Calculus: An Intuitive and Physical Approach (Second Edition) (Dover Books on Mathematics

8 reviews for Calculus: An Intuitive and Physical Approach (Second Edition) (Dover Books on Mathematics

1. Julie_Smith<span class="a-icon a-profile-verified-badge"><span class="a-profile-verified-text"></span></span>

   Rated 5 out of 5

   March 19, 2023

   5.0 out of 5 stars Best ever

   I was able to teach my 12 year old daughter calculus with this!!!

   Helpful? 0 0
   Israel

   Rated 5 out of 5

   March 15, 2023

   5.0 out of 5 stars Unique approach

   This explains math using the physics that was used to create the math. It does ask you to solve your own problems (And often figure out what the probl...More

   This explains math using the physics that was used to create the math. It does ask you to solve your own problems (And often figure out what the problem is to begin with).
   This is some of the most fun I've had with a math textbook.

   Helpful? 0 0
   Chris Watson

   Rated 5 out of 5

   August 11, 2022

   5.0 out of 5 stars Excellent for a refresher or as a reference

   I first took calculus over 20 years ago and always did well in math, so I wanted a text that I could keep as a refresher (for studying more advanced s...More

   I first took calculus over 20 years ago and always did well in math, so I wanted a text that I could keep as a refresher (for studying more advanced statistics) and reference for things I may have forgotten. So my experience with the book may differ from someone who has never been exposed to calculus before. In my opinion, this book is an excellent introductory text for single variable calculus. While it is a bit dated (it's a reprint from 1977), given its low cost, compactness, and how comprehensive it is, I think its value is unbeatable (especially compared to current university calculus texts).
   
   While there *are* some drawbacks/negative aspects, I think they're pretty minor but they should be pointed out either way:
   
   1) Typos -- there are a non-insignificant number of typos throughout. Some of these are trivial to spot, while a few were in the answers to select exercises. I spent time scratching my head trying to match the printed answer when it turns out there was a typo. This might be a bigger concern for absolute beginners.
   2) Graphics -- the figures are clearly very dated and don't have captions. However, this isn't really a problem until the later chapters on functions of more than one variable, and even then I thought they were clear enough.
   3) Content -- I found the book a bit verbose in some places, but this may be more appreciated by a beginner. Also, if you will never take introductory physics, you might struggle with or be frustrated by how many of the examples and exercises are specific to physics problems (even though this is, historically, how calculus came about).
   4) References -- since the book is so long, it would have been nice if the author included page numbers when referring back to a particular chapter/section/equation. He sometimes does this, but it isn't a big issue.
   
   Overall, I don't think anyone who will need to use calculus would be disappointed in having this book around. There are chapters and sections marked as optional, a comprehensive list of integrals of different forms at the back, and the author explains concepts intuitively. For the most important theorems and ideas, I use post-it tabs for quick reference.

   Helpful? 0 0
   Dr. Terrence McGarty

   Rated 5 out of 5

   June 18, 2017

   5.0 out of 5 stars Great Classic for Everyone

   I got this for my grandson who is off to University and studying Civil Engineering. It is a classic, very reasonably priced, and presents calculus in ...More

   I got this for my grandson who is off to University and studying Civil Engineering. It is a classic, very reasonably priced, and presents calculus in a classic manner. Frankly why one would spend $250 for a calculus book weighing fifteen pounds and containing more pictures than the Louvre I do not know. This is a substantial book but it is superbly organized and covers calculus in a manner that meets the needs of the engineer, scientist and perhaps the budding mathematician. It is an applied approach however. The organization is perfect, introducing one element logically atop the other.
   
   I would recommend that any engineering or science major have a copy of this to see how "it is really done" after the spend the large sums demanded by someone, often not the Professor, unless they are the author as well!

   Helpful? 0 0
   Seong Kook Shin

   Rated 5 out of 5

   July 20, 2015

   5.0 out of 5 stars I always want to understand lots of mathematics better, especially on Calculus

   Having inferiority complexity, I always want to understand lots of mathematics better, especially on Calculus. I bought several books on this topic, ...More

   Having inferiority complexity, I always want to understand lots of mathematics better, especially on Calculus. I bought several books on this topic, but because of short of my free time to study, I couldn't advanced in my calculus skill. In my country, basic calculus is for high-school students. It has some merits compared to other countries whose students learn the calculus on their college life, but has a serious defect; making the student lose the interest to mathematics due to the scoring policy. Thus, I know how to solve/simplify complex equation, how to solve differentiation, and so on, but never fully understood the meaning of them.
   
   Reading this book (I admit, that I just finished to read Chapter 7), brought me the enlightenment of the differentiation and integration, especially the concept of calculus, not just how to solve them. I know other great books on calculus especially for the students. However, being a person who has limited time to study, this book shines above all. (Even for non-English speakers like me.)
   
   There is one minor defect I think, like many mathematics books, it refers to other section and figures in a different pages a lot. Thus it prevent me from reading smoothly sometimes. Most of equations are rendered as images with reasonable size and resolution, so it does not cause problems, although they look somewhat ugly.

   Helpful? 0 0
   Jack

   Rated 5 out of 5

   November 5, 2013

   5.0 out of 5 stars Best calc book I have found yet

   I have only been back into math for the last year after taking a 5 year break. Long story short, I had to build up from prealgebra (PEMDAS!) and now I...More

   I have only been back into math for the last year after taking a 5 year break. Long story short, I had to build up from prealgebra (PEMDAS!) and now I am halfway through a brutal semester of calc. I purchased a few other calc help books but they are either too watered down or overly wordy. This book strikes a very nice balance that text books don't achieve any more. Plenty of pictures, down to earth talk, very detailed explanations, and it even shows you how to derive the equations and the thought process. Used with wolfram alpha, these are a very good combination of tools
   
   Edit: 1 Feb 2013
   
   I am now in Calculus for Engineers which is considered to be a combination of Calc 2 and 3 in one semester (with a little bit cut out). I am still using this book in conjunction with my schools textbook and I often find myself referring back to this one when learning a new concept. I prefer to use the school textbook for problems to work through as they will most likely be similar to the one on the schools exams. I am averaging a 95% in the course so far and considering I had to build from the basics, I think I am on to something. If you are serious about learning Calc, this book is only $20 and college text books range $100-200 easy.

   Helpful? 0 0
   Methaya Sirichit

   Rated 5 out of 5

   August 3, 2010

   5.0 out of 5 stars Should I learn calculus from this book?

   I am currently working through this book. Other reviewers have mentioned all the good points and features of this text. However, given the text is 920...More

   I am currently working through this book. Other reviewers have mentioned all the good points and features of this text. However, given the text is 920 pages long, the reader would normally be required to invest a lot of time working with it. With that in mind, it is natural to ask the all important question: whether this book is really for you? My answer is that it depends on your mathematical backgrounds.
   
   As we know, Kline's approach to this book is intuitive. Kline argued that "intuition" is the way human's mind learns things; and he is right on. Especially with calculus whose essence being a collection of "mathematical methods" fundamental to the understanding of physical world. To study these mathematical methods without understanding or appreciating the physical problems or applications which gave birth to their (the methods') development is therefore meaningless and shallow. On this point alone, Kline's approach is a first rate introduction to calculus. On the other hand, Kline's text despite being quite thick never progresses beyond these intuitive functions; instead Kline spends a lot of space discussing elementary topics like analytic geometry and application in economics or examples from Newton' Principia. Very interesting of course, but one cannot find a rigorous discussion of functions or imaginary number or convergence of infinite series, all of which are essential basics for those who would progress to higher courses in analysis. An important question that it raises is: to whom this text is actually for?
   
   My answer is that Kline's text works best for either those whose high-school math backgrounds is in a pretty bad shape but want to know calculus or for those who have learned calculus a long time ago and are now in a "serious need" for some brush-up. Also for certain high school students who like physics but have never been at home with math, this book is really the missing keystone. There are many other good texts out there like Spivak's or Apostol's or Hardy's Pure Mathematics. These are ideal for college students whose high-school math is still fresh and strong and thus are more able to appreciate deeper/advanced topics like the foundation of number system or analytical treatment of functions. For these students (especially pure-math B.S. students), calculus texts that gear toward analysis (i.e. more rigorous) would better prepare them for future challenges. However, for people like myself, whose math education ended 14 year-ago in high school and who barely remember the cosine rule, working through texts like Spivak's or Hardy's simply lead to a bogged down. It should be remembered that Kline's calculus, first written in 1960s, was introduced during the time when most students were not exposed to calculus in high school. Thus, it was quite a problem when they had to encounter calculus for the first time in college. Back then it would be quite a blunder to demand that kids have to learn both techniques and rigorous foundations of calculus, the first truly "higher math" they ever encountered, at the same time. I think Kline's text was written especially to remedy that problem. However, as most kids of our time are all exposed to fair amount of "intuitive" calculus in their school years, it may not make much sense to require to learn intuitively again in college. Still, I would maintain that even good students would profit much from at least taking a look at Morris Kline's text, for it develops the subject in a strong historical context and is quite broad in the materials covered.
   
   All things discussed, this book is a truly 5-star treatment of calculus. Given the state of education and teaching in our times, no one might ever write like this again.
   
   [Note: PDF file of solution manual (about 260 pages) can be conveniently obtained by writing to Dover Publication. Great job! Dover, for making this book available and affordable at the same time.]

   Helpful? 0 0
   Kersi Von Zerububbel

   Rated 5 out of 5

   September 14, 2009

   5.0 out of 5 stars A classic, non-rigorous introduction - old world style.

   If you have the time, patience, and the inclination to get a strong introduction to Calculus then this book will probably meet your needs. Note I say...More

   If you have the time, patience, and the inclination to get a strong introduction to Calculus then this book will probably meet your needs. Note I say 'probably' because for many of the young folks today the text may seem wordy and overly pedantic. Kline forfeits the graphical techniques of learning for the verbal. So one has to carefully follow the explanations. Later in the book graphical explanations for things like differentiation are explained.
   
   So if you expect a fast paced text like say 'Calculus for Dummies', 'How to Ace Calculus' etc you will be disappointed. What I found helps is to get going with some modern quickie texts like Dummies etc and then go with Kline's work. This helps firm up some theory instead of just learning the mechanical stuff. Also, as others have pointed out, but this needs to be mentioned, the answers to problems can be obtained via a PDF from Dover. They answered my email promptly.
   
   If you want a good reference for introductory Calculus without say the rigor of Apostol's text this is a great investment that should serve you for years to come. Excellent textbook.

   Helpful? 0 0