From Continuous to Discrete

Embark on a compelling mathematical journey that seamlessly transitions from the continuous domain of algebra, differential equations, and analog electronics to discover vital connections with their discrete counterparts: integer equations, difference equations, and digital electronics. While a familiarity with differential equations and analog electronics can certainly enrich the experience, it is not a prerequisite. By leveraging a foundation in continuous mathematics, this book skillfully navigates a diverse array of discrete subjects within a remarkably efficient timeframe, all the while nurturing a solid grasp of the underlying principles. Immerse yourself in an enthralling expedition through modulus equations, the harmonies of music theory, the intricacies of integer equations, the dance of difference equations, the enigmatic Mandelbrot set, the transformative power of Z transforms, the subtleties of sampling theory, the evolution of analog to digital converters, the delicate craftsmanship of digital filters, and the captivating realm of digital communications. Despite the apparent diversity of these topics, they share a common thread of foundational mathematics that unites them. Harmonizing practical applications with theoretical principles, "From Continuous to Discrete" offers effective methodologies for solving real-world problems while still providing a robust theoretical foundation that supports these methods.