Differential Equations An Introduction to Modern Methods and Applications [Hardcover]

Brannan/Boyce’s Differential Equations: An Introduction to Modern Methods and Applications, 3rd Edition is consistent with the way engineers and scientists use mathematics in their daily work. The text emphasizes a systems approach to the subject and integrates the use of modern computing technology in the context of contemporary applications from engineering and science. The focus on fundamental skills, careful application of technology, and practice in modeling complex systems prepares students for the realities of the new millennium, providing the building blocks to be successful problem-solvers in today’s workplace. Section exercises throughout the text provide hands-on experience in modeling, analysis, and computer experimentation. Projects at the end of each chapter provide additional opportunities for students to explore the role played by differential equations in the sciences and engineering.

Chapter 1 Introduction 1

1.1 Mathematical Models and Solutions 2

1.2 Qualitative Methods: Phase Lines and Direction Fields 12

1.3 Definitions, Classification, and Terminology 28

Chapter 2 First Order Differential Equations 37

2.1 Separable Equations 38

2.2 Linear Equations: Method of Integrating Factors 45

2.3 Modeling with First Order Equations 55

2.4 Differences Between Linear and Nonlinear Equations 70

2.5 Autonomous Equations and Population Dynamics 80

2.6 Exact Equations and Integrating Factors 93

2.7 Substitution Methods 101

Projects

2.P.1 Harvesting a Renewable Resource 110

2.P.2 A Mathematical Model of a Groundwater Contaminant Source 111

2.P.3 Monte Carlo Optil³'