calculus in electronics

Ratchit said:

As I said in post #25, everything you need to know is in post #21. Finding the limit of I as R approaches zero, we get
View attachment 100990
Finding the above limit if facilitated by using L'Hospital's Method, as described in any good calculus book.
If V = 10 volts and L = 2 henrys, the current will be 5*t when R=0. Plotting the current curve when R=0.000001, we get.
View attachment 100991
As you can see, the value of the current is about 25 amps at the end of 5 seconds when R = 0 instead of 5 amps when R=2 ohms.

Ratch

Click to expand...

I = 5*t
di/dt=5 Amp per second
Current is increase at rate of 5 amp/sec
Thank you everybody for helping me

vead said:

I = 5*t
di/dt=5 Amp per second
Current is increase at rate of 5 amp/sec

Click to expand...

That is correct if L=2 henrys, V=10 volts, and R=0.

From the graph and calculation, It is correct, but practically I don't think it is valid because current is increasing constantly.

Click to expand...

Yes, the current is increasing in a linear manner with respect to time. When applying a DC voltage across a inductor with no limiting resistor (R = 0 , remember), you can expect the current to be constantly increasing.

Suppose if we calculate current for minute, or hours theoretically value of current will be too high.

Click to expand...

There is no mathematical limit to the value the current can reach if you wait long enough. Of course, the inductor will burn out when its current limit is exceeded.

Can you tell me why our calculation is not valid practically?

Click to expand...

You did not evaluate R as it approached zero in the denominator of your equation. You only used R to determine the time constant was infinity. You needed to evaluate R where it appears in every instance of the equation like I did.

Ratch

tcmtech said:

You have it backwards. Calculus is a mathematical representation of that, not the otherway around. The ability to guestimate was here long before calculus existed and is used by creatures far less advance than us as well.

Click to expand...

I agree but call it what you like, you're still using Calculus.

nsaspook said:

I agree but call it what you like, you're still using Calculus.

Click to expand...

Hello there,

Yeah i dont know about anyone else but i always like to solve a three dimensional diffusion equation before i adjust the temperature or time of my oven when cooking baked potatoes (har har har)

nsaspook said:

I agree but call it what you like, you're still using Calculus.

Click to expand...

No I'm not. I'm using basic analytical skills followed by basic actions.

Just because something can be modeled with a mathematical concept does not make the action itself a mathematical action.

Come on. You're better than this level of trollish behavior.

tcmtech said:

No I'm not. I'm using basic analytical skills followed by basic actions.

Just because something can be modeled with a mathematical concept does not make the action itself a mathematical action.

Come on. You're better than this level of trollish behavior.

Click to expand...

Not trying to be trollish because I think you're understating regular human problem solving capabilities. I view mathematics in this sense as a language that's used to describe quantitative physical or mental processes. That language might be the voices in your head, a mental image equivalent or a symbolic written language used to communicate those processes to others or record the experience. Analytical skills are not random guessing processes and/or pure pattern matching from previous experience. Analytical skills can involve the prediction of the future from the actions of the past/present and sequences of actions to an end using sets of logical rules that clearly out perform random choice or a 'cook book' with novel circumstances. The mathematical action is not the person using a pencil and paper to calculate when the steak is done. The mathematical part in the analytical skill is the use of logic and shared thoughts about that logic using the language of math to access the cognitive resources of other people about what you need to analyze.

nsaspook said:

I think you're understating regular human problem solving capabilities. I view mathematics in this sense as a language that's used to describe quantitative physical or mental processes. That language might be the voices in your head, a mental image equivalent or a symbolic written language used to communicate those processes to others or record the experience.

Click to expand...

Nope. Those abilities and actions are cognitive tools we use that are language independent. Trying to say a certain thought process is a mathematical language is no different than saying it is any other language if said language has a way to describe the thought/action.

I thought this reply in my mind which until I put it in text was language ambiguous being the same thought could be created by anyone and converted to any definable language that can carry its context properly.
Just because a thought process can be written in a hundred other languages other than my American English does not make it or this reply post anything but an thought conveyed in American English. The thought itself is not the language.

Just because a thought can be mathematically expressed does not make the thought itself an exercise in mathematics.

nsaspook said:

Not trying to be trollish because I think you're understating regular human problem solving capabilities. I view mathematics in this sense as a language that's used to describe quantitative physical or mental processes. That language might be the voices in your head, a mental image equivalent or a symbolic written language used to communicate those processes to others or record the experience. Analytical skills are not random guessing processes and/or pure pattern matching from previous experience. Analytical skills can involve the prediction of the future from the actions of the past/present and sequences of actions to an end using sets of logical rules that clearly out perform random choice or a 'cook book' with novel circumstances. The mathematical action is not the person using a pencil and paper to calculate when the steak is done. The mathematical part in the analytical skill is the use of logic and shared thoughts about that logic using the language of math to access the cognitive resources of other people about what you need to analyze.

Click to expand...

I don't think mathematics is a language. No more than shorthand is a language. Without a base language to reference, neither can function. I consider math more of a bookkeeping method. As in bookkeeping, the basic mathematical principle is to keep everything balanced.

Ratch

To me his concept comes off as the " The dog is brown therefore all brown things are dogs.' type reasoning.

I seriously thought he was better than that.

tcmtech said:

To me his concept comes off as the " The dog is brown therefore all brown things are dogs.' type reasoning.

I seriously thought he was better than that.

Click to expand...

I tried, it's fine if you can't see the music and only hear it. There are certain concepts for which mathematics is well suited and there are many where it is not. Using math to describe the taste of that nice steak after its been cooked would be on the not column.

tcmtech said:

To me his concept comes off as the " The dog is brown therefore all brown things are dogs.' type reasoning.

I seriously thought he was better than that.

Click to expand...

Hello there,

This reply is really for both you guys.

What you are saying there could be referred to in formal logic as a "non sequitur" and i think that is a good example.

However, we have to realize that the current argument really belongs under the heading of philosophy, and let me state one definition of that word in the way in which i am using it...
Philosophy:
"The study of the fundamental nature of knowledge, reality, and existence, especially when considered as an academic discipline."

What that really means is that we are trying to arrive at conclusions that follow from the observations.

Unfortunately, there are some questions that dont have just one single answer. That's because in our attempt to find one we dont find just one we find two or more, either or which could be correct if not even both of them. The truth lies in a series of rigorous arguments where each point must be clearly defined, and it's not only very hard to do that it's also possible to set up other sets of arguments that lead to somewhat different conclusions. When this happens the debate can go on literally forever because the final answer depends very highly on the application(s).

A counter example here would be that in your statement if we limited the number of dogs in the study group it may actually be true.

But the example i like to give is one of the most controversial: A hole in the ground.
What exactly is a hole in the ground?
When we try to define this we end up with various problems, especially if we dont limit ourselves to a hole in the ground but also allow a hole in anything, anywhere.
We choose a location, and once we remove the earth from the ground in that location we have what we call a 'hole'. But the 'hole' is made of nothing, so how can it be anything? We assign a simple explanation by calling it a noun, but nouns are man made, so is the hole really anything? We can call it a localized lack of earth, but still there is nothing there where the 'hole' is located so how can we say it is anything at all.

It's this kind of argument that can go on forever unless we set up some ground rules, and in this we also have to remember that when we try to call it something,whatever that may be, that is in itself setting up a ground rule which has, as of yet, no context. We have to decide on the interpretation beforehand about what we are going to allow to be called "real". If anything real has to have physical substance in and of itself, then we cant call a 'hole' anything real, but if we allow all nouns to be called real then it doesnt have to be physical.

So philosophical arguments can go on forever unless you set some ground rules because there is no right and wrong unless there are rules to follow or to contradict.

nsaspook said:

I tried, it's fine if you can't see the music and only hear it. There are certain concepts for which mathematics is well suited and there are many where it is not. Using math to describe the taste of that nice steak after its been cooked would be on the not column.

Click to expand...

No matter how many time that guy says "math is a human language", he did not give any cogent reasons why it should be defined that way. Mostly, he dwelled on methods to teach kids math. That's fine, but it does not booster his "math is a language argument". Can you imagine trying to teach a toddler only math equations and symbols and not uttering a word in any language while in his presence? As I said in my previous post, math has no meaning without a base language to reference. A real human language can express emotions, math cannot. Math can manipulate abstract symbols that represent real world quantities, but that does not make it a language. I think that considering math as a specialized method in general, and a bookkeeping method in particular is the best way to define it.

Ratch

MrAl said:

Unfortunately, there are some questions that dont have just one single answer. That's because in our attempt to find one we dont find just one we find two or more, either or which could be correct if not even both of them. The truth lies in a series of rigorous arguments where each point must be clearly defined, and it's not only very hard to do that it's also possible to set up other sets of arguments that lead to somewhat different conclusions. When this happens the debate can go on literally forever because the final answer depends very highly on the application(s).

Click to expand...

That is the point I was trying to make. The thought process may be viewed to resemble a type of calculus to someone who thinks of the world largely in mathematical terminology but it's not that way to someone, like myself, who doesn't see the world from that view.

I use applied practical mathematics every day yet I rarely consider any thoughts I have to be definable as mathematical. Especially one where I use observation followed by rough estimates and guesses to get something approximated 'close enough to work' as needed.

A good example of this would be some basic machining work I did they other day on my lathe. I needed to bore out a washer a small amount to get it to fit a precision made shaft. I chucked it up, touched off with the boring bar and turned the X axis out a bit to make a cut. After that I put the shaft up to the now larger hole in the washer and it slid in. Good enough!
No measurement of the the washers initial ID Vs the shafts OD were made and no calculations were made to make sure the movement of the X axis was enough. It was all done in a non mathematical operation. The only driving thought behind the whole process start to finish was make the washer fit over the shaft.
Now had I did both ID and OD measurements, subtracted one from the other and added a specific amount more for clearance tolerances, touched off with the boring bar then zeroed out my X axis readout, moved out the specific distance based on the earlier subtraction then did the cut followed by a remeasuring to confirm the depth of cut matched the calculated to be cut value, Then yes that was definitely some mathematical thought processes in action.

Personally in terms of calculus I find it largely to be a the overreaching bastardized creation of half wit wannabe mathematicians. I simply have no use for it due to what I find to be overly complicated processes that typically can be solved using far simpler more direct mathematical methods. I see it as complicating things just for the sake of complicating them which I tend to avoid at all costs. Just because it can be used doesn't make it the best or even correct mathematical tool for the job.

I will not sully the good name of my thoughts by calling them calculus when they can be defined by more fitting dignified terms. To me calling my thoughts calculus is as low as calling a black man the 'N' word. Sorry but my thoughts have more dignity than what I consider that word implies or defines to me.

Maybe some peoples thought processes are deserving of such slanderous description but mine are not.

MrAl said:

So philosophical arguments can go on forever unless you set some ground rules because there is no right and wrong unless there are rules to follow or to contradict.

Click to expand...

Yes, it's a philosophical argument but if you fall in the hole because of a rule (force derived from space-time) called gravity you know it's real.

nsaspook said:

I tried, it's fine if you can't see the music and only hear it. There are certain concepts for which mathematics is well suited and there are many where it is not. Using math to describe the taste of that nice steak after its been cooked would be on the not column.

Click to expand...

The sound (acoustical vibrations) of music goes in my ears and and ultimately processed by my auditory cortex portion of my brain not in though my eyes and visual cortex. Therein lies the problem with me not "seeing the music".

Good video though. I always cringe when people link to mathematics videos but that guy did well.

tcmtech said:

Personally in terms of calculus I find it largely to be a the overreaching bastardized creation of half wit wannabe mathematicians. I simply have no use for it due to what I find to be overly complicated processes that typically can be solved using far simpler more direct mathematical methods. I see it as complicating things just for the sake of complicating them which I tend to avoid at all costs. Just because it can be used doesn't make it the best or even correct mathematical tool for the job.

Click to expand...

On this we totally agree, the concept of calculus is not hard. It's the damn mathematicians who have made it a bastardized creation from simple and intuitive rules to impress you with their tremendous cleverness.

http://djm.cc/library/Calculus_Made_Easy_Thompson.pdf

nsaspook said:

Yes, it's a philosophical argument but if you fall in the hole because of a rule (force derived from space-time) called gravity you know it's real.

Click to expand...

And again as he stated until there are definitions made nothing can be said to be solid definable right or wrong.

Until the hole is given physical dimensions (Length, Width, Depth) and a physical location we all can relate to and work with it has no value or meaning.

As your response sugest you are defining the whole to be on the ground plane and larger than the person yet given the ambiguity of the hole being it has not been defined in dimension or locational values I take it the hole is smaller than my fingertip and located on the ceiling which makes it impossible for a person to fall into.

tcmtech said:

The sound (acoustical vibrations) of music goes in my ears and and ultimately processed by my auditory cortex portion of my brain not in though my eyes and visual cortex. Therein lies the problem with me not "seeing the music".

Click to expand...

That probably due to a lack of mind expanding drugs during your youth.

nsaspook said:

On this we totally agree, the concept of calculus is not hard. It's the damn mathematicians who have made it a bastardized creation from simple and intuitive rules to impress you with their tremendous cleverness.

http://djm.cc/library/Calculus_Made_Easy_Thompson.pdf

Click to expand...

Very true. That's has been my greatest stumbling block with mathematics in my life. Very little good practical application work was ever taught to me so I had to teach myself and in that self teaching I found far simpler ways to approach mathematical problems which largely ruled out the need to ever pursue anything above what I needed to accomplish anything.

My high school algebra and calculus teacher was as pompous half wit fool and everyone but him knew it. Most of my college level math class professors were even worse taught by overbearing closed minded fools with terrible people skills who had their heads so far up their ass they had no clue what was real or not..

The only decent math classes I ever had were in my two years at our state technical college where everything they taught was focused entirely on practical application in day to day technical work related applications hence my general enjoyment of applied mathematics.

tcmtech said:

And again as he stated until there are definitions made nothing can be said to be solid definable right or wrong.

Until the hole is given physical dimensions (Length, Width, Depth) and a physical location we all can relate to and work with it has no value or meaning.

Click to expand...

I define the hole as this one. That hole needed a large amount of physical effort by PGE workers to create after the cable guy broke one of the underground utility wires to my house last week.