A Math & Physics Self Study Course to Prep for AoE

[JenniferG]

It's been so long, 25 years.  I've forgotten all my higher math & physics, and even some Algebra.  I never had a solid foundation in lower math -- never mastered it all.  I think this is why I've forgotten so much.  I got A's in Calculus I, III, Differential Equations and Linear Algebra, and a B in Calc II.  But again so long ago, I just don't remember it.   I do remember I struggled with the homework and took me much longer than it should due to lower math not being mastered.

I just started reading these AoE & LAoE books .. just a few pages.. and I already feel uncomfortable.  I want to thoroughly understand all the laws they talk about, so I decided I need to learn undergraduate college level Electricity & Magnetism physics.   Started reading my old Tipler's Physics books (Third Edition) and I see that one needs to know Newtonian Physics well to understand Electricity & Magnetism.  I've forgotten my Mechanical Physics I took 25 years ago.. got a B in that course as well.. was a struggle.   I can't even do Mechanical Physics because I forgot my Calculus.. cascading all the way down to a lot of forgotten Algebra.

So I decided the other day to just start from floor, Kindergarten math on Khan.  I heard Khan was great for building a solid math foundation so I went with it.  Mastered (100%) K-6th grade and Early Math through Pre-Algebra in 3 days (lots of questions and word problems.. hundreds).  Surprisingly learned a few things: I can do arithmetic much faster in my head and on paper, than ever before.. e.g. quickly identifying prime numbers, and quickly multiplying large digit numbers (in my head even).  Also learned that a square could also be classified as a rectangular rhombus.  Know how to find the area of a trapezoid now lol. Wow!

Now I am 20% through Algebra, and progressing quickly.

The following is the course path I've tentatively chosen.  If you have any other recommendations (other than what I am doing is probably overkill), I'd appreciate it; e.g. resource suggestions.

The courses I've chosen below are 100% free which include many courses from prestigious professors at MIT.  Again comments/suggestions very welcome.

Once I am finished with all of Math and Physics I'll start on AoE & LAoE.

Jennifer's Curriculum Course
(as prerequisites for AoE & LAoE)

Master all of the following math courses:

1) Algebra (Khan Academy)

2) Geometry (Khan Academy)

3) Trigonometry (Khan Academy)

4) Pre-Calculus (Khan Academy)

5) Single Variable Calculus
MIT Mathematics Course 18.01SC – OpenCourseWare [Free]
Professor David Auroux
Khan Academy (supplemental if needed)
Swokowski Calculus (supplemental text)

7) Multivariable Calculus
MIT Mathematics Course 18.02SC – OpenCourseWare [Free]
Professor David Jerison
Khan Academy (supplemental)
Swokowski Calculus (supplemental textbook)

Linear Algebra  (Applications focused, not proofs/theory)
MIT Mathematics Course 18.06SC – OpenCourseWare [Free]
Professor Gilbert Strang
Khan Academy (supplemental)

9) Differential Equations
MIT Mathematics Course 18.03SC – OpenCourseWare [Free]
Khan Academy (supplemental)

After math is mastered above, then on to the physics, which I hope to mostly master:

1) Mechanical Physics
Dr. Walter Lewin MIT Youtube Videos
Tipler's Physics – Third Edition  (supplemental textbook)
Khan Academy (supplemental)

2) Electricity & Magnetism Physics
Dr. Walter Lewin MIT Youtube Videos
Tipler's Physics – Third Edition  (supplemental textbook)
Khan Academy (supplemental)


Then after all the math & physics, start on AoE & LAoE.

EDIT: Dr. Lewin is such a great Physics professor, I will also most likely want to do his free Youtube Quantum Mechanics course as well.  I've already watched a couple of his video lectures on it and am blown away to find out about discrete energy and how electrons change shells instantaneously and in a discrete matter, emitting particular fixed length electromagnetic waves / photons -- buying the light diffraction grating thingy now after watching that video..  I now wonder if we are in a computer simulation LOL!

EDIT:  Btw, I always thought electronics orbited nucleus like planets do the sun.. not the case heh.  Check out this awesome video model  (starts discrete for first few seconds but then simplifies by making the transitions more analog, so we can see what is happening more easily:  )

[rstofer]

That is an ambitious and lengthy program.  I hope you take time out to play with electronics.

You can do a lot of electronics with nothing more than matrices (solved by wxMaxima, of course) and a wee bit of differential and integral calculus (again, let the machine do the work).  It's not until you get to signal processing that differential equations, and more specifically, Laplace Transforms comes into the mix.

But by then, the trig functions, series expansions and calculus are all pretty much required.

This is well beyond what most would consider as hobby electronics.

[JenniferG]

That is an ambitious and lengthy program.  I hope you take time out to play with electronics.

You can do a lot of electronics with nothing more than matrices (solved by wxMaxima, of course) and a wee bit of differential and integral calculus (again, let the machine do the work).  It's not until you get to signal processing that differential equations, and more specifically, Laplace Transforms comes into the mix.

But by then, the trig functions, series expansions and calculus are all pretty much required.

This is well beyond what most would consider as hobby electronics.

I am not sure how much I need to know when designing synthesizers, home stereo amplifiers etc.  That's my main interest right now, for learning AoE.  But eventually I think I'd like to be able to create anything with electronics.  So that's why I figured I just might as well learn all the math and phsyics.

EDIT: I also like the idea of having a quality math & physics education from MIT professors for free.  These courses each cost the attending student about $6000 per class.  I'll be getting essentially the same education for free, that would of cost me $50,000.  I've had not so great professors in the past (community colleges & state university).  With MIT OpenCourseWare, I get the some of the very best.

[beenosam]

I would say what you are doing is overkill. You should just review basic calculus and some differential equations. Then when you understand the math, just do a simple google for topics you don't understand. You don't have to know everything in-depth (though, some here might disagree) to enjoy/do stuff with electronics. You just need an understand of how something works generally, not a full in-depth explanation of what the electrons or holes are doing etc.

I'd say just do a review of calc, diff eq and a good review of Linear Algebra. Worry less about math or academic subjects you don't know and worry more about the circuits first. Most useful things you do with electronics (that are reasonably calculable) is just algebra (matrices). Beyond that you may want to know some calc/diff eq for RLC circuits. Don't overburden yourself, just have fun.

Start small, work your way up. Learn as you work. Google or ask here about things you don't understand then use that to find the formal mathematical/physics definitions.

[rstofer]

Here is a classroom type video series that discusses circuits and, in particular, mesh and nodal analysis.  This is in the early part of the series.  I haven't watched them all:

https://learn.digilentinc.com/classroom/

I'm also of the same opinion as beenosam in that what you have planned is an excellent program, it really isn't necessary for most of what electronics hobbyists (and most engineers) ever need.

You do need DC and AC circuits (especially amplifiers and filters) and you will need complex numbers for AC circuits.  The good news is that you don't have to solve a 5x5 matrix of complex number by hand.

You mentioned Physics and I love Physics - it explains everything!  Well, there is some good news about both Physics and Maxima:  There's a book:

https://www.amazon.com/Classical-Mechanics-Undergraduate-Lecture-Physics/dp/1493932063

It is cheaper on Alibris.com.  Recognizing that wxMaxima is just wrapping Maxima in a GUI, all of the examples will work.

There is also a book on Quantum Mechanics with Maxima (probably out of my league):

http://www.alibris.com/booksearch?keyword=mechanics+and+maxima

Matlab is another excellent tool for which there are many add-ons.  I have the home version with the Simulink, Symbolic Math Toolbox and Control System Toolbox add-ons.  Simulink does a magnificent job of modeling differential equations.  Want to change factors?  Add control knobs instead of constants!

Then there is TINA and LTSpice for simulation, both are excellent but there is some matrix stuff that TINA will so that LTSpice will not.  Search the Beginners forum for 'mesh analysis' and somewhere in Simon's homework problem, there is a neat solution to simultaneous equations with TINA.  There is now a free version but I don't know which capabilities are restricted.
 
You can also model differential equations by building up op amp integrators and summers in LTSpice.  That is about all I have done with LTSpice because I simply don't do a lot of analog kinds of things.  Other than analog computing...

Designing everything except flux capacitors is really a matter of cut and paste.  Everything that can be done with electronics has been done and it's all on the Internet.

[kosine]

I know how you feel. I did a lot of mathematics for a physics degree 20 years ago, and forgot most of it soon afterwards.

But I was inspired to get back on the horse by a friend with dyslexia. He'd been hopeless with numbers at school but found himself needing it for a later-in-life qualification he was taking. He was amazed he could actually do OK with it. Hard work, but he was quite enjoying it!

So I followed suit. Bought a load of secondhand textbooks (let's face it, they're dirt cheap because no one really wants to read them!), watched a load of videos (Gilbert Strang is good), started to make much more sense of it than I ever had before.

I think most of the problem is the way that they teach it in school is shocking. A nuts and bolts approach. "Here's the rules, now go practice them..." It's like learning music with nothing but notes and chords. Only when you hear the music does it make any sense. If you can get to understand Euler's equation (e^i.Pi +1 = 0) you'll know what I mean.

(Hint: numbers can be rotated. -1 is 180 degrees, i is 90 degrees. That's why minus x minus is a plus (two 180s), and why i is the square root of -1 (two 90s). If only they'd told me that at school! The exponential bit is a little harder to explain, but very elegant once you figure it out. It's a short step from there into quaternions which Maxwell used for his theory of electromagnetism (the current textbook equations are actually due to Oliver Heaviside), and beyond that you're into Clifford algebra which is very fascinating indeed..! A little overkill for electronics, but understanding complex numbers is pretty important.)

One thing that I've found particularly helpful is also studying the history of mathematics. All those textbook rules came from someone trying to solve a particular problem, and once you know what they were trying to do, the solution makes far more sense. (I can recommend Morris Kline "Mathematical Thought from Ancient to Modern Times" and anything by Thomas Heath if you want to go right back to the Greeks. This is a really great source : http://www.wilbourhall.org/index.html)

(Despite my renewed enthusiasm, I'm still quite terrible at actually doing any math! But then I don't need to play violin to enjoy Mozart...)

Good luck with it!

[BrianHG]

Hello Jennifer,

     Now I know that these videos are far more basic than what you are looking for, but, for others reading this thread, they have very easy level illustrations of the function of basic electronics, the mathematics which is very useful for engineering the electronics & some physics.  Now, the video run slow deliberately for beginners, but, remember, in your video player, you can set the playback speed to 1.25, 1.5, or 2x.

https://www.youtube.com/user/EugeneKhutoryansky

On this channel, scroll down the page, vertically and horizontally & you'll find all the sections, ie electronics/algebra/trig/quantum mechanics, ect.  As a refresher course, you may discover that you didn't forget as much as you think from your younger schooling years, or, seeing the functions visualized this way for the first time does make some difficulties I had 20 years ago disappear.