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He's a Great Lecturer, But Strang's Book Gives Me A Headache
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 
'* Differential and Integral Calculus - Philip Franklin 
'* Elementary Calculus - Woods, Bailey 
'* The Calculus - Davis, Brenke, ed. by Hedrick 
*' Calculus for the Practical Man - J. E. Thompson  - 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