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It has been a while since I wanted to ask this question, but couldn't find a right forum. My question might come across as trivial, but its important to me to find an answer to that.

Let me give you some background, I was very good in Mathematics until my face off with Calculus. In 11th/12th Std.my Maths Prof. was pathetic, and I ended up bunking all Maths lectures. Hence my Applied Maths base, especially calculus is extremely weak. I am a Computer Science Student and want to catch up in reasonable time but I don't know where to begin as I am unsure about my proficiency in pre-calculus (Linear, Logarithmic, Exponential algebra) stuff as well.

So my first question is where should I begin or In order to understand concepts of calculus what do I need to get hold off first ? And Could anyone suggest a very good book - easy to understand especially for beginners (I have to face the reality that even though I am a Master's Student I am really a beginner as far as Calculus is concerned :D).

Thanks in Advance.

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It's just practice. Calculus isn't hard and if you practice enough it will come naturally. –  simplicity Mar 5 '12 at 23:40

8 Answers 8

up vote 6 down vote accepted

As a primer, I would recommend a series of videos by Gilbert Strang called Highlights of Calculus. Hopefully they're not too basic for you, they certainly won't be too difficult.

As for a textbook, I agree with the recommendations above. Spivak's Calculus is a very good book, but it is also quite a bit more rigorous than your typical 'introduction to calculus' (in many ways it's more of an 'introduction to analysis' - it only starts talking about derivatives around page 200).

Gilbert Strang's textbook was also mentioned above. If you appreciate his teaching style in the videos, you'll find his textbook very similar - very casual and intuitive. On top of that, it's freely available in pdf form from here.

These are just 2 good texts I've been exposed to over the years. Personally I'd recommend staying away from Stewart's textbook, but that's probably just a bad experience on my part. Normally I'd unequivocally recommend Strang's book to a beginner, but with your background you might prefer the more systematic approach of Spivak.

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You should check this long list of free books (including the one by Dr. Gilbert Strang from MIT): see The textbooks panel here

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They should reprint the book by Dr. Gilbert Strang. (Looks old style format), but it is a great book. –  Jeremy Carlos Mar 15 '12 at 0:04
    
I second the recommendation of Strang's book-I think it's the best of the relatively recent crop of standard calculus texts. –  Mathemagician1234 Mar 17 '12 at 7:50
    
This link is only redirecting to mathbuntu.org I edited the answer accordingly –  Jean-Claude Arbaut 5 hours ago

I used Spivak's Calculus in secondary school, and was able to teach to myself most of the material- the book is very thorough and elegantly told.

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I'm not a big fan on Spivak's book. James Stewart book is better. –  simplicity Mar 5 '12 at 23:45
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Spivak is WAY too hard for the average student just beginning to study calculus and it's important for such students to also learn the practical aspects of the subject in addition to theory. I think Gilbert Strang's CALCULUS is a much better choice in this regard. –  Mathemagician1234 Mar 5 '12 at 23:59

Before you begin, as you suggested, I would definitely go over those "Pre-Calculus" topics such as exponents, logs, graphs of rational functions, etc. In addition, consider brushing up on your algebra skills, if needed. Algebra seems to be the bane for many in Calculus.

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Good advice-although Euclidean geometry is becoming something of a lost art which is also hurting many coming into calculus for the first time. –  Mathemagician1234 Mar 6 '12 at 0:25
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Second this answer by adding more suggestions. Go over your high school math textbooks first. Then study the Calculus book you used in your college or another good book(there are plenty of them)by doing the exercises. –  scaaahu Mar 6 '12 at 2:41
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I just made my post a community wiki so others can feel free to add to my suggestions at any time. Obviously each person has their own tastes for intro Calc books. Nonetheless, I would also have to agree that Spivak, as mentioned below, is not intended for a student such as the OP. –  Joe Mar 6 '12 at 5:13

Things to consider in order to succeed in Calculus .

  1. Start covering all *(at least) few important topics Algebra,TRIG,PRE-calculus from Sal's Khan Academy.

  2. Once you Mastered that skill than get thro Calculus-Single variable from Khan and MIT's 18.01 along side with Prof.Gilbert Strang's book.Side by look Highlights of calculus from the same prof.

  3. Once you master in single variable move over Multi-variable take Mit's 18.02 along.

'''If you feel that your done then step into Engineering techinques by Strang which covers DE,Linear algebra and other applications of calculus'''

Epilogue: In order to succeed in Math Practice,Practice and Practice

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If you are a engineer, i suppose you should read the applied calculus book instead of the pure one, since most of the calculus material are available free online, while applied calculus not

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I would recommend the books advised to study calculus to students preparing for IIT JEE ,because thats when we begin our journey of understanding calculus.

Some of these are,
ML Khanna
Arihant Series (Differential calculus and Integral calculus)

You can easily find these books at a bookstore near you because they are super popular.

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I love the Schaum's Outline series since decades!

The "format" of the books in the series is as follows:

  • the book is divided in chapters
  • each chapter starts with a brief presentation of the important topics
  • then a couple of pages follows, with questions and a fully worked out sample solution
  • finally there are extra questions posed where only the answer is given somewhere else in the book

Usually the questions not only train the topics but extend the topics as well.

This way you are learning by solving problems.

For a standard topic like calculus, they have different books for different levels. I am pretty sure you'll find a suitable one.

Recently I started to buy them as ebooks.

There were some very cool entries in the past. For example I still have a copy of Real Variables, a Schaum's Outline on Lebesgue integration.

Personally I profited the most from the Schaum's Outline on Ordinary Differential Equations. Also helpful to me were the ones on Linear Algebra, Advanced Calculus, Complex Variables, and Partial Derivatives.

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