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Learning Calculus (Again)

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#1 Ira

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Posted 14 February 2011 - 09:43 PM

I took calculus in college but remember nothing about it. Is there a good course/book/video/web site where I can learn it, especially as it applies to science? I am willing to pay up to $250.

/Ira

#2 imjeffp

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Posted 14 February 2011 - 10:28 PM

Would you be willing to pay $254.95?

#3 Joel F.

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Posted 14 February 2011 - 11:05 PM

TRY MITOPENCOURSEWARE.

in the left hand side click on science then MATH.

Click on Math 18.01 Fall 2006 and you should find most of what you need there.

GOOD LUCK!!

#4 Mary B

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Posted 14 February 2011 - 11:27 PM

Try here for free math help I took calc 2 years ago at 48 years old. Made my head hurt :lol:

#5 deSitter

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Posted 15 February 2011 - 12:12 AM

There used to be a series of little yellow books like "Teach Yourself Algebra" - they were small and had practical knowledge but not dumbed down, just get to the point and start calculating. The one on calculus was good, I used it for problems when I was teaching it. I don't know if these are still around. Also the Schaum's Outlines, which are however very condensed.

Hey I found it!

-drl

#6 Zdee

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Posted 15 February 2011 - 09:15 AM

Khan Academy has a lecture for pretty much every topic covered in a three semester Calculus sequence (they are free, of course :grin:).

#7 star drop

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Posted 15 February 2011 - 12:06 PM

Dave, thank you for the link. Lots of good FREE stuff there.

#8 Zdee

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Posted 15 February 2011 - 02:34 PM

Your welcome, Ted. Enjoy! :grin:

#9 Zdee

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Posted 16 February 2011 - 04:39 PM

Ira, here is an entire modern Calculus textbook online.
Each section of each chapter (including exercises) is in pdf format.

Also, If you want to go with a teaching company course, look into this one: Understanding Calculus
It has 36, 30 minute lectures, and it's now on sale for $79.95


#10 Napersky

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Posted 13 March 2013 - 07:30 PM

Ira,

How has your learning experience of Calculus been? I have just started seriously studying it using the Dummies book by Wiley.

Mark

#11 Joel F.

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Posted 13 March 2013 - 10:04 PM

Calculus is very hard to learn alone. Most books are very poor especialy if you want to use it for science.

However, some newer ones ever have student solution manuals to go with them. Try the Perry and Ellis series as their books tend to be good.

#12 mich_al

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Posted 14 March 2013 - 08:01 AM

Calculus is very hard to learn alone. Most books are very poor especialy if you want to use it for science.


Not too sure I ever learned it the normal way! I got through all the classes and even had a minor in math. Never used much of it in my career. Computer Science major but had to work WAY harder at the math classes.

#13 FirstSight

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Posted 14 March 2013 - 10:34 AM

There's a wonderful (and mercifully compact @235 pages) old paperback classic "Calculus Made Easy" by Silvanus Thompson. Although it was originally published way back in 1910, it's easily the most articulately understandable explanation of all the essential basics of what usually sprawls across two full semester classes. Though it's nearly a century old, the writing is fresh and clear enough that it could have been written yesterday; I owned the book for a year before I realized it wasn't something recently written.

I particularly recommend Chapter 14 ("On True Compound Interest and the Law of Organic Growth") for the clearest explanation I've ever come across for why the transcendental number e arises naturally in the course of any sort of compounding growth, which is both quantitiatively rigorous and yet free of the dense, nearly incomprehensible gobbldeygook most mathematicians writing texts insist upon imposing on us (losing countless baffled, bored students in the process).

ISBN #0-312-11410-9 (I have the third editition, printed in 1980).

#14 gavinm

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Posted 14 March 2013 - 02:19 PM

Integrated Physics and Calculus (Rex & Jackson) - actually makes it relevant (and almost interesting..almost)

#15 Ira

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Posted 14 March 2013 - 09:41 PM

Sigh...I never started, like so many things in my life...sigh...

/Ira

#16 rookie

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Posted 14 March 2013 - 10:49 PM

Would you be willing to pay $254.95?


The Teaching Company puts out a lot of great cources on all sorts of topics. The teachers are usually top of their field, highly recognized in their specialty or nationally awarded. It's helpful to me to learn better by having someone explain and discuss with audiovisual aids, than me trying to read a book on my own.

I have several courses related to science and history. The courses also go on sale frequently in the year for at least 60% off the original price. So, if you are interested, do a price check throughout the year.

#17 ColoHank

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Posted 15 March 2013 - 10:16 AM

Calculus is very hard to learn alone. Most books are very poor especialy if you want to use it for science.

However, some newer ones ever have student solution manuals to go with them. Try the Perry and Ellis series as their books tend to be good.



I recall that any page full of formulas and calculations in my old college Calculus textbook would typically be followed by a summarizing sentence that stated something like, "Thus, it is easy to see that..."

Easy for the guy who wrote the book, perhaps, but not for me.

#18 Napersky

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Posted 15 March 2013 - 10:57 AM

There's a wonderful (and mercifully compact @235 pages) old paperback classic "Calculus Made Easy" by Silvanus Thompson. Although it was originally published way back in 1910, it's easily the most articulately understandable explanation of all the essential basics of what usually sprawls across two full semester classes. Though it's nearly a century old, the writing is fresh and clear enough that it could have been written yesterday; I owned the book for a year before I realized it wasn't something recently written.

I particularly recommend Chapter 14 ("On True Compound Interest and the Law of Organic Growth") for the clearest explanation I've ever come across for why the transcendental number e arises naturally in the course of any sort of compounding growth, which is both quantitiatively rigorous and yet free of the dense, nearly incomprehensible gobbldeygook most mathematicians writing texts insist upon imposing on us (losing countless baffled, bored students in the process).

ISBN #0-312-11410-9 (I have the third editition, printed in 1980).


Thanks just what I need to fill the gaps in the Dummies books. Dummies breaks Calculus I into 3 sections: Limits,
Differentiation and Integration. Although I have nearly completed the Limits section I have no handle on it whatsoever in fact I found I need alot of Algebra review.

Mark

#19 CounterWeight

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Posted 26 March 2013 - 01:19 AM

I have many shelvs of math books and probably at least two are applications of the calculus... This is IMO the real crux of it all. Calculus by itself and as originally introduced by Newton and Leibnitz would only require a few pages to fully describe. But you need to apply it to something unless you are after the pure mathematics arena.

Most calculus texts are an overview or review of things you learned in algebra, trig, and geometry with the concepts of calculus applied to them. In the many years since the introduction, uses / applications have been found in possibly every math.

A problem can be approached as an exercise in statistics, or same problem through the calculus lens. In versatility this also could be extended into operator theory, theory of functions. So as N.D. Tyson mentioned in one of his talks it's 3 pages of information with another few hundred of applications.

What i often found and recently in a greatly reduced capacity found in my tutoring is that it is the 'application' of calculus that folks find troublesome. They maybe weren't keen on algebra or trig and here are pages of nothing but.

"Where and what is calculus in this" and why look at it this way?

An extremly good question! Often it's a vehicle to apply to systems where more than one thing is changing and there is some convenience to looking at it that way.

I had a prof that after three boards scribbled in trying to derive something commented "whoops I made a mistake back at the beginning" and started erasing all the boards... class groans...

Then he remarked "you sometimes if you are working this hard you may be using the wrong branch of mathematics"...

Cooly he rewrote the problem with vectors using polar rotation and it took two lines...

The reality is we are doing these things all the time in our minds without realizing it. I'd say you probably use calculus all the time, you just don't call it that. There are entire books on 'ordinary differential equations' or 'calculus of variations' or 'advanced engineering mathematics' or what have you.

So here is IMO the 'thing'. You can apply calculus to nearly anything. The 'building block approach' ordinarily and usually starts by using themes from algebra or statistics or trigonometry and then often geometry - so if you are uncomfortable with any of it/that your are in for some mental pummeling, and the dreaded 'it becomes obvious' or the dreaded 'QED' or at worst entirely skipped manipulations and simplifications will cause you to want to skip it.

So my advice is to do a meaningful and thorough review of statistics, algebra, especially 'trig', and plane and spherical geometry, and what and why something constitutes a 'proof' and what is an 'existence theorem'. Those last difficult to over emphasize.

Though I arrived at my own conclusion that "these calculus books are written to show what calculus can bring to the table" it's on deaf ears if the underpinnings and what is possible with them is not front row center. You'll miss the "Aha!" (at least potentially).

Add to this that the problems discussed are (usually) ones that we know the answers to and that is why the 'building block' approach and often aching recusive refrences to the other maths. That and the endlessly irritating 'pure math' approach that here is "example" and to show it works we'll apply it to this particular problem (the reader left to surmise that the problem represent a class of problems of a type and that in fact is all it is good for).

If you are interested in a specific application of calculus I recommed also to get a book that is specifically about that to see concretely what is 'coin of the realm'.

I also like to recommed Stewarts 'Concepts of Modern Mathematics' as well as Littlewoods 'The Skeleton Key of Mathematics' as companion texts to take along the journey.

Best of luck and have fun :)

#20 WaterMaster

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Posted 27 March 2013 - 11:01 AM

All of my undergraduate calculus was just so much theory and rote memorization. It wasn't until I was working on my doctoral minor in biostatistics that it all began to make sense.

Context helps. :ubetcha:

#21 Napersky

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Posted 30 March 2013 - 08:00 PM

... Calculus by itself and as originally introduced by Newton and Leibnitz would only require a few pages to fully describe...Most calculus texts are an overview or review of things you learned in algebra, trig, and geometry with the concepts of calculus applied to them.... So as N.D. Tyson mentioned in one of his talks it's 3 pages of information with another few hundred of applications.

...it is the 'application' of calculus that folks find troublesome. They maybe weren't keen on algebra or trig and here are pages of nothing but.
..




Yes, the table of contents from Calculus books I have certainly show that it is a system that is applied to algebra, trig, Geometry, analytical geometry etc, all maths.

I put aside the Dummies text and bought the text that Richard Feynman learned Calculus from at the age of 10. It is titled, "Mathematics for Self Study" CALCULUS for the Practical Man. Part of the practical man math series.

Am I smarter than a 10 year old Genius? Can I grasp it. Maybe, maybe not.

:)

I believe the real test of Genius IQ is not some population Gaussian but rather can one master Math.

#22 Napersky

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Posted 30 March 2013 - 08:12 PM

I was recently mocked in an email from another site where one of the people wrote,

"Mark, aside from reading this book, (NOT EVEN WRONG) how are you qualified to judge physics and math at that level? In September 2009, you posted that you were teaching yourself math and physics, and looking at a web-site who's highest level was elementary calculus, basic pre-university stuff, or at best, first year. Have you progressed in 3.5 years to the PhD level?"

No Herr Professor I have not arrived at the Phd level neither have I arrived at learning elementry Calculus. I guess that some Physicists are just unable to defend and articulate their String Theory Multiverse theories and defend them without resulting to ad-hominem attacks of your sort.

#23 Napersky

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Posted 30 March 2013 - 10:56 PM

You Tube, Feynman studied Calculus at 13.

http://www.youtube.c...h?v=GoHbFVU2LBk

http://www.feynmanphysicslectures.com/

#24 Napersky

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Posted 30 March 2013 - 11:27 PM

Feynman's Throat Singing Conference in Mongolia Tuva.
Last 8 minutes:

http://www.youtube.c...6C801BDAE668CB2

Hear throat singing 1st minute

http://www.youtube.c...6C801BDAE668CB2

Perhaps the physics consultant of the Big Bang Theory decided to have Sheldon Cooper learn throat singing because of this story.

#25 Niels2011

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Posted 23 April 2013 - 03:07 PM

I'm enloying "The Theoretical Minimum: what you need to know to start doing physics" by Leonard Susskind and George Hrabovsky, 2013. This might fit the bill in a different way: it's not a calculus book, but it covers calculus amongst other maths and physics. I've just covered limits and part of the chapter on differentiation. Integration will be next. It's pretty good, challenging, but well explained, with excercises and worked answers. Designed for people who were interested in high school maths and physics, and then followed another career, but now want to go back to that interest again and go beyond popular science - so me and some of us here! It's just out so I thought it was worth highlighting. Also there are some excellent video lectures by Leonard Susskind on YouTube Stanford covering this material I think, so that might work well together. I've only checked out a couple of his cosmology lectures so far and liked them, which is why I noticed this book.






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