Sidebar of a Student's Lament
Though I'm not much a fan for chatting too lightly about it, this year I've been a student of an electronics and computing program at an online university, namely DeVry University Online (DVUO) in DVUO's associates program in the DVUO ECT department. It's a challenging program, I consider, but the challenge is not always only in the course material itself. Firstly, there's the matter of trying to be a student of an electronics and computing program at DVUO, with lab, while not living anywhere near a formal DVUO campus. I've received quite some stunning items, at that  in one item, a nice shiny black box, with all sorts of "bizarre" electronics things inside. It's nothing I could wish to carry around, for any purpose, but it's what DVUO sent to me  one Knight Electonics ML2010. I also own an oscilloscope, now. I can count, on two hands, how many times I've needed either of those expensive items of equipment, candidly. That I'm able to afford those items, on a scholarship, I'm grateful for that much. In regards to the educational model in practice, however, a scholarship does not divert my criticisms about the very expensive model of it. That's one thing, then. Being a student, there, is yet another thing.The course textbook we're using  to my point of view  prevents entirely an axiomatic, if not simply rote approach to AC circuit analysis. In one point of view, it might seem simply practical  the analysis methodology presented in the course's textbook, and the parallel methdology presented in the course's lectures  but it is not in all ways a thorough methodology. In my experience, it's a very tedious methodology, and the book leaves a number of gaps, with difficulties. The book, itself, leaves some "gaps" about analysis of some specific combinations of {R,L,C} circuit elements within a series/parallel {R,L,C} circuit onto an AC power source.
Secondly, the course's lectures use a different notation than the book. The course's textbook uses polar notation, throughout. The lectures use rectangular notation, for those complex calculations. Though it might seem that the calculations might possibly "Make more sense" when conducted only with formulas in a rectangular notation, however  considering that I've been studying, this semester, a textbook using polar notation, throughout, and though a corresponding formula may be produced in a rectangular notation, for any formula in a polar notation, but it's a wide gap in syntax and semantics between the two respective types of notation. I prefer the polar notation, but it's "Just not working out," to me, for analyzing the circuits that the book does not present a methodological model for. It's with a sense of chagrin, then, that I begin to wonder if I've studied with the wrong sort of notation? I'm not understanding the relations of voltage, current, and reactance, in magnitude of phase angle, for a couple of types of circuit if from a perspective of polar notation, and corresponding calculations of geometric sums, parallel equivalent values, and arctangents of a specific quotient. Sure, the arctangents are easy to calculate in Common Lisp, and a radianstodegrees conversion is easy enough likewise, but the whole polar notation is something I now elect to "Take a break from," to be sure I can analyze the same circuits, in a model using rectangular notation. I'm now in week 5 of an eight week course, and it seems rather pressing to me.
More broadly: I'm concerned that, for one thing, a pedantic iteration of the same formulas for the same types of circuit, ad infinitum, may not really help one to learn how to analyze circuits. It would, at least, serve to assist towards applying formulas, and perhaps understanding "some of" how those formulas relate to any exacting electronic, electromagentic, dielectric, or more broadly electrochemical qualities of individual circuit elements, and circuit elements in parallel and in series.
I'm concerned, furthermore, about whether the course program, itself, has really equipped "We the students" to understand enough of the essential mathematics of electrical science, even insofar as the calculus. Although I'd studied some of the differential calculus and the integral calculus, before college  in "high school," namely  but that was some years ago. I am not presently equipped to analyze a differential curve for change or variation in voltage or current within a circuit of an alternating current. When I read [Nahvi2004] I can see that there's more of math to the matter, and I may be able to ascertain some of what that math would be, if I understood the same disciplines of mathematics, presently. Perhaps it would not be a panacea, but it might help towards understanding the basic principles of electrical science, and any number of corresponding geometric models, in mathematics.
Pragmatically, there are a couple of types of {R,L,C} circuit that  in all candor  I simply don't know how to analyze, at present. Here's the full set of {R,L,C} circuits, then, in diagrams that I've made, myself, towards a sort of reference sheet for manual circuit analysis. I'll denote that these graphics are public domain, in how I'll license my own work, at that.
The Simple Series and Parallel {R,L,C} Circuits 
Fig. 1: RLC Circuit 
Fig 2: R//L//C CircuitThe R(X//X) Circuit

Fig 5: C(R//L)The R//LC Circuit
The X//(RX) Circuits 
C//(RL) 
L//(RC) 
Between calculations of phase angle, net reactances, and net impedances, the axiomatic approach that I thought I'd been learning from the course's textbook fails me, in that the book does not provide a a complete model for computing the impedance, in its magnitude and phase angle, for the following:
 C(R//L) i.e capacitor in series to parallel RL mesh
 correspndingly, L(R//C)
 L//(RC) i.e. inductor in parallel to series RC branch
 correspondingly, C//(RL)
The text lecture materials of the course illustrate a methodology divergent from the course's textbook, in that the course's textbook utilizes polar notation throughout the computations, whereas the course's lectures use rectangular notation, "This week." Of course, I understand that there's a mathematical correspondence between polar and rectangular notations, however the semantic and syntactic differences  between a view of the math in the two notations, respectively  it may seem like a pretty broad difference.
In the process of this process, I've learned a few additional things, such that I would wish to denote here, in short:
 That MathML is not immediately well supported on the web.
 There's MathML support in Firefox
 There are web plugins
 ...whether or not for a short "notes sheet"
 ...or a full, public math and science portal
 [Bookmarks]
 That Google's Picassa tools can be useful for sharing graphics representations of electrical schematics
 ...without their corresponding models, albeit, in any single hardware definition language (HDL) such as VHDL, Verilog, or the perhaps less Fortranlike EDIF format
 That a "Single EDA platform" cannot be comprised only of a set of software tools, but must be accompanied of a corresponding methdological model at least insofar as circuit analysis
 Evidently, there are multiple methdologies that may be applied in circuit analysis.
 I may tend to prefer a methodology utilizing of Thevenin's and Norton's theorems addressed to AC circuits [OMalley2011]
 That's not being taught in the course, though, and it may take some time in study, to "Relearn" the same material, from a perspective of that more principally extensional approach
 It's apparently a viable methodology for analysis of AC circuits
 ...referencing an additional textbook [OMalley2011] in just how that textbook is, itself:
 There's an EDA platform alternate to NI Mulstisim, namely: Cadence OrCAD Capture [Info][Download page]
 In one's own opinion, Cadence's Engineering Data Management (EDM) platform looks pretty thorough and well presented, too
 A "Popup" solution for the commercial shop, no doubt!
 Extensible like OrCAD Capture, I'm sure.
 DVD "en route"
 In free/open source software (FOSS) platforms compliant with the Debian Free Software Guidelines (DFSG) there's also XCircuit
 XCircuit is available on Microsoft Windows platforms in a standalone edition (with prerequisites) or as a Cygwin package (with the package manager handling the installation of the prerequisites, as a good package manager system would)
 Of course, on Linux platforms, one could use the respective package manager to install XCircuit from the respective upstream software package repository, in like as a Linux distribution may provide.
Presently, I'm thinking to restudy all of {R,L,C} circuit analysis, with a focus toward polar notation and Common Lisp to make the semnatics of it more manageable. Then, I could possibly "Check my results" with XCircuit and NGSPICE  assuming a certain reliability in NGSPICE, as about circuit modeling for conventional, analog {R,L,C} circuits..
I don't expect I'll be writing much about the results, immediately. Candidly, it's "a homework thing", too.
A Reference Bibliography onto Electrical Science and Correspondence in Mathematical Systems
Nahvi2014

Nahvi, Mahmood and Joseph A. Edminister. Schaum's Outline of Electric Circuits.
6th edition. McGrawHill (New York). 2014


Spiegel1971

Spiegel, Murray R. Schaum's Outline of Advanced Mathematics for Engineers and Scientists.
McGrawHill (New York). 1971


Lipschutz1959

Lipschutz, Seymor, Dennis Spellman, and Murray R. Spiegel.
Schaum's Outline of Vector Analysis. 2nd edition. McGrawHill (New York). 2009


Ayres2013

Ayres, Frank and Elliott Mendelson. Schaum's Outline of Calculus.
6th edition. McGrawHill (New York). 2013


OMalley2011

O'Malley, John. Schaum's Outline of Basic Circuit Analysis.
2nd edition. McGrawHill (New York). 2011
