Calculus, Vol. 1: One-Variable Calculus with an Introduction to Linear Algebra (Second Edition) (Volume 1) by Tom M. Apostol Summary and Reviews
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Book Reviews of Calculus, Vol. 1: One-Variable Calculus with an Introduction to Linear Algebra (Second Edition) (Volume 1)
Book Review: Both joy and nobility of abstract math in this book (V.2)
Summary: 5 Stars
This book is for students who enjoy mathematics and who care to understand advanced calculus the way it should be. I haave Ph.D in math. and went cross many advanced calculus books through my career. I found Apostle's book to be the best in three fundamental respects, first, he treat each subject deeply and masterfully leaving no confusion in the reader's mind- see for example his treatment of several variable differentiation .Second, in advance he penpoints the main issues of each subject and discuss complexity of developing theory and generlizing theorems toward more advanced levels. Third, he supplied in his book very intersting and illuminating collections of exercises throughout the book. If you think you are a mathematically oriented thinker you should study advanced calculus the way apostol exhibited in his book. I just say this is a distinguished book for a distinguished student.
Book Review: Simply the best!
Summary: 5 Stars
This is still the text for Math 1a, the first Calculus course taken by CalTech students. That says a lot. It was published in 1967, and this is the edition still used. This says even more. A great book even though, like ALL college texts, it is way, way, way OVERPRICED! I wonder what it cost in 1967? Get it through your local library's interlibrary loan program and preview it before you consider spending the money. If you need something easier try getting one of those books with "Business" or "Life Sciences" sharing title space with the calculus.Book Review: Real Math for Real Mathematicians
Summary: 5 Stars
Apostol's Calculus, Vols 1 and 2, are my calc bibles. It is unfortunate that more undergraduate curricula and textbooks don't follow the axiomatic, yet cleanly-written style of Apostol. Standard texts (e.g. Stewart) pull theorems out of the error without proof, as if the point of taking calc is to get it done and over with as quickly as possible.To be sure, Apostol isn't for everyone. If you are fascinated by color pictures and your primary interest is to learn the bare minimum, buy another book. But if you want to get more out of your undergraduate calc, whether you're a math or science major, or you're studying on your own (I meet both criteria), Apostol is the way to go.
This is a must if you're thinking of taking any higher math. Worth the bucks, it'll save you in the long run.
Book Review: Value in Diversity
Summary: 5 Stars
Apostol's presentation differs from the standard order and content for a calculus course, but is the more useful for it. Introducing integration first is historically more accurate and sets the tone for the rest of the book. This is not a "plumbers" book but the examples inform the abstraction very well. This book does not bog down in the tedium of analytical geometry and figure recognition which is too often the case elsewhere.I am using the book for self-study as a middle-aged adult and find the presentation makes sense of things from other sources. The intellectual level is demanding but not unreasonable--challenging without being overwelming. While the introduction of linear algebra may no longer be needed for introductory calculus students, presenting it in the context of the calculus ties thing together nicely.
Book Review: Where Does It Fit?
Summary: 3 Stars
I like this book, but I will not use it as my choice for textbook. The modern approach is to seperate the subjects covered by this two volumes back to where it belongs. Linear Algebra should not be taught in Calculus per se. I don't favor integration first, defferentiation later particularly. For science and engineering classes, I recommend Stewart's for lesser workload classes or for science students, Swokowski's for heavier workload classes or for engineering students, Spivak's for math students or science students. I found Tom's book is not suitable for entry-level students. My question is why repeat again for advanced student? Teach them other subjects by specialized textbooks. Tom's does not fit into any of the scheme. In marketing term, this book has no market nitch. It belongs to the library as reference book. Again, there are many much better written books than Tom's. For math students, they can move on after either Spivak's or Stewart's to Rudin's Principles of Mathematical Analysis or Marsden's Elementary Classical Analysis, then, to Royden's Real Analysis for Lebesque Integration and Measure Theory or Rudin's Functional Analysis for Operator and Spectral Theory in Banach and Hilbert Space. Linear Algebra has two trails. For science and engineering students, Strange's is the choice for its modern computer concept and application. For math students, Peter Lax's is better than Tom's. Where does this book fit? It was once the choice of textbook for advanced students. Now, many things have been changed ranging from students' math level to computer application to the cruching of middle layer in math education. Today, Topology is no longer taught as a seperate course. It has been crushed into early section of Analysis course followed by Differentiation, Integration and Measure Theory. If you have $200 to buy Tom's book (2 Vol.) and follow his other book to Mathematical Analysis and you have plenty of time to study and do its homework with a very good reader to correct them for you, yes, you can consider to buy it. If you are on a fast track to broaden your exposure in modern math, forget about it! Your time can be put into better use. Enjoy sunlight and your life!