I can also highly recommend "The Art of Electronics" by Horowitz and Hill.
My dad had "Electronics for Scientists" by Malmstadt et al., 1962. His employer put a bunch of scientists through an electronics course.
The contrast was pretty remarkable. It's all about vacuum tubes, with some introduction of transistors. The 1st edition of AoE had a reasonable amount of material on digital circuits for back then, but I imagine a similar contrast between 1984 and today.
The span of 40+ years has certainly changed how I do electronics.
Surely this is like recommending a Knuth book (TAoCP?) to someone wanting to learn 'CS fundamentals', which.. sure?
Your picture is simple enough; but you have mixed up dq (this is the dependent function on the Y-axis) and dt (this is the independent variable on the X-axis) infinitesimals. Their ratio is simply the instantaneous rate of change of electric charge w.r.t. time which is what is the instantaneous electric current. As to the cross-sectional area of a wire varying over its length and how it affects current through it, you can neglect it for short wires and using a specific wire gauge for all normal electronics.
> There needs to be an even more grounded book in electronics, something that you can show to a guy who literally has no idea about electronics in the slightest bit and by the end of the book, the guy is a master at it
Electronics = Physics+Mathematics+Logical Thinking and there can be no shortcuts to its study. You have to put in some effort to study the subject. However things have been simplified and modularized to such a great extent nowadays that you can learn and do a great deal without understanding much of the mathematics and physics involved. The submitted book link in this post is a good basic one to start from.
Say a roomba.
You might not know how or why each component works in detail at the end, but instead understand why the board is laid out the way it is and where each component controlling the functions and logic live, what might be broken, and whether and how to repair. I think if I were an impatient student with an interest in electronics that’s what I’d want. Then go back and study individual components, math, physics, and theory.
You could make a whole series: radio boards, home appliance boards, PC motherboards, car boards, etc.
There is plenty of material and videos on the web if you search for it; also a book The Art of PCB Reverse Engineering: Unraveling the Beauty of the Original Design by Ng Keng Tiong.
Reverse Engineering: Mechanisms, Structures, Systems & Materials by Robert Messler.
Product Design: Techniques in Reverse Engineering and New Product Development by Kevin Otto and Kristin Wood.
The Hardware Hacker: Adventures in Making and Breaking Hardware by Andrew "bunnie" Huang.
The problem you are running into is that every book starting in the late 1970s has taken the approach that you must know math intuitively to first translate the subjects being taught and to understand the modeled behaviors they represent.
Intuitive approaches have largely been ignored and avoided since then, and its acted as a gatekeeper ever since to prevent people from going into Physics, Science, and the other more technical fields.
This behavior follows practices of ideology common to gnosticism, which as a TL;DR is the idea that some people are allowed access to secret knowledge and others aren't, and only such masters can tell and determine who should have and be able to learn that knowledge. It is a completely refuted false ideology when it comes to objective reality, has no basis, and is quite evil since in practice to do this you impose a complex system of torture to ensure anyone seeking this knowledge that is deemed unworthy by some arbitrary measure is conditioned towards PTSD, just like any dystopia. They are made to believe they just aren't good at math.
This was a purposeful choice made by the boomer generation of teachers in their professions, given the widespread adoption was systematic. They simply followed what they were taught by the NEA, and that is why things are falling apart today. Knowledge of critical education was withheld, options were withheld, and by constraining thought they enforce a path of control, and the dynamics which inevitably culminate in destruction or annihilation given sufficient time because they don't stop making these changes. It gets to a point where you have people who are no better than dependent parasites on the labor of few educated, but not necessarily intelligent people. Hubris naturally occurs in such people.
The limit is also a calculus item. There is a derivative which is the instantaneous rate of change at a point (the slope is the average rate of change between two points) the single point and limit technique is always with respect to some other measure, and a integral which is the area under a curve at a single point, as the change between the points goes to 0 (i.e. a limit).
You use the delta form of the limit to calculate derivatives before you learn and have proved the shorthand methods with delta epsilon rigor. Its quite abstract, and the vast majority of the material is useless to a non-math/Engineer major. You need to understand this before you can read this.
> Does this equation actually take the effect of this fluctuation
No, the equation shown is a theoretical model, in math. In many cases, you are taught lies initially because they are simple, and a pedagogical tool called lying to children has been used since the late 70s, in various forms though wasn't called that until the 90s. Then you have to unlearn those lies as you progress through gnosis.
The best way to learn these things that I've seen that is still in use today is called Lumped Matter Discipline. It makes certain assumptions about the type of components in use to simplify the equations to basic algebra. You still need to know Calculus enough to Derive Maxwells theorems when those assumptions don't hold. One of the assumptions made is that charge buildup is 0 (iirc), in other words the second derivative, or the derivative of dQ/dt is 0, which is the acceleration or rate of rate of change.
The MIT OCW videos cover these simplifications, its dry, but its better than 99% of the other material out there aside from maybe the Oliver Heaviside Lectures at the turn of the last century which are public domain.
The flowing water pipe analogy which brainwashed/indoctrinated people use to teach is intended to purposefully mislead, maybe not by the instructor, but by the person they took it from.
Understanding the process of diffusion of charge and the need for isolation is the correct way to be thinking of these things.
If you don't know Ohm's law. You don't know what a resistor is. You've never built a simple circuit. Then this book may not be for you. Or it may if you're willing to put in the effort.
I googled and found one example: https://ww1.microchip.com/downloads/aemDocuments/documents/A...
AoE is extremely practical. I think the debate here is what exactly are "fundamentals" for electronics. I read AoE with high school physics and some hands on tinkering (mostly with exposure to software in embedded systems) as my background. At that point in my life I found it readable and enjoyable. It will help you get to the next level. Probably skipped some sections that weren't of interest though. I probably built my first electronic circuit in elementary school (some lights, switches, battery, etc.). If you just have no clue of anything electronics then yes, this is not the book for you. But it still is "electronics fundamentals" despite that.
It reminds me of my first time trying to learn assembly language when I was in my early teens. I just could not make any sense of it. I knew a little bit of PASCAL and BASIC at the time and that was just alien territory. When I came back a few years later after some exposure then it all came together.
Try going back to the book ;)