4.0 out of 5 stars
A thorough introduction to calculus, April 1 2011
This review is from: Calculus: Single Variable (Paperback)
Calculus is required for engineering, physics, chemistry and scientific statistics, besides mathematics. It is so important that in some universities, physics begins their first semester covering basic calculus. Differential calculus gives rules for the slopes or rates of change of general expressions or functions. These rates of change are called derivatives. Integral calculus shows that the rate of change of an area under a curve is given by the formula for the height of the curve and so the area itself is found by the inverse operation of differential calculus or the anti-derivative.
A knowledge of basic differentiation and integration would be so straightforward to impart at high school and so useful, but usually it is not. Ontario used to cover calculus in Grade 13 which I believe is now defunct.In BC over the last 20 years, simple ideas on calculus seem to drift in and out of Grade 12.
So why do some physics departments cover calculus in the first semester? Because the large majority of first year math courses on calculus take so long to get to the actual calculation of rates of change: so long that often integral calculus is reached only in the second semester, and this is what the physics programs need.
There are a great many good texts on single variable calculus available. Robert Adams' text is certainly one of the most thorough and complete of these. I have not taught from this text, but I was very favourably impressed by the companion text on Calculus of Several Variables which I consider the finest text on this topic that I have ever seen. I only wish it had been available when I was an undergrad 56 years ago.
Anyway, the single variable text covers the usual first year material including series and power series, a very good chapter on ordinary differential equations, and brief but useful introductions to Fourier Series and complex numbers. The examples in the text are interesting and seem to cover most of the difficult points that I can remember. The presentation is very careful and yet very readable and the author attempts to prove every result. It is a wonderful text for a mathematically inclined student. A weaker student would require direction on which sections to study, in my opinion.
There is no mention of vectors in this sixth edition which was a disappointing surprise since my 3rd edition of the several variables text refers to vector-valued functions of a real variable as being covered in the single variable text. A significant omission from a practical view point.
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