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I used to consider Stewart's Calculus as an ideal beginner text but this book by Gilbert Strang tops it significantly. This is a great book if you have been away from calculus for a number of years and now want a fairly in-depth treatment beyond the "Calculus for Dummies" genere. Things are presented very well and the tone is almost conversational. For the self-learner who has the time and inclination this text is ideal. There are a goodly number of diagrams and examples.

To top it all off this book is available for free at the MIT Open Course website: [...]
In addition to the textbook the website has the Instructor's Manual and the Study Guide.

Excellent resource specially considering how expensive even mediocre calculus textbooks are today. I purchased a used copy since I find reading textbooks on the web gets old real quick. A must have.
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on July 18, 1998
If you intend to teach yourself calculus, or if you are looking for a text for review, this one would be an excellent choice. The topics are well explained and well motivated by applications. The book covers a wide array of topics and each of them is clearly developed. I would choose this as the text for a class if I were to teach it. I certainly recommend it for those learning outside the structure of a classroom.
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on July 31, 2012
Clearly, for some people, Strang's book is better than anything else that they've encountered. Good for them. But for me, when reading it, I feel like a schizophrenic person is yelling at me. All the short sentences, exclamation marks, and off-topic tangents make it "conversational" for sure, but they also distract from the concepts and make the book harder to read. Honestly, I tried reading it - I read the introduction, I read different parts throughout the book, but the same thing kept happening. I've gone through many, many calculus books, and yes, many of them are the same, but I don't think that a book being different makes it necessarily better in this case. If Strang's style resonates with you, more power to you, but I must warn all those looking for a "clear" exposition that his writing (at least in the 1st edition) is completely all over the place, and has given me a mini-migraine.

To give a minor example of his machine gun rapid fire style of writing, at the beginning of the derivatives section he writes:

"This chapter begins with the definition of the derivative. Two examples were in Chapter 1. When the distance is t^2, the velocity is 2t. When f(t)=sin t, we found v(t)=cos(t). The velocity is now called the derivative of f(t). ... [and later...] Note that 'f is not ' times f! It is the change in f. Similarly, 'delta t is not ' delta times t. It is the time step, positive or negative and eventually small."

His characteristically short sentences make me feel like I'm reading a genius 4th grader's work. Maybe it helps students who can't read long sentences, but it makes it less conversational for me, and has the effect of making the text feel robotic and jolty.

I also don't understand Strang's obsession with talking about derivatives and integrals in terms of lists of numbers, and the differences between them. The way he talks through calculations instead of writing them down explicitly is very confusing, and I can only imagine even more confusing for someone learning calculus for the first time. To give an example from his section on integrals, "Now look again at these same numbers - but start with v. From v = 1,2,3,4, how do you produce f=1,3,6,10? By taking sums. The first two v's add to 3, which is f_2. The first three v's add to f_3 = 6. The sum of all four v's is 1+2+3+4=10. Taking sums is the opposite of taking differences."

Now, how that is supposed to illuminate the Fundamental Theorem of Calculus in a real way (as he uses it in the next paragraph) is beyond me. I find it much more confusing than the standard background for the FTC.

In conclusion, if you really like short, beat poet-esque lines of writing, and verbal discussion of mathematical calculations, this book is definitely for you. But if you're coming off of Stewart or Edwards or Thomas, looking for a more in-depth discussion of calculus, I would invite you to consider your other options before buying this book. At least go take a look at it - it's available for free on the MIT Open Courseware website, because you may not be getting what you think you're getting.

As far as good books other than the standard Stewart, Thomas, etc. (which I find to be much clearer and better than Strang), I would recommend any of the following:

'* Calculus: An Intuitive and Physical Approach - Morris Kline (available from Dover in paperback)
'* Differential and Integral Calculus (two vols.) - Richard Courant [somewhat at a higher level than an ordinary calc treatment]
'* Calculus (two vols.) - Tom Apostol <- a very rigorous, and often pretty difficult set
'* Calculus with Analytic Geometry - Earl Swokowski (very much like Stewart, Thomas, et al)
'* A First Course in Calculus - Serge Lang
'* Calculus - Michael Spivak <- somewhere between Apostol and Stewart in terms of difficulty, but a widely renowned Calc I/II book
'* Calculus and Linear Algebra (two vols.) - Wilfred Kaplan and Donald J. Lewis <- a really great integration of calc with linear algebra, it goes from a review of precalc through multivariable calculus
'* Calc I, II, III - Paul Dawkins (available if you search Google for Paul Dawkins calculus, it's "marketed" [free] as a study guide of sorts or lecture notes, but I find it to be as good if not better than any textbook. Full of examples too)
'* Intro to Calculus and Analysis - Courant, Richard; John, Fritz- this is more of an analysis text, but could be useful to someone who's already completed their calc I-III and wants a transition to analysis

And finally, if none of that or the standard texts float your boat, you could always try some of the more archaic, and more conversational texts, available online or on Amazon in various places:

'* Calculus Made Easy - Thompson [1910]
'* Differential and Integral Calculus - Philip Franklin [1955]
'* Elementary Calculus - Woods, Bailey [1922]
'* The Calculus - Davis, Brenke, ed. by Hedrick [1912]
*' Calculus for the Practical Man - J. E. Thompson [1931] - a somewhat strange book, but it covers most of the calc concepts
'* Calculus: Basic Concepts for High Schools - L. V. Tarasov [date unknown] - This book deals with Calculus by means of a Socratic dialogue between teacher and student. Can't say whether it works or not as it was too odd for me to spend much time on.
'* A Course in Pure Mathematics - G. H. Hardy

I hope that if this book isn't right for you, one of the other ones on this list is! Best studying!

~ A fellow math student
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on June 23, 2006
I first saw this book as a MIT textbook. Read it briefly and absolutely loved it. I learnt Calculus many years ago and hope I had this book then. The book is so clear written and easy to understand. I am buying this book for my son now. I am sure it will be a great help for anyone reads this.
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on April 3, 2007
This is a great self-teaching text. I'm currently in high school and I wanted to get a little ahead of the game so I searched for online calculus texts and found this one. The website ( MIT Text Publications) has all the chapters in pdf format complete with the answers to the odd numbered questions. Uses interesting examples such as the application of calculus to physics and economics.
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on April 14, 2010
I have read a great many calculus books at all levels. In my opinion, this is the best single
book currently in print for a first course in calculus - especially for those who will go into applied mathematics, engineering or physics.
Strang is one of the best, if not the best, teachers of mathematics in the United States.
The treatment given in this book is physical and brings the subject to life. Strang uses the odometer and speedometer
to give an initial motivation for the differential and integral branches of the subject. This is a simply brilliant approach.
Although many ivory tower math
types might disagree, mathematics is not just a set of formal rules like a game of chess. The true importance of
mathematics is to provide a language
to describe the physical world around us. Any introductory calculus text that ignores this fact is doing
the student a terrible disservice. This is why, although I have much respect for these texts, I would never recommend the treatments by Apostol or
Spivak for a first course in Calculus.

In summary, I give this book my highest recommendation.
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on January 21, 2012
I've used many Calculus books throughout my 20+ years of college teaching, and can predict the organization of the table of contents of most published texts. With few exceptions, they are all virtually the same. Gil Strang's masterpiece is one of those few exceptions.

Strang begins his Calculus text with Calculus. Indeed, by the end of the second section (first chapter) he has already presented the essence of the Fundamental Theorem in a painless, easily understood manner. And, while no review section is explicitly included, Strang clearly recognizes where students are likely to have holes in their knowledge and delicately repairs them with his skillful manner of presentation.

Strang focuses on ideas first and rigor later. He uses traditional vocabulary and symbolism, but not until the student is comfortable with the ideas that they describe. He masterfully presents Calculus in a pedagogically sound manner and with a friendly, conversational voice.

Traditional texts work well for only the brightest students - of course, any text works well for the brightest students. This text works well for all of them. If you're daring enough to break tradition and do what's right for your students, please examine Strang.

Oh... and did I mention that an electronic edition of this text is available for free though MIT's Open Courseware? In this case, you really do get far more than you pay for!
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on March 28, 2000
This book has excellent explanations, and is well organized. Usefull as a reference, and to teach yourself calculus. I used it all through college as a supplement (and sometimes replacement) for the assigned text.
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on October 29, 2010
I would really encourage people to check this text out online. I am amazed at the facility with which professor Strang introduces derivatives and integrals. I have never before seen the Fundamental Theorem of Calculus explained in terms of simple sums and differences. Derivatives and Integrals are introduced in terms of simple sums and differences. I still can't get over this. Strang starts out with an odometer and speedometer and uses them to explain what calculus is. The conversational tone is outstanding and all of the materials are available via MIT. I only wish that I had learned calculus from this text the first time around. It is evident that Strang understands calculus to the core, and that few other calculus teachers do. A superb listing of available online texts is on the following website: [...].
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on April 8, 2014
I have downloaded the pdf version of this superbly well written book. It is clear, concise, to the point, and yet conversational in tone.
Strang knows his audience and maintains the proper level of rigor without dumbing down the material. He knows that too much rigor too soon creates intellectual rigor mortis. As always, if you are not well prepared in precalculus you are conducting an exercise in futility studying Calculus and you will be really intellectually dishonest to criticize the author. This book is highly suitable for self learners who are well prepared and motivated. If you are not well prepared and highly motivated studying Calculus is an exercise in\ futility.
If you go to "MIT OCW Calculus Gilbert Strang" you will find videos of his Calculus lectures. As good as his books are, this is really
his arena. He is one of the two or three best lecturers, in any subject you will ever see. His blackboard notes and remarks are an
absolute treat. When he develops a topic he leaves no stone unturned and no loose ends. His lectures are like listening to a piece of music where each time you listen you hear something that you did not hear previously.
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