laplace Transform. Convolution. Piecewise-Defined Functions and Periodic Functions. Delta Functions. Power Series and Modified Power Series Solutions. Series Solutions: Preliminaries. Power Series Solutions I: Basic Computational Methods. Power Series Solutions II: Generalizations and Theory.Modified Power Series Solutions and the Basic Method of Frobenius. The Big Theorem on the Frobenius Method, with Applications. Validating the Method of Frobenius. Systems of Differential Equations (A Brief Introduction). 35. Systems of Differential Equations: A Starting Point. Critical Points, Direction Fields and Trajectories.