Brushing up on Calculus

[JenniferG]

Actually going to relearn it because I haven't used it in 30 years.  I got A's in Calc I , II and III but really forgot it all sicne I didn't use it in computer science.

Should I go with old school calculus book (like I learned from way back then).. or the Early Transcendentals James Stewart calculus book?    (I plan on doing mostly analog electronics related to music synthesizers.)

Also does anyone know which editions of the James Steward calculus book do not have CD's.. personally it really irritates me having a cd envelope glued to the inside of the book leaving rings on the adjacent pages.  I wont' use a CD and I don't care about which version because I know they all teach the same things.  Does the 3rd edition have a CD?  It's 1994.  I can get that one for like $6.

Another book I see recommended is the Larson Calculus book.  Don't know which to go with it, but leaning towardes James Steward.

[MikeK]

"Calculus Made Easy".  Originally written by Silvanus Thompson, but modernized by the inimitable Martin Gardner.

[JenniferG]

"Calculus Made Easy".  Originally written by Silvanus Thompson, but modernized by the inimitable Martin Gardner.

I glanced at this and it does seem like a great book as well. I will get it in addition to the Stewart (or Larson) text.

EDIT: I'll actually start with this Calculus Made Easy book , go through that in its entirety first before going through the textbooks.

[MikeK]

It appears there are newer editions of CME.  I've been working through the Gardner (1998) edition.  Got it on abebooks.com.  I like it, because it has plenty of exercises.  And I trust Gardner.  I haven't seen the 2020 or 2022 editions.

[JenniferG]

It appears there are newer editions of CME.  I've been working through the Gardner (1998) edition.  Got it on abebooks.com.  I like it, because it has plenty of exercises.  And I trust Gardner.  I haven't seen the 2020 or 2022 editions.

I bought the same one you're reading just now off Amazon.  Excited about it.  I like that it reads more like a novel and is wordy.  I read a lot of people buy these as gifts before someone starts a calculus class; so it'd be perfect for me.. should make going through the Calculus book easier.   Hoping to go through Calc I & II in a month or so at home.. maybe two months.  I don't know if Calc III is used much in electronics or not.. I remember doing a lot of 3D integration in the book and line integrals.

https://www.amazon.com/Calculus-Made-Easy-Silvanus-Thompson/dp/0312185480

[TimFox]

I highly recommend anything by the late Martin Gardner, including his "Annotated Alice" books.

[JenniferG]

I highly recommend anything by the late Martin Gardner, including his "Annotated Alice" books.

Ya know, believe it or not, I've never even read Alice in Wonderland, so that'd be a good way to read it

[ledtester]

For brushing up on your integration skills I'd suggest looking through the videos by blackpenredpen and dr peyam:

https://www.youtube.com/@blackpenredpen

https://www.youtube.com/@drpeyam

[TimFox]

I highly recommend anything by the late Martin Gardner, including his "Annotated Alice" books.

Ya know, believe it or not, I've never even read Alice in Wonderland, so that'd be a good way to read it

It's an excellent way to read Alice, since the book contains the full text along with explaining the jokes.
I love the French translation of "Jabberwocky" that he quotes.  "Il brilgue: les tôves lubricilleux..."

[rstofer]

As to Stewart, I have the 8th Edition in paperback and the 8th Edition (Metric) in hardback.  Neither have CD jackets.  It is the textbook at the local university.  No, I didn't take the course, I bought it as reference for the work my grandson was doing.

As to Calculus Made Easy, I have the original version without Gardner's annotations and another version with the edits.  I like the idea of infinitesimals used by the author, it is very intuitive when thought of as just algebra.

Other resources:

CalcWorkshop.com (pay site) is excellent.  Worth every dime!
Khanacademy.org is also excellent.
Symbolab.com for getting solutions
Desmos.com for plotting functions

I contribute to the last 3 sites and I paid for 2 or 3 years of Calcworkshop while my grandson was majoring in Applied Mathematics.  Worth every dime!

When I compared these out-of-pocket expenses to the cost of tuition, the price was insignificant.  Even an entire year of CalcWorkshop is less than most textbooks.  It was a simple decision to subscribe.

Have fun!

[rstofer]

Also, do a search for "3blue1brown calculus' and scroll down to the list of videos.  There's an array of topics.  Grant Sanderson (3blue1brown) used to work with Saul Khan (Khan Academy).  The animations are excellent!

https://youtu.be/WUvTyaaNkzM    <= a good place to start

[BillyO]

Has calculus changed in the last 40 years?  I still use what I learned in university back then and it still seems to work.

[JenniferG]

Has calculus changed in the last 40 years?  I still use what I learned in university back then and it still seems to work.

Right, so that's why I think I am going with the 1991 edition of James Stewart Calculus for $11  in very good condition used   I don't have my original Swokowski Calculus book anymore.

[CatalinaWOW]

The calculus is very useful basis for things widely used in electronics but has little direct application in its own right.  So if you are aiming for differential equations, Fourier and Laplace and others carry on.  Otherwise you might be better served by boning up on linear algebra, boolean logic and other fields.

[BillyO]

Right, so that's why I think I am going with the 1991 edition of James Stewart Calculus for $11  in very good condition used   I don't have my original Swokowski Calculus book anymore.

Smart move.  I don't think the sort of calculus we use in electronics has actually changed a lot since the mid-late 1800's when Cauchy, Maxwell and Riemann worked in methods to deal with complex numbers.  I did a 2nd degree in mathematics (my first was in physics) and touched on some pretty weird stuff, but that does not seem to have leaked very far from the ivory tower.

[TimFox]

The calculus is very useful basis for things widely used in electronics but has little direct application in its own right.  So if you are aiming for differential equations, Fourier and Laplace and others carry on.  Otherwise you might be better served by boning up on linear algebra, boolean logic and other fields.

I definitely second his recommendation for linear algebra, which is incredibly important.

[JenniferG]

The calculus is very useful basis for things widely used in electronics but has little direct application in its own right.  So if you are aiming for differential equations, Fourier and Laplace and others carry on.  Otherwise you might be better served by boning up on linear algebra, boolean logic and other fields.

I'm good with boolean logic.  I did ace calc i, ii, ii, linear algebra and differential equations in college.  I do remember the laplace transform and thought it was neat.  But I forget how to do it all lol.. forget all the notation as well.   After calc I want to relearn diffy q and linear algebra.   Should I skip multivariable calculus or is that used a lot as well in electronics?  Like Calc ii is the prerequisite for Diffy Q if I recall. I remember taking Diffy Q and Calc III the same semeseter.

[rstofer]

I doubt that there has been much of a change since the time of Newton.  One thing that has changed is using computers to solve the problems.  Riemann Sums is a nice way to solve integration problems and, given a couple of hundred thousand steps, is quite accurate.  Maybe it takes a couple of seconds to do the calculation?

The Calculus probably hasn't changed but I'll bet the presentation has.  Calculus described for math majors is different than Calculus described for engineering majors.  University of Florida has this dual track approach.

Lots of color graphics will be found in modern textbooks.  Not so much in older versions.  Nevertheless, I buy a lot of used books and perhaps they don't have color graphics but at least the price is right.

Stewart 8th Edition has color graphics, CME has none.  I think color graphics brings a lot to the dance.  Sure, I got along without them 50+ years ago but I would rather have them than not.

Having coded Riemann Sums in Fortran, all I have to do is replace the function and I get the area under the curve in less than 2 seconds.  Of course, that gives a numerical solution, sometimes we want an analytic result.

[rstofer]

All of AI is based on linear algebra and everybody needs to get a taste of that.  Even the simple Digits Recognition problem is working in 784 dimensional space.  A wee bit hard to visualize...  That problem and its Neural Network solution is the "Hello World of AI".

In grad school there was a required course in Linear Algebra and we spent most of the time talking about solving simultaneous equations.  If we only knew what was coming at us...

Oh, and you absolutely MUST have a command of statistics (which leaves me hurting) to get anywhere with data analysis and machine learning.  I hated statistics!

[westfw]

Has calculus changed in the last 40 years?

Well, I might wish for either a more theoretical (mathematics) approach, or a more practical (to EE) approach, than what I went through in college.  Seems that that involved a lot of guesswork, rotememorization, and practice, on how to manipulate artificially constructed equations into forms that you could differentiate and integrate and so on.  Nowadays, you can get software that will do the mechanics for you...

[Terry Bites]

There are some good refresher courses on https://brilliant.org/calculus/
You gotta love an animation!

[xrunner]

There are some good refresher courses on https://brilliant.org/calculus/
You gotta love an animation!

As somebody asked - calculus hasn't "changed" ... not sure how it could. But I'm sure modem ways of teaching and animation can be very helpful and explanatory - rather than looking at "dry" sure why not? 

[rstofer]

I have always thought that 'partial fraction expansion' was the most tedious part of Inverse Laplace Transforms and math in general.  The good news is that Khan Academy has at least 4 videos on the topic.  When I took the class, the slide rule was 'state of the art'.

It takes Octave less than a second to expand while I wonder if I would ever get the right answer.

Code: [Select]

Ȁ>> syms x
>> partfrac(x^2/(x^3 - 3*x + 2))
ans = (sym)

      4           5           1
  --------- + --------- + ----------
  9*(x + 2)   9*(x - 1)   3*(x - 1)^2
                         

>>

Octave is free (GNU Software) and is reasonably compatible with MATLAB.  I highly recommend becoming friends with either.

[TimFox]

Mathematics can change as new definitions, axioms, and theorems are invented or discovered.
The Fundamental Theorem of Calculus (as proven by Newton and Leibniz in the 17th century) is the beginning of what we now call calculus, but there are lots of developments since then, such as Cauchy's Mean Value Theorem in 1823.
(Yes, I know that there was earlier work on calculus before Newton, upon which Newton and Leibniz based their work.  Such is progress and change in mathematics and science.)

[MrAl]

Hello there,

There is a free Anton pdf (or large set of images) floating around on the web you can download for free.  It's a full book used in colleges, or at least some versions are.  I happen to use one myself in college long time ago but then we switched to a Swokowski edition but i dont remember the edition.
Swokowski was the best calculus textbook i have ever seen.  The illustrations and explanations were really vivid.
Anton is good too though being a full complete book for free download cant see how you can go wrong there.  It may not be available in pdf format but in a set of file downloads that are images.  Page by page images of the entire book.
The edition also has a lot to do with the quality and it's hard to tell which the best ones are, but most of them will give you a pretty decent education in this subject area.

As to other things related, a lot of modern theory is written in a form using State Variable Differential Equations which you can get started with by studying regular ODE's.  There is a lot of theory and a lot of applications in electronics using ODE's and SVDE's.  Very worthwhile.

Also for circuits i would say Laplace Transforms, and for frequency things like synthesis i would say Fourier Series and Fourier Transforms.  If you intend to go digital with that Z Transforms also

The thing about calculus is that you can get down into the theory behind a lot of stuff with that, and if you really want to understand the way things work get at least a little into partial differential equations.

These are all very interesting topics too.

Of course a textbook on calculus based engineering circuit analysis cant hurt and get you very familiar with circuit analysis which of course is a prerequisite for design.

Now as to checking your work, you will find that a lot of books have practice questions but not all of them have the answers in the book itself, sometimes you have to get a second answer book to go with it.  What else helps though is automatic software.  The stuff of today can beat down a lot of calculus even some differential equations.  You can use that software to check your answers to the practice questions.

Oh and you can also ask questions on forums like this one but im not sure if this one has a section for math.