Calculus, One-Variable Calculus with an Introduction to Linear Algebra

Rating:
Summary: Where Does It Fit?
Review: 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!

Rating:
Summary: Pretty good explanations!
Review: 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. I'm 12 now, and I am taking Stanford's follow-up course (Multivariable Differential Calculus) which uses the second half of this same text. I like it!

Rating:
Summary: substance w/o the frills
Review: 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. What I appreciate most is his axiomatic approach. He builds up everything as opposed to the numerous calculus cookbooks out there. Every theorem has a proof.

Rating:
Summary: Couple your Calculus with *ENGLISH*
Review: I've only browsed Apostol's Calculus and came here to see what others thought about it. Consider this a review of the reviews: these reviewers may or may not understand calculus, but one thing's for damn sure--none of them understand English. May I recommend Strunk and White's Elements of Style to these reviewers?

Rating:
Summary: take this simple quiz
Review: if you are the kind of student who thinks the area of a triangle is: "Mmmm...(1/2)BH, or is it (1/3)BH? Oh well, who cares, I can always look it up anyway." then this book is probably not for you. But if you have wondered whether the number given by that formula changes when you change which of the three sides of the triangle you call the base, then this book is exactly what you have been looking for. The author of this book assumes you are bright and curious, the kind of student it was written for at Cal Tech. Professor Apostol has made an enormous and thoroughly successful effort to explain in intellectually honest detail exactly what is going on, and how everything is proven rigorously. In this same vein, Spivak's book is more fun, and Courant's has more physics and applications, but this one is the most scholarly. The linear algebra was an afterthought, added to the original work when that craze swept the subject in the 1960's. In general, great works are best in the first edition before the publisher convinces the author to modify his original vision. In my opinion the linear algebra does nothing to enhance the presentation of one variable calculus, and should have been left out, but it won't hurt you.

Rating:
Summary: Excellent Text and Useful Reference
Review: If you're looking for a calculus and linear algebra text with good discussions, useful examples, and challenging-but-doable problems, then this is the text for you. This was my freshman year core math text, and I keep going back to it when I need to refresh or clarify my understanding of the basics. It's the type of text that makes lectures unnecessary. This is one of very few texts that will be irreplacable for decades

Rating:
Summary: CALCULUS
Review: tHERE IS A EXCELLENT BOOK.

Rating:
Summary: Calculus Volume 2 (Tom M. Apostol)
Review: This book contains a lot of information, and is rigorous, with many proofs and a vast array of problems. However, it is weak on worked examples and in explaining the concepts clearly. Diagrams are kept to a minimum. I used this book during an undergraduate Calculus course, and found that it did not help me to grasp the fundamentals of the subject. There are much better books available e.g. Stewart, which cover much of the same ground in a much simpler format. In my experience, only the ablest students were able to benefit from Apostol's dense writing style and scarcity of worked examples. Apostol does, however, include sections on matrix algebra and calculus which are not available in many other textbooks. There are also solutions to many of the problems at the end of the text.

Rating:
Summary: Both joy and nobility of abstract math in this book (V.2)
Review: 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.

Rating:
Summary: Great introductory text
Review: This book was used for my introductory calculus class. Though some reviewers believe that this text isn't suitable as a first introduction to calculus, I didn't have any problems with it, and as far as I know no one in my class did either. Quite the opposite, in fact. The detailed proofs and derivations made material that might otherwise be difficult easy to understand. The introduction of linear algebra before multi-variable calculus (which is covered in volume II) makes some of the more abstract concepts in multi-variable calculus quite straightforward. In general, the proofs are detailed enough for someone with no prior experience in a proof oriented class to understand, but concise enough to not be tedious

Four years after having taken my first calculus class, I still remember how to apply techniques such as taylor series and lagrange multipliers because, rather than just throw out formulas and laundry lists of steps, Apostol goes through derivaions that engender a deep understanding of the mathematics behind the techniques.