1. Mathematical Preliminaries

This chapter delves into the mathematical foundations crucial for electric circuit analysis, covering a wide range of topics from basic trigonometric functions to complex differential equations. It begins with an overview of essential mathematical concepts, including degree and radian measurements, trigonometric functions, and their relationships. The chapter then explores the period and phase difference of trigonometric functions, providing practical examples and graphical representations. It also covers exponential functions, unit step functions, and unit impulse functions, explaining their properties and applications in circuit analysis. Complex numbers are introduced, along with their geometric interpretation and operations. The chapter further discusses derivatives, integrals, and their applications in solving differential equations. It also includes a section on partial fraction decomposition, demonstrating its use in solving complex rational expressions. The chapter concludes with a focus on the Laplace transform, highlighting its role in solving differential equations and analyzing linear systems. Throughout the chapter, practical examples and MATLAB applications are provided to illustrate the concepts and techniques discussed. This comprehensive review prepares readers for more advanced techniques in electric circuit analysis, making it an invaluable resource for professionals in the field.