Circuit Theory/Circuit Theory Introduction
Who is This Book For? 
This book is intended to cover two courses typically called "circuit analysis" and "signals and systems" in a one semester course. An attempt is made do this without a knowledge of ordinary differential equations. 1st and 2nd order differential equations can be solved using phasors and calculus if the driving functions are sinusoidal. Skipping the application of pulse, step, sawtooth, ramp, etc. driving functions to circuits leaves time for a more intuitive understanding of poles, zeros, transfer functions, Bode plots, and convolutions as they apply to circuits.
For those that have already had differential equations, the Laplace transform equivalent will be presented as an alternative while focusing on phasors and calculus.
This book will expect the reader to have a firm understanding of Calculus specifically, and will not stop to explain the fundamental topics in Calculus.
For information on Calculus, see the wikibook: Calculus.
What Will This Book Cover? 
This book will cover linear circuits, and linear circuit elements. The goal is to emphasize Kirchhoff and symbolic algebra systems such as matLab mupad or mathematica at the expense of node, mesh, Norton, etc. A phasor/calculus based approach starts at the very beginning and ends with the convolution integral to handle all the various types of forcing functions.
The result is a linear analysis experience that is general in nature but skips Laplace and Fourier transforms.
Krichhoff's laws receive normal focus, but the other circuit analysis/simplification techniques receive less than a normal attention.
The class ends with application of these concepts in Power Analysis, Filters, Control systems.
The goal is set the ground work for a transition to the digital version of these concepts from a firm basis in the physical world. The next course would be one focused on modeling linear systems and analyzing them digitally in preparation for a digital signal (DSP) processing course.
Where to Go From Here 
With a basic knowledge of electric circuits and electricity concepts under your belt, there are a number of different paths available for study.
- For a technician version of this course which focuses on the real rather than the idea, expertise rather than theory, on algebra rather than calculus, see the Electronics wikibook
- Take Ordinary_Differential_Equations now that you have a practical reason to. The math class should ideally feel like an "art" class and be enjoyable.
- To begin a course of study in Computer Engineering, see the Digital Circuits wikibook.
- For a traditional "next" course see the Signals and Systems wikibook. There should be an overlap with this one.
- The intended next course would have a name such as A New Sequence in Signals and Linear Systems or Elements of Discrete Signal Analysis.