First year college CALCULUS and PHYSICS, I can teach. Send PM

[RJSV]

   Hey there folks:
   Students and others involved with basic CALCULUS and PHYSICS are welcome to ask questions.   I did quite well in first 2 years in college, including requested tutor one on one, or sometimes a small group of students wanted help in a casual study time meeting in library or school dorms.

   Topics include some basis / justification for Newton's math development and the kinetic physics he explored.  Send an on-topic question, or even sometimes a 'stupid' or seemingly wide question;  I'll try to respond!

   I've also done plenty of mechanical drawings, like old-school draftsmen, having good 3-D perception...(maybe not perfect).

[liaifat85]

Hope you will find a student here. You can also post your resume in freelancing websites.

[armandine2]

the second problem in Hagen Radio Frequency Electronics - stumped me 

[RJSV]

   I'm only interested in the subject matter, so any EEVBLOG member can ask questions; not interested in paid tutoring.

[RJSV]

   Armendine2:
   Thanks for question, but that's more advanced engineering, with supporting math.
Interesting question though: They give you the answer, then ask for how that is so.
   Maybe senior college level complex.

   My emphasis here is mainly about rates, derivatives, and integrals, with relation to gravity fields and static electric field basics.  Something like Maxwell's equations I can only follow along.
So, I'd call it basic 'Newtonian' math, essentially the first year or so, for any student starting college school in 2022, or sooner.

   Derivatives, and integrals, and motivation for inventing 'The Calculus', often termed as 'Analytic Geometry'.
   I'm considering just make a post just covering those aspects, and let folks read and comment if they have questions.  For example, the static field equations dealing with forces are identical for GRAVITY or ELECTRICAL.

[RJSV]

(having some difficulties, uploading pictures).

   Here is a sample, narrative on differentiation as a calculus function.  Suppose your function is X to power of 14.  Idea is to apply the differentiation on that equation.
   Just for sake of brevity let's just mention a rote action or series of memorized actions:
First, take the exponent, and bring it down, to be a multiplier now.  See diagram showing that, as rote action for now.
   Then, with the original exponent, subtract one, and put it back (as exponent of equation).
Result is your answer, that is, 14X exp13, as shown at bottom of diagram.

[RJSV]

   Now then, you maybe have only rote or mechanical feel for this so far.  But be aware (I'd say) the functional pairing where a process of INTEGRATION is performed, by moving backwards up the diagram...plus another item.
   But basically the two functions are opposites paired by the fact you could go 'back and forth' between the two,...each one simply reversed the other, with the caveat that you will need to bring in an unknown CONSTANT, when integrating.  That way, your X exp14 function will literally become (X exp 14) +CONSTANT which might be zero.

   There's some more detail, but it can be pointed out that INTEGRATION has a sort of higher amount of info in the result, and conversely doing a differentiation has a quality of losing or destroying info.  Kind of like a status level, for each of the two converse functions.

   More, more, and more to follow, thanks

[RJSV]

(Sorry if you have to download the pictures ?
...seems like the thumbnail pictures would gum up someone's system memory ?).

   So...that last diagram, and intro is an important aspect of how the so-called 'Integration Solution Tables' have been built up, by many folks, as some integration functions are not intuitive (in structure).
   But you can observe, and when asked, "What is the integral of 14 X exp13 ?" you can say:
  "Ahha, I've seen that..." and plus you (should) know to also add a constant term.
The constant has to be solved, usually by some other route, try zero and see if your numbers work, in that situation.  Like, perhaps you know that the answer, when X is 40 is 570, but your trial run is giving 550;  then you know you need a constant of '20' to fully define your answer.

   Congratulations, you've just solved one of many Integration problems.  Other mathematicians have applied this 'backwards process' to build up a so-called Table of Integrals.  I think that might be in Wikipedia.
   To solve your particular integration problem you would scan the tables, for a match, or at least similar solution.  And, of course, you will need that nasty constant as well.  At least the table saves some of the work.

   A quick explanation of the constant, is that Differentiating a constant will give you zero as answer.  Now since Differentiation is a function involved with 'rate of change' of something, you can accept that a constant, like '20', doesn't change over time or other variables, so the rate is zero.
   But looking at that the other way, something that has a rate of change, like '20 degrees per fortnight' is going to have a formula like:
   Degrees = 20 X T

   You can differentiate that, getting '20', the rate.   But suppose it's
   Degrees = (20 X T ) + 81
That also will give same answer, rate is 20.  But notice that you've lost a portion of your info, as the 'rate' of any constant will just drop out as a zero.

[RJSV]

   So now continuing the dialog, on Integrals and on Differentiation, most of the real detailed solutions were worked out long ago; and many engineers never have to deal with 'solving' some complex Integral in their day to day work. 
   It just helps to illustrate the hierarchy relation.
You might encounter a very complex function, such as [e to exp jwt] or [e to power exp sin X jwt] etc.  No way most folks can (explicitly) solve those signals processing related Integrals at least not directly and on paper.  But this whole explanation serves as an intro to the new and somewhat strange concepts such as infinitesemals, and limits.
   In that intro, important geometry comes into play (that's Newton's Analytic Geometry).  Put in simple terms, the area under a curve helps define Integrals.  An Integral (in geometry sense) is performed by the addition of all the little pieces, which sounds like common sense.
But then, you have to adjust your thinking, as the process involves shrinking the width of those pieces, while simultaneously getting more and more individual additions, along the integral's boundaries (start and stop points along the horizontal axis).
   Differentiation, or rate of change of some function is fairly intuitive.  Newton worked with concepts of LIMITS, that is, for example, when a complicated curve has a slope at some point that isn't precisely apparent, performing the differentiation can give you the precise answer, using the limit concepts.  This is without going directly to the curve and measuring but rather by using or transforming the curve's equation, to get to the function defining slope (rate of change relative to horizontal axis, like time).
   Pretty powerful tools, for those times.

[Rick Law]

   Hey there folks:
   Students and others involved with basic CALCULUS and PHYSICS are welcome to ask questions.   I did quite well in first 2 years in college, including requested tutor one on one, or sometimes a small group of students wanted help in a casual study time meeting in library or school dorms.

   Topics include some basis / justification for Newton's math development and the kinetic physics he explored.  Send an on-topic question, or even sometimes a 'stupid' or seemingly wide question;  I'll try to respond!

   I've also done plenty of mechanical drawings, like old-school draftsmen, having good 3-D perception...(maybe not perfect).

How recent did you finish quite well?  I ask because things are changing rather fast these days.

If your goal is to have an income as tutor, SAT used to be the big money maker a few years ago and may still be.  Often, you have High School kids looking for tutor a few month before SAT hoping to get a better score for college application or hope for a merit scholarship.  That was a rather big market and may still be one.  These days, some top universities are eliminating SAT as primary admission so they can get a more diverse student body.  Even UC-Berkeley  eliminated SAT/ACT as of May 2020.  Harvard eliminated SAT/ACT for class of 2027 (4 years means 2023 admission).  So, I am not sure SAT is still a good market.  It is worth a moment of consideration if income is your goal.

[RJSV]

   Thanks, Rick:
   Turned 70 this year, so...I'm focused on ability to walk, any distance, otherwise I'd be making good freelance dog walking and other animal care services locally (Oakland, Ca).

   In early 1970's I was getting requests to tutor, from classmates, first couple of years in
college .  Physics test scores, like 100, or nearly so; meanwhile math tests near perfect, so there's that.
   One person commented: "...Rick, you really know your shit...". Regarding the calculus math help I was giving.
   Newton, himself, I hear wasn't always up to modern comprehension standard, either, lol.
I appreciate your comments, as I didn't clarify (otherwise I'd post in 'jobs'.)
   But please comment on any errors you might see, as I really should dig up a couple books, to boost my memory.

[Rick Law]

Ah...  We are neck and neck in age...  So we saw similar world in our walks of life.

Now back to the main thing:  From your reply, it sounds like you are spreading the good by sharing your gift of understanding with others.  I admire that.

I was a Physics major, left with a masters degree and moved into the business world to make a living.  For about 6 years, I volunteered at a parent operated weekend school with (at a high) of just under 400 students.  Having the kid attend more schools during weekends on top of "regular school" is typical "tiger mom" behavior, so I've seen a lot of hard working kids and hard pushing parents.  That said, quite frankly, since you are good at Physics and Calculus (even if good just for the first two college years), you possess the analytical skills, math skills, and wisdom as much or more than I could muster.

One thing I do want to emphasize: the will to understand.  When I was in graduate school, I was a TA.  So I had my share of teaching Physics and the accompanying math.   Many who fails to learn failed because they were just trying to "get-by" instead of really understand.  In my opinion, the three legs are: (1) Basic math skills, (2) Analytical skills, (3) The ability to think abstract and apply the abstract to the physical world.  These skills are useful in Engineering, Business world, and even in personal matters.  For the failed, in their haze to just "get pass this course", they want to just do the mechanical "find the right formula and plug the numbers in" without really trying to understand the reasoning behind.  Thereby, besides often failed to figure out "the right formula", they also missed the opportunity to learn skills that could help them with almost every aspect of their life.  Well, actually, I think you probably already know what I just said in the above paragraph...

This is one that you likely don't know.  Prior to my retirement, my colleagues were often puzzled that my degree was in Physics instead of some business degree.  They ask, and I told them: "The physics I learn, I hardly ever use.  The problem solving skills I build in my study of Physics, I use every day."

[RJSV]

   Respectfully, no; You are wrong in that last concept.  I am a Polymath, which we are required to disclose, (although the meetings are in undisclosed location).  Seeing parallels everywhere, regarding re-using one topic or avenue, into another.  Even just the pure feeling
of discovery translates fast, across boundaries, while explicit concepts stay in the box.

   Since there's no boss / taskmaster over me, I actually get a little thrill, when some new (mistake) I've made is pointed out.
A person with Masters degree in physics could very easily end up in something like, say, Criminal Forensics !
======================================

   Anyway, a couple thoughts, when you mentioned generational things in common, I recalled how disappointed I was / am that Jimi Hendrix died.  That's a creative genius right there.  He was consistently the highest grossing performer in those times!  (I'm into biographies of creative people).

[Rick Law]

...
A person with Masters degree in physics could very easily end up in something like, say, Criminal Forensics !
...

I believe people with the 3 skills ( Basic math skills, Analytical skills,  The ability to think abstract and apply to physical world) can do anything because those skills are not specific to a discipline.  Of course to succeed, one needs other attributes such as continuous learning, conscientiousness, stamina, etc. etc. etc.

Criminal Forensics is interesting but too close to evil.  I often look at air crash investigation shows and wish I had a part in it.  That is a bigger problem that presents more challenges and likely with more resources.

Anyhow, for people at our age, we are basically in "God's waiting room".  The big guy may call us in any time but hopefully not so soon.  If it pleases you to do things without a boss or master, by all means.  Besides, what you choose to do, if successful, would make the world just a little bit better -- however little that bit is, better is better and it is better to have if just one more person educated just a little more by your effort.

[MrAl]

the second problem in Hagen Radio Frequency Electronics - stumped me 

Hi,

This problem from reply #2 can be solved by following the description very carefully, which means calculating the power reaching the load RL (PLoad) with a lossless network inserted as indicated, then calculating the maximum power the generator could ever produce in the load (PMax), then calculating the ratio PLoad/PMax which is the fraction they are asking for.

The maximum power the generator could ever produce in the load is obtained from the Maximum Power Transfer Theorem.

[RJSV]

   Here today, I've got an example of how it's useful to understand (fundamentals) of Differentiation in early physics.
   Mechanical 'laws' of motion say that when you hold a bowling ball in one hand, and a feather in the other hand, evenly, then both will drop to ground the same way, when released at the same time.
   Now I worked this out in my home, no books and no WIKI...

   A Quiz question:
   Please describe the forces on the two objects, as you hold them.  The downward force is considered 'static' just simply because there isn't any movement, relative to, say, an Earth frame of coordinates.
  I'm better off using a baseball, and with the bowling ball (measuring) say 20 times the weight, of the baseball in your other hand.  Assume this question wants a narrative answer, rather than strictly numbers.

   The classic equation, likely co-invented by others besides Newton, classic equation is:
                   F = M A

   Now, as I will be teaching soon, that equation reflects result of doing TWO separate differentiations.  It's a hierarchy where the first differentiation is performed on the position (equation or function of time elapsed ), while the second differentiation gets you to that acceleration equation, above.
  O.K. then, so let's go ahead and drop both test objects, at same time, watching them drop and hit ground, all the whole staying abreast of each other.  Must do this in a near-vacume of course,
but say you've got the rocketry...
   It's easy to point out that the 'heavy' bowling ball will likely need more FORCE from gravity, vs. the 20X lighter baseball.  But since the movement or falling behaviours are same you can conclude:  The bowling ball needed 20X the force, for this equivalent falling characteristics.
Somehow the uniform gravity field is pulling on the two different objects precisely proportional, to each of the weights.
   I haven't discussed that force yet, but it turns out to be proportional to any two bodies.  For the bowling ball that would be:
   Weight of Earth X weight of bowling ball
And, of course, same for a second object dropped; that's Weight of Earth X weight of second object...the baseball.
   (Don't get mixed up, as each falling object is separate from the other, as the gravity force operates on each (ball) completely separately).

   So, assuming that your static force equation has that multiplication of the two interacting weights (one object, with the Earth, in two parallel trials), you can start to prove or at least verify that formula, which turns out to involve each of the two weights, with some constant in there.  It's inescapable, as you will observe that in each separate trial, the different forces work to create identical outcomes, in movement measured relative to elapsed time.  The lighter baseball, (as second object), gets a smaller force, meanwhile the heavy bowling ball (again, as second object relative to Earth's mass), will get a larger force...just enough so that the outcome, ACCELERATIONs, and subsequent falling positions is the same.
   Only conclusion is that ANY weight object will fall just the same as another.
You just have to get air friction out of the test, like on the moon.
   Q.E.D.

thanks for reading!

[RJSV]

   Had to use WIKI for a second, the term for MASS in the English system is 'SLUG' (I thought so), while 'pounds' is literally a force equivalent.
In Metric system it's done in a more sensible 'kilograms and Newtons' setup, a somewhat trivial distinction that perhaps causes more arguments, (and physicist's bar-fights) than it should.
   Stepping on the scales, I cause a force of 192 pounds, or thus about 6 slugs of mass. Right then.
In Europe, in Metric system of weights and measures, it's expressed in MASS, first (kilograms) and, rarely, in terms of force on scale springs, in NEWTONS.  That's actually more sensible but in the end a trivial distinction, unless you are looking for a...' Physics contest'.

   But I'm eager to get back to describing the whole hierarchy thing, concerning derivatives and integrals related to basic mechanics of movement.
   Static electric fields also behave in very similar ways, concerning electric charge amounts between objects, rather than gravity originated forces.
   Soon, perhaps tomorrow, coming !

[MrAl]

Hi,

'pound' can be a weight or a force, but when it is a force it is often clarified using the name "pound-force".  The abbreviation is usually "lbf" for pound force and just "lb" for pound.

I suppose that once you introduce in the context the force as a pound-force, you might revert to the simpler name of just 'pounds' once it has been established that you are talking about a force, or just use the abbreviation "lbf".  I guess it is up to the author.

[jpanhalt]

"lbl" is the symbol for poundal.  Thus, pound mass and poundal force are as "logical" as kilogram mass and Newton force.  I never thought of "lbl" as just a way to distinguish the two.

[Haenk]

I really think your offer to help is nice.
*However* at least we, back then, had formed smaller groups of 4-5 people, for learning, repeating (in my case, early on, constructing) - so an answer was usually availabe within minutes or even immediatly. There was always someone who could teach the others, if the need should be. So the whole group could proceed very fast, and I don't think there ever was a need for remote teaching.

[TimFox]

In high-school physics (US in 1965), one important concept new to the students was the difference between mass and weight.
The course employed both metric and customary units.
To keep the customary units consistent, we used mass in slugs and weight/force in pounds (avoirdupois).
Of course, in metric, mass is in kg and force/weight is in N.
We were warned that some engineering used mass in lb av and force/weight in poundals.
Similarly, we were warned that some metric engineering used kgf for force/weight (especially pressure in kgf/cm²).
Since then, my mnemonic to convert between N and lb is to remember that 1 kg at mean sea level weighs 9.8 N = 2.2 lb.

[IanB]

To keep the customary units consistent, we used mass in slugs and weight/force in pounds (avoirdupois).
We were warned that some engineering used mass in lb av and force/weight in poundals.

I think that slugs and poundals were theoretically used, sometimes, maybe in the past.
In my field (chemical engineering), you would find in US Customary Units that mass is measured in lb_m and force is measured in lb_f. The relationship between them is expressed with the constant g_c, which appears in many formulas.

[RJSV]

   Ha!   See how this works ?  Putting a 'diversion' subject, after the more real Calculus musings I had posted, I inadvertantly caused a distraction, so no real substantial criticism got into (yesterday's) activity!  Going to remember this one, just in case.

   I'll supply a diagram, but the idea is to illustrate 3 levels, that being Position, Speed (or velocity), and, up top, Acceleration.  In gravity field the position (freely falling object) is proportional to the square of time elapsed.
   Taking derivative, of position you end up with Speed or Velocity, which is proportional to elapsed time, looking like F (t).  Finally acceleration is just a constant, that being a derivative (of the speed equation).  That is simply noted, that a constant has no rate of change with respect to time.

   Please don't get too confused, with notation, because the variable 'X' is used in various contexts, either as an unknown or as a horizontal variable as in ' X axis, Y axis' etc.

Hank; I had an advantageous daily schedule in college, because of having the Calculus math class in 'Period 5',...just following lunchtime at period 5, so that several of us students could do informal study group, by showing up to the room a half hour or so early before teacher came in.  So, we even used the blackboard in there as we debated, argued and taught each other, (sometimes making friends!).

[RJSV]

   Part of the explanation for how acceleration affects movement speed (free fall) is that the speed increase is compounded due to acceleration being constantly acting.
So you've got a speed that got built up until now, and also have acceleration due to the downward force exertion persisting.  So it makes sense, that velocity or 'speed' keeps building and it's believable that result is proportional to the square of time.
   In this context, the horizontal axis for function is 'time', and vertical graph axis is F(t).

   Much similar to various bouts of money inflation, and how it's a compounded effect.

[RJSV]

   One of our roommates is Mechanical Engineer; I cruised his bookshelf and grabbed an older physics book to browse, as I usually don't see the kind of presentation that seems 'logical'...(oh well).
WOW, that book weighs a TON and the many pages are super thin, packed with text and very few graphics / diagrams.  Using net search engines also not so helpful, wanting to get a more general formula.  Distractions as most descriptions seem to want to jump around, inserting for example, some quiz questions on things like:
   What is the power consumption, relative to time, of a freely falling body, vs. TIME ?
Stupid smartness, lacking any real 'narrative' descriptions...
   What I wish to do, short term, is get all the full terms into the Position / Speed / Acceleration equations (for more fully description).