Customer Reviews

Advanced Calculus (4th Edition)

5 star:		(10)
4 star:		(1)
3 star:		(3)
2 star:		(0)
1 star:		(4)

 

 

This book is simply the best that I have found for math texts. Kaplan does not expect much from the reader; he explains basically everything besides Calculus I material. Kaplan's writing is lively and is (relatively) easy to read. He gets to the point and keeps everything easy to follow. I am still in awe about how much material (look below) he was able to fit into this relatively small book and still keep it so clear. The examples are clear and concise. The problems in the book compliment the understanding of the material; they start out easy and guide the reader to do more difficult problems. This book is MORE THAN SUFFICIENT FOR SELF-STUDY.

Contents: Linear Algebra, Partial Derivatives, Vector Calculus, Multiple Integrals, Sequences and Series, Fourier Series, Complex Variables, and Ordinary/Partial Differential Equations. This is a conservative list.

The price may appear steep, but the content and clarity of this book more than make up for it.

Any student who is taking analysis/advanced calculus course should read chapter 2 of this book, especially if he is confused or is struggling on the excellent but relatively abstract/concise texts of Rudin, Apostal, Bartle, Marsden et al. I've never seen a book which can explain the concept of Jacobian and Inplicit function theory in such a clear way!!

Although my regular textbook is excellent(Larson, Calculus,7th edtion), but there are just ideas and theories which are not explained or expanded. I love Kaplan's Advanced Calculus for the following reasons:
1. It is very logical, everything goes step by step. If there is anything you have not learned or have forgotten, he refers you to specific earlier sections. And if there is something he does not explain, he refers you to other resourses.
2. The book is lean and super clean. Although I do appreciate our regular textbooks's wordiness which is great for a beginner like me, I also love reading this book which goes straight to the core.
3. While some books look lean but are actually dry and really hard to chew, this book is easy to follow. And it really gives you a feeling that you are learning math, you are not just learning some techniques.
4. Even though there are a couple of out of date notations like a reviewer has pointed out, like he writes "ln" as "log", but it really does not interfere reading and understanding.
In short, the book is a gem, every page is worth its paper.

I learned from this book during my sophomore year advanced calculus class. The best thing about this book -- answers to all the problems are included. What a novel idea -- answers! I can't speak for others, but I can still remember doing problem after problem from this book and knowing that I could always check my understanding, or lack understanding, of the material by checking my work against the answers.

As to why do I think this book is for engineers and non-theoretical science majors? Very simple, it does *not* cover real analysis as the books by Rudin, Shilov or Johnsonbaugh and Pfaffenberger (my favorite). These other books follow a very traditional approach -- axioms, lemmas, theorems, corollaries. Kaplan's book presents all the mathematics that an engineer, etc. will typically need and with a clear explanation. You won't find delta-epsilon proofs here, but you will find multi-variate calculus, vector differential and integral calculus, orthogonal functions and expansions (Fourier series), complex variables, and ODEs and PDEs. Everything is covered. The explanations are generally very good. There are examples, and of course, answers to the problems are included.

You can think of this book as a Schaum's Outline on Advanced Calculus, but with real explanations, not just statements. I'm not knocking Schaum's Outlines. I own several of them.

I study this book entirely in a calculus review. The points are:
1- The exposition is clear and didatic even in points difficults and delicates
2- The sections are short and with exercises in growing level of dificulty with much adequates hints
3- It's necessary to resolve all (or half all) exercises because there are many new stuff there
4- There are responses to all exercises with is good for self study (like mine)
5- There are very litlle typos
6- My only question is that the book would have more exercises
(I supply this doing exercises of other books like M.Boas)
So I recommend this book based in my (good) experience

This is *the* book for learning advanced calculus. It covers calculus of several variables, vector calculus, infinite series, fourier series, functions of complex variables, conformal mapping, PDEs, and applications. The book is highly readable for those with a background in calculus/linear algebra (even though there is a preface section on linear) and I believe it would be fine for self-study. If/when questions do pop up, there's always #math on IRC EFNet!

This text gives a much deeper treatment than what is found in the typical undergraduate textbook for Calc I, II, and III. I would recommend it especially for engineers and physicists who want a much deeper understanding of multivariable calculus without necessarily learning to prove everything, and I would recommend it for advanced math students who want to build some more intuition about calculus before trying to plow through a basic analysis text like Rudin's Principles of Mathematical Analysis.

I have used the earlier edition of Kaplan's excellent text on Advanced calculus from early 1960's...I have studied and taught this subject and I always like to refer to this book....excellent and solid foundation in advanced caluculs for any student

This is the absolute worst mathematics book that I have ever attempted to use. I would rather stick my head in a vise than try to learn anything from this book. Here are the four of the worst offenses:
1. The book is not self-contained. One must constantly refer to other books to work the exercises. Write a complete book next time, jerk.
2. If "mathy" were a word, it would describe this book. Where are the applications? You won't find anything practical here. Boring!
3. How about some examples? That would be nice. Unfortunately, examples are few and far between. Think water in the desert.
4. How about some organization? Nope, you won't find it in this book. It will lope along for several sections, then "Boom! Here are some random exercises. Good luck! I hope you've understood everything perfectly until now, cause this is comprehensive, baby!"
This book is required for my class or otherwise I would throw it into a cesspool. When I'm finished with my class that's just what I will do.

I bought this book with a simple aim: I want to self-study the calculus of multivariable AGAIN, something that I have forgotten and, sad to say, never mastered before. After browsing for other books I picked this one because i) this book has a pretty good review score ii) the author Wilfred Kaplan.

Unfortunately, my decision is not really good.

This book first introduces the vector and matrics, then begins with differentiation calculus of several variables, followed by vector differential calculus. Next it talks about integration (integral, vector). The second half of this book discuss infinite series, fourier series, complex variable and differential equations (both ordinary and partial).

After reading the first 3 chapters I realize some difficulties. Firstly, I don't really think the author is good at presentation. There is too much words, too much formulae and you just can't grasp the idea. Secondly, there is a lack of examples. I am not a genius and I need examples for illustration. I really need examples for illustration. Thirdly, there is no demonstration of practical use of the theorem/formulae. It looks like a calcules "dictionary" rather a textbook.

I don't know. Maybe mathematics books are all like this. But if you have seen some good books before, you probably feel the same as me.

My recommendation is: this book is for course, not for self study.