This chapter provides the reader with a brief refresher course on the mathematical apparatus crucial for modeling of dynamic systems. Sections 2.1 and 2.2 present basic concepts and terminology of vector and matrix algebra. Definitions and basic operations on complex numbers are introduced in Section 2.3. Section 2.4 is devoted to one of the important methods for solving differential equations – the Laplace transform. Sections 2.5 and 2.6 discuss the types of differential equations widely encountered in modeling of common dynamic systems and develop methods for solving these equations. Section 2.7 introduces the mathematical foundation for deriving transfer functions and creating block diagrams of various linear time-invariant dynamic systems. Section 2.8 presents a brief overview of solving differential equations numerically, with MATLAB and Wolfram Mathematica.
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