Like the blades of grass on the front cover of this book, mathematics used to describe nature is at once beautifully simple and infinitely complex. Calculus strives to illuminate both of these aspects o our world.
Classroom-proven around the world, this classical text has been praised for its high level of mathematical integrity, including complete and precise statements of theorems, use of geometric reasoning in applied problems, and a diverse range of applications across he sciences. The Sixth Edition features a separate chapter on differential equations and numerous updated Maple examples.
I first read this as a student and I still have a copy.
It starts out as a good introduction. You would need to understand algebra and trigonometry, at high school level. But it explains all the basic concepts of calculus, especially differentiation, and its inverse operation: integration. It also says a lot about Taylor series.
Later, it moves on to advanced topics, such as vector calculus.
The author explains all topics very clearly, and makes it seem quite easy.
The questions in this textbook were fine and suitable, as they helped develop a solid understanding of the concepts presented - but good God the verbal explanations in this textbook are terrible. The style of writing is beyond convoluted and the explanations for proofs, equations, and so on are just awful. If all you want to do is solve mathematical questions then this textbook is fine, but if you're looking to teach yourself mathematics then I would not recommend this book at all. 2.5/5
The main advantage of this book compared to other calculus books is the more generalized manner in which subjects are treated. For instance, maxima/minima points are explained for n-dimensional functions. Most books give only the formulas for 2-dimensional functions because the generalization requires some linear algebra. Also, implicit differentiation is very well treated, is the only book that I found with generalization for this.
The main disadvantage is that the explanations and derivations are not so well explained as in James Stewart's calculus books for instance, but they are still pretty good. I was able to follow most of them.
I used this book to recap the calculus needed for deep learning.
In many ways, introductory calculus is a difficult subject to teach properly. Calculus is in a bit of a difficult place in mathematical pedagogy; it is a subject of paramount importance with broad application to nearly every natural science, yet a rigorous treatment is difficult to provide at a simple level as the theory is far more complex than meets the eye. Typically engineers and applied scientists will never need to see the inner workings in substantial detail (and most never do, unless they take courses in real analysis), yet this can at times provide a frustrating lack of clarity on the motivations and derivations of calculus. I have read a few calculus texts, and I have found that texts written for a first introduction are either at a level of too much handwaving (such as in Stewart's calculus) or of too much detail for a typical student without a background in mathematical proof (most analysis texts). I believe this text does a good job at teaching calculus at a level appropriate for a first introduction, yet with enough additional detail and optional proofs in the exercises to come away from it with a more satisfying understanding of some of the workings under the hood. For example, some of the exercises in this text do a good job of going above and beyond by guiding the reader through the derivation of Stirling's formula, the gamma function, more difficult methods for integration, and applicable results. Some chapters are not as complete as others, and other texts would be more appropriate (in the case of exterior forms and some of the vector calculus content). Overall, I would recommend this textbook as an excellent first introduction to calculus with enough difficulty and detail to remain interesting and provide a satisfying explanation for non-obvious results.
A good book on Calculus, very detailed with proofs, explanations of the theory, and plenty of examples. A good book to get a better understanding of the subject, or as a reference. However, I believe the books structure, which has a lot of mathematical proofs sprinkled throughout, would make the subject more confusing to those just learning or still gaining familiarity.
A extremely good book which introduces calculus to anyone at any level. It can be a hard read, but with some supplementation with khan academy and other online resources this will make you well known with the subject.