Synopses & Reviews
This text is intended for use in a course in differential equations for student of pure and applied mathematics, the physical sciences, and engineering. The text is designed to be extremely flexible and includes both theory and applications. The text has been written and designed so that the applications can be covered or omitted without a loss of continuity of core topics. The odd-numbered chapters of the book cover the core theory of differential equations with basic applications, while the even-numbered chapters include extended applications from engineering and the physical sciences. In addition, the text includes optional coverage of dynamical systems. Where appropriate, the author has integrated technology into the text, primarily in the exercise sets. Chapters 2, 4, and 6 also include Computing Supplement Sections that are devoted to using numerical methods to solve differential equations.
Table of Contents
Introductory Survey Chapter 1 First-Order Equations 1 Solutions and Initial Values 2 Direction Fields 3 Integration 4 LinearEquations 5 Exact Equations (Optional) Chapter Review and Supplement Chapter 2 Applications: Dynamics & Equilibrium 1 Population Dynamics 2 Velocity in a Resisting Medium 3 Equilibrium Solutions (Optional) Computing Supplement Chapter 3 Equations of Order Two or More 1 Introduction 2 Oscillatory Solutions 3 Nonhomogeneous Equations 4 Nonlinear Equations (Optional) Chapter 4 Applications: Dynamics and Phase-Space 1 Mechanical Oscillators 2 Electric Circuits 3 Phase-Space and Periodicity Computing Supplement Chapter 5 Introduction to Systems 1 Vector Equations 2 Linear Systems 3 Matrix Operators Chapter Review and Supplement Chapter 6 Applications: Dynamics & Stability 1 Multicompartment Mixing 2 Interacting Populations 3 Mechanical Oscillations 4 Stability for Autonomous Systems Computing Supplement Chapter 7 Fundamental Matrices 1 Matrix Exponentials (and more...)