Showing posts with label James Stewart. Show all posts
Showing posts with label James Stewart. Show all posts
Monday, September 7, 2009
Calculus
Product Description
Success in your calculus course starts here! James Stewart's CALCULUS texts are world-wide best-sellers for a reason: they are clear, accurate, and filled with relevant, real-world examples. With CALCULUS: EARLY TRANCENDENTALS, Sixth Edition, Stewart conveys not only the utility of calculus to help you develop technical competence, but also gives you an appreciation for the intrinsic beauty of the subject. His patient examples and built-in learning aids will help you build your mathematical confidence and achieve your goals in the course! About the Author
James Stewart received his M.S. from Stanford University and his Ph.D. from the University of Toronto. He did research at the University of London and was influenced by the famous mathematician George Polya at Stanford University. Stewart is currently Professor of Mathematics at McMaster University, and his research field is harmonic analysis. Stewart is the author of a best-selling calculus textbook series published by Cengage Learning—Brooks/Cole, including CALCULUS, CALCULUS: EARLY TRANSCENDENTALS, and CALCULUS: CONCEPTS AND CONTEXTS, as well as a series of precalculus texts.
Thursday, August 6, 2009
Calculus: Early Transcendentals
I have used this gargantuan book for three semesters now. This book is proof that quality does not equal quantity (1100+ pages). The book has lots of pictures, which I suppose is why it is so big. How do color photographs of nature scenes aid one's understanding of calculus? Answer: they don't...period.
Yet for such a large book, coverage is quite sparse. The coverage starts with a slow introduction to functions, which I suppose is good for high-school students or students who lack the most basic mathematical background, but not for typical college students. Very little of the coverage has any depth, and too many proofs are 'outside the scope of this book'. By the time Stewart gets to vector calculus (covered in a single chapter), the coverage has become pure cookbook. For instance, divergence and curl are given as formulas, with no real discussion of their significance.
Also, the book is organized very strangely. For instance, parametric equations and parametric surfaces are discussed in separate chapters. Even worse, the relationships between parametric curves, scalar fields and vector fields (the three types of multivariable functions) are never discussed. Perhaps it was just hard for me to see the relationships because they were on opposite sides of an 1100-page phonebook!
Suggestion to Mr. Stewart: If you feel your book really needs to be so long winded, at least break the book into two or three volumes. Carrying my books to class shouldn't feel like boot camp!!! My friends think I'm carrying bricks in my backpack!!!
And to the students: if you have a choice in the matter, consider either Apostol's "Calculus" or Spivak's "Calculus". If you are really adventurous, try Courant or maybe even Rudin. Also, for a pretty-good intro to vector calculus, check out Schey's "Div, Grad, Curl". I have taught calculus courses with this and other books, and this one is actually pretty good.
I disagree with those reviewers that say that this is a "proof-oriented" book. Yes, many of the important theorems in calculus (the Fundamental Theorem of Calculus, the Mean Value Theorem) are proven, but the topological ones like the Extreme Value Theorem and Intermediate Value Theorem are not (perhaps that's too much to ask of a first-year course for non-majors, however). There is an overuse of color in the text, and the accursed box is drawn around way too many things, logically equating theorems, definitions, principles, and terminologies specific to the book like "The Closed Interval Test".
What the book is very good at is providing lots of real-life examples and problems. In fact, these save the book. Each chapter teases some of the more interesting ones (how fast does a turkey cool after you take it out of the oven?) There are extended problems called "Applied Projects." I was particularly impressed with those from the related rates and optimization sections. Problems like these are what turned me on to math. Just a few more theoretical problems would complete the picture, however. Many students can calculate derivatives of functions, but few will come away with an idea of what functions and derivatives really are.
In summary, this is very good book for non-math majors (e.g., engineers). It needs only be supplemented in class with the foundational material. For majors, however, I recommend Spivak's _Calculus_ book.
Yet for such a large book, coverage is quite sparse. The coverage starts with a slow introduction to functions, which I suppose is good for high-school students or students who lack the most basic mathematical background, but not for typical college students. Very little of the coverage has any depth, and too many proofs are 'outside the scope of this book'. By the time Stewart gets to vector calculus (covered in a single chapter), the coverage has become pure cookbook. For instance, divergence and curl are given as formulas, with no real discussion of their significance.
Also, the book is organized very strangely. For instance, parametric equations and parametric surfaces are discussed in separate chapters. Even worse, the relationships between parametric curves, scalar fields and vector fields (the three types of multivariable functions) are never discussed. Perhaps it was just hard for me to see the relationships because they were on opposite sides of an 1100-page phonebook!
Suggestion to Mr. Stewart: If you feel your book really needs to be so long winded, at least break the book into two or three volumes. Carrying my books to class shouldn't feel like boot camp!!! My friends think I'm carrying bricks in my backpack!!!
And to the students: if you have a choice in the matter, consider either Apostol's "Calculus" or Spivak's "Calculus". If you are really adventurous, try Courant or maybe even Rudin. Also, for a pretty-good intro to vector calculus, check out Schey's "Div, Grad, Curl". I have taught calculus courses with this and other books, and this one is actually pretty good.
I disagree with those reviewers that say that this is a "proof-oriented" book. Yes, many of the important theorems in calculus (the Fundamental Theorem of Calculus, the Mean Value Theorem) are proven, but the topological ones like the Extreme Value Theorem and Intermediate Value Theorem are not (perhaps that's too much to ask of a first-year course for non-majors, however). There is an overuse of color in the text, and the accursed box is drawn around way too many things, logically equating theorems, definitions, principles, and terminologies specific to the book like "The Closed Interval Test".
What the book is very good at is providing lots of real-life examples and problems. In fact, these save the book. Each chapter teases some of the more interesting ones (how fast does a turkey cool after you take it out of the oven?) There are extended problems called "Applied Projects." I was particularly impressed with those from the related rates and optimization sections. Problems like these are what turned me on to math. Just a few more theoretical problems would complete the picture, however. Many students can calculate derivatives of functions, but few will come away with an idea of what functions and derivatives really are.
In summary, this is very good book for non-math majors (e.g., engineers). It needs only be supplemented in class with the foundational material. For majors, however, I recommend Spivak's _Calculus_ book.
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