# What would it take to learn Calculus at a practical level?

#### bullzai

Joined Jan 19, 2015
42
The highest math classes that I took WAY back were technical math (for electronics technology) and pre-Calculus. I recall not enjoying pre-Calc so much, but I think I did like things like trigonometry. Playing with micro-controllers has rekindled my interest in electronics. How would I go about gaining functional ability in Calculus so I could work with and understand circuits better? Or would I be better off just cobbling things together?

#### crutschow

Joined Mar 14, 2008
27,008
For analog circuits you don't necessarily need to know calculus well to understand circuits but you should understand the basics of integration and differentiation.
You do need a good working knowledge of basic algebra and complex numbers.
Complex numbers (phasors) are needed to understand and design AC circuits.
A Google search should give you some basic references and tutorials for those subjects.

#### #12

Joined Nov 30, 2010
18,217
Calculus at a practical level?

Calculus 101 and 102
First semester Integral Calculus and second semester Differential Calculus.
Of course, you better be up to snuff on your algebra and trig!

Calculus is mostly a way of thinking about the change in this for the change in that. Calculus generally isn't concerned with, "The answer is 42." If you can think in those terms, you can get a good feeling for the overall picture. You will eventually arrive at 42, but Calculus is only a way to get there.
Analog design is mostly concerned with, "The answer is 10 thousand ohms and 0.01 uf."
I am a third rate analog designer. I never got a good grip on Calculus, but I have designed thousands of circuits (that actually work).
If you are willing to settle for being able to design most of the circuits you need, you don't need Calculus.
The totally amazing stuff can be presented here at AAC for some really good designers to help you.

And remember, it's only my opinion.

#### andrewmm

Joined Feb 25, 2011
1,256
I'd say

for practical circuit design you don't need calculus

A lot can be learn by doing and 'rules of thumb'

Have a go, enjoy, see where it takes you.

Let the war begin,

#12

#### bullzai

Joined Jan 19, 2015
42
"Practical Electronics for Inventors" (1st edition) got me thinking. Attached in a table from page 27 about what type of math is needed or helpful. Do you agree with it?

#### #12

Joined Nov 30, 2010
18,217
I thought the title of the Thread said, "practical".
Three different people just told you that you don't need Calculus for that.
Now you post the requirements to analyze the most difficult circuits in the world.
So, what do you want to do? Build practical circuits or analyze non-sinusoidal, non-continuous functions?

#### bullzai

Joined Jan 19, 2015
42
I thought the title of the Thread said, "practical".
Three different people just told you that you don't need Calculus for that.
Now you post the requirements to analyze the most difficult circuits in the world.
So, what do you want to do? Build practical circuits or analyze non-sinusoidal, non-continuous functions?
Good question! Maybe I want to expand my understanding and ability. If so, it would only be for personal growth and challenge. I will never /need/ to know any of this and I probably won't make any money knowing it!

#### #12

Joined Nov 30, 2010
18,217
I understand that. I took Chemistry in College, knowing full well that I would never be good at chemistry. I just wanted some of it in my back pocket in case I had to keep working with the electronics required to interface with real world chemical sensors. Ya' know, if you're good at chemistry, you can count the number of electrons that will become available at the sensors!

#### bullzai

Joined Jan 19, 2015
42
Ya' know, if you're good at chemistry, you can count the number of electrons that will become available at the sensors!
Could be important! Well, if reaching the next level requires a massive effort, it might be more productive to skip it. heh Complex numbers came up more than once though.

#### WBahn

Joined Mar 31, 2012
26,398
The highest math classes that I took WAY back were technical math (for electronics technology) and pre-Calculus. I recall not enjoying pre-Calc so much, but I think I did like things like trigonometry. Playing with micro-controllers has rekindled my interest in electronics. How would I go about gaining functional ability in Calculus so I could work with and understand circuits better? Or would I be better off just cobbling things together?
The calculus doesn't really come into the circuit design so much as it often comes into solving the problem that you are trying to solve in order to get it to a point that you can start designing a circuit for it. In other words, the amount of math that you need is driven more by the kinds of problems you are trying to solve via electronics more so than it is by the electronics themselves. The more math you are conversant with, the wider the range of problems you are prepared to tackle. But there are lots and lots of problems that don't require calculus or higher math to solve -- almost certainly enough to provide a lifetime's worth for the hobbyist.

As far as the electronics are concerned, on the one hand calculus (or higher) is needed to really describe and understand what is going on with almost any circuits beyond basic DC circuits. One the other hand, a lot of work has gone into removing the higher level math from the practical level as possible -- this is not only to make them accessible to people that don't have the higher math, but also because even people that do have the necessary background are still more apt to make mistakes applying it than when applying lower level math. When you work with phasors in AC circuits, for instance, what you are really doing is working with the Fourier transforms of the differential equations that describe the circuits. But actually doing that is a royal pain in the ass -- force a student to do it for just one first order circuit and they suddenly become very motivated to learn phasor and, later, transform methods. So we analyze the components and their behavior once and come up with useful ways of describing the circuits (using "phasors" and "impedances" or, at an even lower -- and more restrictive -- level "reactances") that allow us to use less sophisticated math tools (algebra and complex algebra) to work with the circuits.

#### bullzai

Joined Jan 19, 2015
42
Wow, so unless I want to be an electronics...scientist(?) or solve more complex problems, just stick with the given equations and datasheets? I did learn about phasor diagrams in school. I guess when explanations include more complex math it makes me feel like I'm missing the party! haha

#### wayneh

Joined Sep 9, 2010
17,152
I learned calculus well enough to use it on the job (nothing to do with electronics) and even remember it 35 years later. I took a sum total of one year of high school plus one 5 credit (i.e. killer) semester in college. I don't think that's all that much. It's hard to recall but I'd bet a lot of that year in high school was not specifically spent on calculus. I also had differential equations but that's...different.

Calculus was an aha moment for me, like pulling the curtain away from the wizard of Oz. So for me personally, I'd recommend learning it even if you barely use it. It's a great tool for viewing the world, like learning some history or philosophy.

#### #12

Joined Nov 30, 2010
18,217
Calculus was an aha moment for me, like pulling the curtain away from the wizard of Oz.
I never quite got there. I only got close enough to know somebody is behind the curtain, but the "Aha" is still a nebulous suspicion of a world I can't quite see.

#### wayneh

Joined Sep 9, 2010
17,152
I never quite got there. I only got close enough to know somebody is behind the curtain, but the "Aha" is still a nebulous suspicion of a world I can't quite see.
I kind of feel that way about quantum mechanics. I studied it and even did well compared to my colleagues, but never really "got it".

#12

#### bullzai

Joined Jan 19, 2015
42

#### OBW0549

Joined Mar 2, 2015
3,566
I have no idea whether this will help or not, but I found it rummaging through my pile of .pdf files. I think someone here (I don't remember who) posted it a while back and I grabbed it.

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#### bullzai

Joined Jan 19, 2015
42
I have no idea whether this will help or not, but I found it rummaging through my pile of .pdf files. I think someone here (I don't remember who) posted it a while back and I grabbed it.
Will definitely take a look. Thanks.

#### Papabravo

Joined Feb 24, 2006
15,779
Using Prof. Thompson's book I estimate that about six months of diligent reading and problem solving will get you where you need to be.

#### DickCappels

Joined Aug 21, 2008
7,279
But Thompson's book makes the techniques accessible to students with no prior understanding of calculus. True, it is a very dense book -a lot is done in those few pages.

#### WBahn

Joined Mar 31, 2012
26,398
I don't have Thompson's book. Does it explain what a derivative or integral are, or does it just show how to evaluate expressions that contain them?