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

As a seventeen-year-old sitting in physics class, I remember staring at a board full of kinematic equations. The goal was to memorize the formulas and learn how to apply them. But when test day came around, I had forgotten all of them. Memorization has never worked well for me. What stuck with me wasn’t the formulas, but the moments when I actually understood why things worked. That’s why I really appreciated how this book handled similar topics. Unlike my high school physics class, Kline doesn't just present formulas—he builds them from first principles, showing you how they come to be. It’s not about memorizing a cookbook full of calculus recipes; it’s about really getting it. This book shines when it comes to differentiation and integration. Kline takes you on a journey through the ideas, not just the mechanics. He even gives you a taste of partial derivatives and vector calculus. You can think of it as covering traditional Calculus I and II, but with an intuitive, big-picture focus. If you’re like me—someone who learns by understanding rather than memorizing—this book might be exactly what you’re looking for. It skips some of the formalism, but in exchange, it gives you a lasting, intuitive grasp of calculus. Don’t expect Spivak level formalism though. It may cut corners to convey intuition.

***On the Book I already have taken basic calculus courses not that long ago, so I used this book more for reviewing and "honing" purposes, and I couldn't be more pleased with it. The author details many derivations that were skipped in my calculus courses, for example the derivatives and integrals of inverse trig functions, the formulas of which us clueless students were forced to memorize. After reading this book, never again would I have to futilely batter my brain cells in the frantic search for a formula I was not able to retain - this is the best quality about the book. Ordinarily, students would be taught math (or any other subject) in a way that would induce them to score well on tests. This technique is shallow and often cuts corners, as some steps are left out for fear that it may confuse the test-taker, who inevitably takes his test unthinkingly. Kline's [the author] teaching philosophy is different. He sets out everything in detail and with clarity, so that the student may himself solve problems without resorting to formulas or hoping that test problems would not differ from the drills he has solved. Furthermore, the practice problems in this book are engaging, and Kline has take great pains to show how every mathematical technique can be used in real life. Some of his practice problems also asks that the student prove some thing or other (it is not all application), and this allows the principle to further sink in the brain. A solutions manual is not included in the book, but may be requested, for free, from Dover. The details of how to do this is described in one of the front pages where the copyright information is found. The solutions manual could also be found in Dover's website. It is in pdf form and is something like 250 pages. The solutions in the solution's manual do not merely list the correct answers. It also describes how to get to that answer. There are some typos, so there may be moments when no answer of yours would be correct now matter how and how many times you get at it. I do not believe the typos are anything major, since it can be obvious when something is a typo. Besides these atypical moments, the solutions manual could be regarded as having the infallibility of God, and with inducing the same soul-enriching effects. Some people may complain about the wordiness of this book, but the "wordiness," in my opinion, aids in the understanding: it is a blow-by-blow description of the proofs and model problems. It could be skipped; I mostly don't. I highly recommend this book. ***On Amazon: I have already bought a book from Amazon before, purportedly new, but when I received it, its spine was wrinkled, a fabrication error I suppose. It was also evident from a number of other minor damages that Amazon does not take good care of the books in its store. The book was far worse-looking than many of the used books I bought from outside sellers. Now, I bought another book from Amazon, this one, and it was no surprise that it was worn-looking and evidently manhandled by whoever was in charge of Amazon storage. I was willing to overlook that, what I can't abide by is the stains I found on pages 347-351, and goodness knows how many more stains and surprises lie in wait. Is Amazon trying to pass off used books as new? I am sick of how Amazon handles its products.

I felt obligated to write this review, because as a good but rusty math student, I would like to help others find the right book according their own needs. First, back in my day, I studied 4 semesters of Calculus in college and considered myself to be good at math at the time - but that was 30 years ago. After my high school daughter came to me asking for help with deriving functions, I was in search of a primer that would be more comprehensible to me than her school text book. I ordered this book and was sadly disappointed at first. It is long, with small print and almost philosophical about math. I found it to be no better than her class text book when it came to reminding me of the rules for deriving functions like the product, quotient and chain rule. I ended up ordering a book with the word "dummies" in the name though I won't say exactly which one and that suited my purpose immediately. In 30 minutes it all came back to me and I was able to sit and help her understand the basic concepts at a high school level and work through homework problems. Now back to this book - the next day I picked up this book again and began reading it without the pressure of needing a quick, to the point answer or lesson. I began to read it, not as a text book, but more like an academic novel about math and that is when things started to click. It gave me a new appreciation for why calculus is important, how the derivative is not just the slope of the tangent, but the direction of a line at any given moment and why that is important to motion, targeting moving objects (military applications) and light striking lenses (optics). Ah, that is very cool stuff to wrap ones head around after many years of work that required little more than a 5th grade education in my corporate IT job! Given my new appreciation of this book, I will be reading more as I hope to understand concepts and drivers behind more advanced math concepts - both as a reminder of what I forgot and for new enlightenment. I don't expect to use this book to advance my own problem solving capabilities - although it may help in that respect too - but rather to gain a more enlightened appreciation for Calculus. The book includes exercises and problems along the way as well as answers for about half of them - an excellent complement to help one confirm they're grasping the material. In summary, I would not recommend this book if you're new to Calculus or trying to get through a high school or college level course - but if you're a advanced math major or even an old guy who wants to get a better appreciation - almost an academic, theoretical or philosophical appreciation - for advanced mathematics then this is the book for you. Just don't use it as a primer to help your impatient high schoolers and who need quick answers and bulleted minimalism.

Un libro muy completo que enfoca el aprendizaje del cálculo de la manera en que fue concebido, rompe el esquema tradicional de fórmulas y orden en el que se enseñan los diferentes temas en curriculum académico, proporcionando una base mucho más sólida para entender futuros temas en las diferentes aplicaciones de otras materias. Recomendado para nivel bachillerato y licenciatura.

Il testo è validissimo anche se certamente datato. Tuttavia lo consiglio a chiunque voglia farsi un'idea del come si trattava l'analisi nello stile puramente anglosassone che ritengo comunque didatticamente molto valido anche se lontano dallo stile tenuto nelle università italiane.

Excelente material para estudo detalhado do Cálculo numa abordagem intuitiva e perfeita para o aprendizado e revisão de conteúdo autodidatas. Indico fortemente Calculus - Morris Kline

Comment font les anglo-saxons pour être aussi clairs, pédagogiques et pour donner envie de faire des maths et de la physique? Si vous voulez le savoir lisez le bouquin du prof. Kline (également auteur édité par Dover d'ouvrages sur l'histoire du Calculus). Le livre traite du Calculus comme l'appellent les anglo-saxons, en gros le cours d'analyse de 1ère année de fac mais avec des compléments sur les coniques, la géométrie analytique et surtout des tas d'applications en physique ou en économie. On est toujours guidé, encouragé à continuer, toutes les notions sont introduites dans une perspective utilitaire et en expliquant pourquoi on s'est intéressé à développer ces concepts. Si vous vous êtes demandé en cours de maths "mais où veut on en venir?" le bouquin est fait pour vous. En plus un anglais facile à understand et pas cher, comme toujours chez Dover: moins de 25e pour plus de 900 pages.

Morris Kline is amazing. He knows how to really teach. There are too many mathematicians/physicists writing texts that gatekeep those who aren't already at their level. What's the point of teaching if you don't want 100% of your students to learn (not necessarily ace) enough so that they understand the WHY and not just from an "that's just how it is". Teaching a subject intuitively reduces the friction that one gets as they progress to higher maths, because you're able to connect the tools, concepts and techniques as well as understand why such tools were created in the first place. Math arises out of the need to understand physical phenomena. Sure, there are those who do math purely for the pleasure of mental gymnastics but that's their own field to play in. I'm a physics undergrad and I wish I had read this first before the stuff they had us go through in uni. It would have been much easier for me to employ the math in physics studies. Diving right into rigorous texts is a disaster, and only benefits those who have already learned the subject prior. That is a position of advantage. In my opinion, rigorous books only serve to train your comprehension of advanced academic texts and should be tackled in the second year of undergrad at the earliest. On the other hand, other calculus textbooks are oversimplified, which is the again a disastrous way to introduce calculus. Thanks to this book I get the chance to relearn calculus but better equipped this time. It's perfect for self studying and reads in a very natural way.