calculus made easy!

November 22, 2013

The Annotated Alice‘ of Lewis Carrol and Martin Gardner – was (finally) returned a couple of weeks back by my dear Rama and I was fondly leafing through it, before sentimentally returning it to the library shelves. It is currently rubbing shoulders with the books of the likes of  Isaac Asimov, JBS Haldane, Erwin Schrödinger, Enrico Fermi, Paul Dirac, Albert Einstein, Robert Oppenheimer et al and should be feeling happy now; what a work of deep scholarship!

Rest in peace, Martin. You lived to a ripe old age of 96 and also did a great job of living, all the while!

Having thoroughly enjoyed (actually a lame word like ‘enjoyment’ does begin to describe the pure exhilaration one feels studying a Martin Gardner or a Douglas Hofstadter or a Richard Feynman) ‘The Annotated Alice’ among many other works of Martin, I am reminded of that 1910  gem ‘Calculus Made Easy‘ of Silvanus Thompson which was later updated and edited by Martin in 1998. ( I just realized that this classic, a real classic at that, has completed hundred years of its existence!)

Now, what is oh so great about the book?

One may feel, after all, the phantoms of differential and integral calculus  don’t trouble me anymore – so what’s the point? Besides, I got a good grade in Math 101 (also in Math 505) – I am in a cushy job with an MNC as an ‘engineer extraordinaire’ spending my time (and earning my megabucks) in daylong meetings, boring conference calls & excruciating powerpoint presentations and…  –   and so, why the hell  do I even need to go through that drivel again…

I would say that  you have to read this because as the book says (and delivers on the promise,  faithfully):

“Calculus Made Easy: Being a very-simplest introduction to those beautiful methods of reckoning which are generally called by the terrifying names of the Differential Calculus and Integral Calculus“

I would say that the book is indeed beautiful – it restores your faith in the pursuit of knowledge.

That Science and Math are not pointless.

That they are creative.

That they are actually fine arts.

That they also happen to have real life applications – gazillions of them!

Now, I ‘studied’ in one of the well-known schools/colleges (which ought to know better, siddhir bhavati karmaja (chapter #4 of the bhagavat gita and all that), but I really wonder as to how this book was not used at all in our undergraduate years! Not even a passing mention of the book was made!! (But I should remember with gratitude  that the physics department of my school indeed used the delightful Feynman Lectures on Physics – so it was not all gloom)

I really feel that Mathematics HAS to be approached via ecstatic books such as these.

I chanced upon the Thompson book on calculus when I was trying to desperately understand & solve some practical problems of heat transfer in the wasted days of my entrepreneurship – and I was thoroughly bowled over by this incredible book. Really.

There were also other books (by Piskunov et al) that I really began to appreciate subsequently – but all this was some 10 years after I graduated(!) from my alma mater.

Believe me, this book would make mighty sense to a reasonable 12 year old or even younger ones – if the mind is prepared. Hence, given half-a-chance, I would plan to sneak this in to the erdkinder’s minds. Wish me  good luck.

Here’s a scanned picture of a page of the book!

This is the title page of the St Martin Press edition (1998).

The original Macmillan version of the book without Martin’s contribution is available in the public domain. While it is not the same as the later  St Martin’s version – it is STILL a great work.

Enjoy! Math is actually fun! Calculus definitely IS!!

Children are like sponges. Their concept of beauty is still unspoilt. Their cognitive capabilities are still good, in spite of TV, pointlessly obscene birthday bashes and Helicopter parents. They normally & instinctively would gravitate towards (and absorb/internalize) fine things in life, given a set of meaningful choices. Faith? Hope?? Let us see…

JournalEntry# 4th June, 2010.

18 Responses to “calculus made easy!”

  1. Maru Says:

    Thanks for this post sir. I chanced upon a PDF version of Calculus Made easy. Hope it would make my winter nites a sleepless one. :D

  2. Packirisamy N Says:

    Thanks for the information.

  3. Ramanan Jagannathan Says:


    Thanks for introducing this book. As Mr Maru has mentioned the original is available as a pdf. i got it at

    Please continue to introduce such books to laymen like us.

    Thanks again

    • ramasami Says:

      ரமணன், மரு (மாரு? மாறு??)

      நீங்கள் சுட்டியுள்ள இந்தப் பிரதியும் அழகானதுதான் – ஆனால் அதில் என்னருமை மார்டின் கார்ட்னர் அவர்களின் கைவண்ணம் இல்லை.

      ஆகவே, ஸெய்ன்ட் மார்ட்டின் பதிப்பகப் புத்தகத்தை நான் வெகுவாகப் பரிந்துரைக்கிறேன்.

      கால்குலஸ் நாமம் வாழ்க!

  4. Yayathi Says:

    Thanks to Mr.Ramasami for recommending this book and to Mr.Ramanan for providing the link to the PDF. This is an excellent book for beginners/practicing Engineers. For someone like me who pursued post graduate studies after few years of working (that too in Sales/marketing), if I had this book that time, this would have been like Meenakshi Ammal’s Samaithu Paar :-) . Also, the chapters on “Organic growth” would be useful for MBA students without mathematical background but would like to understand how the fundamentals of calculus are used in the area of financial derivatives.

    On the comment “I am in a cushy job with an MNC as an ‘engineer extraordinaire ….’”, I would like to share this: Couple of years ago, out of the 6000 people that passed the Financial Risk Management exam (world wide), roughly about 3000 were Chinese/Korean/Japanese (based on their names, not nationality) – there were hardly about 200 or so Indian names and even in that the South Indian/Tamil names were in the range of 10 or 20. I was expecting the numbers would be higher for India. There could be multiple reasons – not many people knowing about the exam or they do not think there is scope for growth or not many people actually like jobs that require quantitative skills.

    if you know any such books on number theory, please post them.

  5. gopinath Varadharajan Says:

    Dear Sir,

    Prof. CK Raju has an interesting take, and I do verify with other scholars.. (his claim on geometry, calculus went from India, esp Aryabhata..)
    His main point of contention is, if they (Greeks/Romans) don’t know multiplication and fraction, how could suddenly calculus / trigonometry invented?

    ( source appropriation prevailed due to Church Fatwa!!..)



  6. gopinath Varadharajan Says:

    :) I don’t think rest of India will catch up any time soon !!
    BTW, I’m trying to learn Vedic calculus (or difference equation, as specified by prof.Raju) If you know any materials for beginners please pass it on.

    • Dear,

      There is a framing issue with ‘Vedic’ at various levels. In any case the heights of math reached in Bharat post-date vedic times, no?

      There are a huge bunch of things that one can read – off the cuff, I would say, to start with, please read George Geverghese Joseph, David Pingree, and a brilliant math/science lady prof from Newzealand, whose name I forget. :-(

      There is also this professor Ramasubramaniam at IIT-B as also a funda group from TIFR.

  7. gopinath Varadharajan Says:

    ok thanks will look into all these authors. I need to restart (drop all my previous knowing!!) as a kid student. Got one link.

    Framing issues are there and difficult to catch, but being aware will help to cross verify. IMO.

    We cannot construct temples like Kailash, Angkor wat etc.. without mathematics excellence so we did peak but as I observe all natural events are cyclic and hence the peak has to bottom out. Our history is the worst case model:(

  8. A couple of points/notes:

    1. Pingree types while generally good/scholarly, unfortunately ALSO claim that astronomy of Bharat is not original and from Babylon. (of course without any evidence whatsoever, even to the extent of cooking up data like Jeyamohan) – now I recollect the name of the NZ lady – Kim Plofker; she is reasonable, I think.

    2. Anyday – K Ramasubramanian/IIT-B, MD Srinivas, MS Sriram, KV Verma et al are preferable, because they are scholarly, very invested and have demonstrable integrity.

    3. Please start from Dharampal’s ‘Indian Science and Tech in the 18th Century’ – just read the math chapter(s) at least and then go back as much as possible.

    4. Sources, sources, sources… this is imp.

    May be one of these days, I will write a short note on where to go for authentic stuff – because I have suffered lotsa frustration trying to figure out things for myself.

    Again Helaine Selin – her incredible compendia on nonwestern thoughts/ideas/science/tech/meds are STELLAR. They give a vast/deep sweep of the entire trajectories…

  9. gopinath Varadharajan Says:

    Thanks. 1. Read thru some of her articles and one video. She ( Kim Plofker) seems on middle ground (all happened in parallel!!)

    2. Sure will do, already knew KR’s works and others noted.

    3. Will do , I guess Dharmapal’s is the first to open this box of Vedic math?

    4. All these sources are sitting in Vatican Library and rest of them are with China :)

    Helaine Selin :- oh so many books she wrote… will check.

    • OK, thanks for the feed-forward. But one thing again please:

      1. If you use the term veda/vedic generically in terms of ‘knowledge/wisdom/whatever’ it is fine. But if you are actually calling the fine math that our Bharatiya ancestors developed as springing from the chatur-vedas or those ancient times, perhaps it is not correct.

      2. After going thru many sources over a few decades, talking to a few scholars, I can confidently say that we had reached great heights in many fields including math; with no actual parallels anywhere else in the world, of course! Actually the list or exhilaration would be endless. But, they all happened much after the original vedas were committed to writing.

      3. So, no. Sri Dharampal did not do anything like that. But please read the sources. And, please do understand the transmission directions…

      4. Ma’am Selin was a system integrator. Brilliant and scholarly librarian. In a true sense of the term. But she is not any originator of any idea. May be we had many like her in Takshashila Odanthapuri Nalanda Kanchi…


      • Gopinath Varadharajan Says:

        100% agree on Point #1 & 2. But without that “dharmic framework” we might not have reached those peaks…

        #3.Sure will read Dharampal’s works, I have a huge list !! and accumulating..

      • Sir, kinda yes. Now we have reached a point wherein we can’t discuss all this ad infinitum in this comments-section.

        If you feel like, let us carry on the discussions over emails. Send me a ping. (but beware, I take my own sweet time to respond, but respond, I will!)

      • gopinath Varadharajan Says:

        Understood. Pls reply to vgopinathATHotmailDOTcom
        ( :) np take your time..)

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