Differential Equations
Graphics, Models, Data
1. Edition September 1998
704 Pages, Softcover
Wiley & Sons Ltd
Short Description
This text provides lively reading, with compelling applications, projects, and experiments that supply readers with opportunities to explore the relationship between the parameters in a differential equation and the process it models. Its goal is to teach readers to use differential equation as an investigative tool, not just to verify results. Visual exploration of solutions via slope fields, direction fields, phase plane solutions, and other graphical interpretations are emphasized. Also, graphical and numerical techniques are covered early on.
Viewing stained glass from different angles or in various lights is necessary to discover its many qualities. Likewise, viewing solutions of differential equations from several points of view is essential to fully understand their behavior. Lomen and Lovelock provide an active environment for students to explore differential equations by using analytical, numerical, graphical, and descriptive techniques, and for students to use ODEs as a natural tool for modeling many interesting processes in science and engineering.
Autonomous Differential Equations.
First Order Differential Equations - Qualitative and Quantitative Aspects.
Models and Applications Leading to New Techniques.
First Order Linear Differential Equations and Models.
Interplay Between First Order Systems and Second Order Equations.
Second Order Linear Differential Equations with Forcing Functions.
Second Order Linear Differential Equations - Qualitative and Quantitative Aspects.
Linear Autonomous Systems.
Nonlinear Autonomous Systems.
Using Laplace Transforms.
Using Power Series.
Appendices.
Answers.
Index.
