From Continuous to Discrete: Integer Equations, Difference Equations, and Digital Electronics

This book builds on algebra, differential equations, and analog electronics to better understand integer equations, difference equations, and digital electronics.   Readers who are unfamiliar with differential equations or analog electronics will still be able to follow most of this book, although knowledge of them will certainly be a benefit.  By building upon this knowledge and establishing some key connections between analog concepts and their discrete equivalents, it is possible to cover a large amount of topics in a relatively short amount of time while still maintaining a solid understanding.  

Some of the topics covered include modulus equations, music theory, integer equations, difference equations, the Mandelbrot set, Z transforms, sampling theory, analog to digital converters, digital filters, and digital communications.  Although these topics may seem broad and scattered, the underlying mathematics that supports them is much more universal.

Striking a good balance between practical applications and theoretical concepts, From Continuous to Discrete, gives practical examples and methods to real world problems with sufficient theoretical background to understand why the methods work.