Now available in paperback! An introduction to the calculus, with an excellent balance between theory and technique. Integration is treated before differentiation--this is a departure from most modern texts, but it is historically correct, and it is the best way to establish the true connection between the integral and the derivative. Proofs of all the important theorems are given, generally preceded by geometric or intuitive discussion. This Second Edition introduces the mean-value theorems and their applications earlier in the text, incorporates a treatment of linear algebra, and contains many new and easier exercises. As in the first edition, an interesting historical introduction precedes each important new concept.
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Now available in paperback! An introduction to the calculus, with an excellent balance between theory and technique. Integration is treated before differentiation--this is a departure from most modern texts, but it is historically correct, and it is the best way to establish the true connection between the integral and the derivative. Proofs of all the important theorems are given, generally preceded by geometric or intuitive discussion. This Second Edition introduces the mean-value theorems and their applications earlier in the text, incorporates a treatment of linear algebra, and contains many new and easier exercises. As in the first edition, an interesting historical introduction precedes each important new concept.
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Most Helpful Customer Reviews
21 of 22 people found the following review helpful
Format:Hardcover
Apostol's Calculus is the definitive book on Calculus for anyone who wants to be a mathematician. Historical notes, intuitive ideas, clear definitions, demonstrations, all is there, from natural numbers to Stokes' Theorem. His applications of linear algebra to multivariate calculus are among the best I have seen on calculus textbooks Better than this, only a book on Mathematical Analysis.
54 of 64 people found the following review helpful
Format:Hardcover
Few books in the mathematical literature have given me so much pain as this one. Freshman year, I took a heavily theoretical linear algebra class with Tommy II as the textbook, and then the next term I took multivariable calculus out of this book as well. In either case, this book was my first experience with the material, though as an "introductory" text it should have done the job. Suffice it to say that neither experience was terribly positive.
My problem is that Apostol never seems to try to motivate ideas well, and he uses cumbersome, nonstandard, and occasionally inconsistent notation. His proofs can be inelegant and opaque at times. He is far too sparing on geometrical intuition as a way to understand the material, preferring to talk in symbols rather than pictures. (This is especially true in the first five chapters on linear algebra. His multivariable chapters are well-illustrated, but calculus on R^n seems to be trivial once calculus on R is under your belt from a good introductory book like Larson/Hostetler/Edwards at a high-school pace. Thus, the motivation is needed least where it is used most.) As a result, I feel that I still don't intuitively understand how operators work on inner-product spaces, even after trying to remedy my deficiencies for a year and a half now.
I attributed my lack of understanding to my stupidity, but then I found myself learning exterior forms from Arnol'd's excellent mathematical mechanics book and groups from Dummit/Foote's superb abstract algebra text - and understanding the exposition perfectly. And I started to feel that this book is the thing at fault.
If a prospective reader is prepared for the terseness and difficulty of Apostol, I recommend that s/he go straight to the real math rather than settling for this obfuscated treatment of inroductory subjects. It is no harder to learn the rudiments of metric topology than it is to learn Apostol's open balls, and it seems no more inspired to take on Halmos' linear algebra classic, with its intimations of Hilbert space, than it is to struggle through Apostol's treatment. (The former seems to combine considerable difficulty with terse, but wonderful, motivation, but don't take my work on that: I'm only forty pages into it!) But the books are more inspired, and the math is far more general and beautiful.
My recommendation: learn your calculus (and potentially your first linear algebra) patiently but thoroughly from a prosaic, worked-example-ridden, 1000-page monster, then go straight to the upper undergraduate/early graduate classics for the real fun. Tommy II, caught somewhere in the middle, has no place in this plan.
My problem is that Apostol never seems to try to motivate ideas well, and he uses cumbersome, nonstandard, and occasionally inconsistent notation. His proofs can be inelegant and opaque at times. He is far too sparing on geometrical intuition as a way to understand the material, preferring to talk in symbols rather than pictures. (This is especially true in the first five chapters on linear algebra. His multivariable chapters are well-illustrated, but calculus on R^n seems to be trivial once calculus on R is under your belt from a good introductory book like Larson/Hostetler/Edwards at a high-school pace. Thus, the motivation is needed least where it is used most.) As a result, I feel that I still don't intuitively understand how operators work on inner-product spaces, even after trying to remedy my deficiencies for a year and a half now.
I attributed my lack of understanding to my stupidity, but then I found myself learning exterior forms from Arnol'd's excellent mathematical mechanics book and groups from Dummit/Foote's superb abstract algebra text - and understanding the exposition perfectly. And I started to feel that this book is the thing at fault.
If a prospective reader is prepared for the terseness and difficulty of Apostol, I recommend that s/he go straight to the real math rather than settling for this obfuscated treatment of inroductory subjects. It is no harder to learn the rudiments of metric topology than it is to learn Apostol's open balls, and it seems no more inspired to take on Halmos' linear algebra classic, with its intimations of Hilbert space, than it is to struggle through Apostol's treatment. (The former seems to combine considerable difficulty with terse, but wonderful, motivation, but don't take my work on that: I'm only forty pages into it!) But the books are more inspired, and the math is far more general and beautiful.
My recommendation: learn your calculus (and potentially your first linear algebra) patiently but thoroughly from a prosaic, worked-example-ridden, 1000-page monster, then go straight to the upper undergraduate/early graduate classics for the real fun. Tommy II, caught somewhere in the middle, has no place in this plan.
18 of 20 people found the following review helpful
Format:Hardcover
I'm currently taking an honors calculus sequence at the U of WI, and have used this book and the first volume for the past three semesters. Needless to say, you have to take Apostol with a grain of salt. Although the no-frills style and lack of worked examples is upsetting to many students who are used to pictures, thorough examples, and color, these volumes cover a lot of material in a small space. And also beware; my professor and others in the math department have found errors in definitions and theorems, and the archaic notation is off-setting at times. Basically, if you're looking for straighforward information (written by a mathematician, for a mathematician), you've found the perfect book. If you're looking for an easy-to-read and understand book, keep searching.
Most Recent Customer Reviews
best for math majors
if you have gone through the vol 1, then you do not need my review. I feel vol 1 and 2 are the best calc books for math majors. Read more
Published on June 29, 2009 by S. Shaikh
A nice continuation to the first volume.
This volume is the hammer of the two volumes, where as the first volume would be the nail. Once you've master volume one it's time to start digging for gold; the basics one learns... Read more
Published on May 12, 2008 by MAO
Not your starter book
The author is a world renowned mathematician, with many beautiful achievements under his belt. I would not include this popular textbook in this category. Read more
Published on May 8, 2008 by Liviu I. Nicolaescu
A classic, richness in knowledge few books attempt anymore.
I used these books (Vols. 1&2) in my last two years of high school back in South America. I remember long nights of bad coffee and cigarettes locked in my room reading it over and... Read more
Published on May 15, 2006 by Andres G. Vidal-gadea
A righteous calculus text
This one of the more righteous books in the author's oeuvre and that is saying something! The subject matter is closely akin to a course I took in Freshman year however it... Read more
Published on September 19, 2005 by Cornell 07'
Review of Tommy Volume 2
I am currently enrolled in BC Calculus in my high school as well as linear algebra at a local college. What better way to learn both together than with Tommy. Read more
Published on December 27, 2003 by Tina M. M. Silverman
substance w/o the frills
I was looking for a solid reference book and was quite fortunate to stumble across Apostol's two texts. His writing is clear and concise. Read more
Published on July 2, 2001 by Cengiz
Calculus Volume 2 (Tom M. Apostol)
This book contains a lot of information, and is rigorous, with many proofs and a vast array of problems. Read more
Published on May 24, 2001
CALCULUS
tHERE IS A EXCELLENT BOOK.
Published on February 3, 2001 by ANGELA DE MIRANDA COELHO DA ROCHA
Pretty good explanations!
I took a course in Linear Algebra & Multivariable Calculus through Stanford U. that used the first half of this as a textbook when I was 11. Read more
Published on November 6, 2000
Inside This Book
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First Sentence:
Throughout mathematics we encounter many examples of mathematical objects that can be added to each other and multiplied by real numbers. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
kth unit coordinate vector, open subrectangles, annihilator method, central limit property, dimensionality theorem, uncountable sample spaces, continuous scalar fields, diagonal matrix representation, finitely additive set function, sequential counting, unit coordinate vectors, piecewise smooth path, nonhomogeneous system, infinite sample spaces, unbiased die, ordinate set, lim ilf, same linear transformation, compound experiment, content zero, determinant function, real linear space, determinant changes sign, symmetric transformation, indicial equation Key Phrases - Capitalized Phrases (CAPs): (learn more)
Solve Exercise, New York, Therefore Equation, Exercises In Exercises, North Pole New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Throughout mathematics we encounter many examples of mathematical objects that can be added to each other and multiplied by real numbers. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
kth unit coordinate vector, open subrectangles, annihilator method, central limit property, dimensionality theorem, uncountable sample spaces, continuous scalar fields, diagonal matrix representation, finitely additive set function, sequential counting, unit coordinate vectors, piecewise smooth path, nonhomogeneous system, infinite sample spaces, unbiased die, ordinate set, lim ilf, same linear transformation, compound experiment, content zero, determinant function, real linear space, determinant changes sign, symmetric transformation, indicial equation Key Phrases - Capitalized Phrases (CAPs): (learn more)
Solve Exercise, New York, Therefore Equation, Exercises In Exercises, North Pole New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 12
books:
See all 12 books this book cites
- Modern Probability Theory and Its Applications (Wiley Classics Library) by Emanuel Parzen on page 570
- Principles of Numerical Analysis by Alston S. Householder in Back Matter
- Interpolation and Approximation by Philip J. Davis in Back Matter
- Introduction to Numerical Analysis: Second Edition (Dover Books on Mathematics) by F. B. Hildebrand in Back Matter
- Ordinary Differential Equations by Jack K. Hale on page 181
See all 12 books this book cites
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