Introduction and Preliminaries
This chapter presents an assortment of material, covered in varying degrees of detail, which is needed as background material for the rest of this book. Students with a strong background in mathematics can probably skim some of the sections in this chapter. Section 1.1 discusses why differential equations are important to study in engineering. Section 1.2 discusses functions in mathematics, which is important not only because functions are solutions to differential equations but also because it helps define the types of variables that appear in differential equations. Implicit functions are also reviewed. The most important sections in this chapter are Sections 1.3 and 1.4 because they present new material that is used throughout the entire book related to the types of differential equations and their solutions. Section 1.5 reviews concepts from mechanical and electronic systems, including the properties of the common elements that make up simple electromechanical engineering systems. Finally, Section 1.6 presents the most basic method to use a computer to determine an approximate solution to an initial value problem for a given ordinary differential equation. More advanced numerical methods are considered in Chapter 12, but this introductory material is presented so that, even in the earliest chapters, students can check their work using a computer-solving method.
KeywordsDifferential Equation Angular Momentum Rigid Body Constraint Force Viscous Damper
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