|
Title: Calculus: An Intuitive and Physical Approach (Second Edition)
Purchase
Item
Manufacturer: Dover Publications
List Price: $26.95
Our Price: $16.50
|
|
| Customer Reviews: |
| Calculus: An Intuitive and Physical Approach (Second Edition) by Dover Publications Great teaching book | I started using this book as a review several weeks ago and so far am very happy with it. I am currently working through n book on tensor analysis and calculus, and found some of my old calculus and advanced calculus background not quite up to the task since it had been many years, so was looking for a painless way to review some of the concepts, and this book turned out to be a good choice.
Dr. Kline spent his whole life being passionate about teaching mathematics, and it shows. It does use a more intuitive approach, which Dr. Kline points out is far more appropriate than the rigorous approaches in an introductory book on calculus. He points out that the more rigorous ideas of uniform and nonuniform convergence, limits, and continuity, which are the basis for calculus, eluded the greatest mathematical minds for 200 years, and yet new students are asked to understand them in many basic calculus books. Dr. Kline thinks this approach is wrong and so concentrates on a more intuitive approach. He points out that even the great Cauchy, the founder of rigor in the mid nineteenth century, didn't get all of these concepts right himself. I think it works much better and makes the book much more enjoyable.
The coverage is very complete with clear, concise discussions of all the topics. At over 950 pages, this is a lot of material here for the price. I already had Dr. Kline's book, Mathematics for the Non Mathematician, and liked that, so when I was looking for a review, I was influenced to get this one out of a number of recent calc books, such as the Dummies series. Dr. Kline also feels that the best way to motivate the study of math is to show its practical examples rather than just show purely mathematical concepts. I am okay with either approach as long as the discussion is easily understandable, having suffered through numerous books that weren't in my long and checkered career of trying to teach myself more math since I left grad school. Overall, a fine book on the subject that accomplishes its stated goals. | | Calculus: An Intuitive and Physical Approach (Second Edition) by Dover Publications Disappointing text, some good applications | | When it comes to explaining the basic theory and techniques of the calculus this book is essentially no better and no more intuitive than the usual low-level introductory books; it comes with the usual quasi-pedagogical idiocies, such as guessing limits from numerical calculations and so on. The word "intuitive" in the subtitle is misleading (at least to me, "not formal" does not imply "intuitive") but the word "physical" is more justified. There are indeed quite a few interesting physical applications. One interesting application, known already to Newton, is this: dig a straight, friction-less tunnel from New to Paris; then if you jump down the hole in New York you will arrive in Paris about 43 minutes later. Another interesting application is projectile motion with air resistance. Assuming that air resistance is proportional to velocity, F=-Kx', we find that F=ma reads x''=-kx' for the horizontal component and y''=-g-ky' for the vertical component (k=K/m). With initial firing velocity v and angle A the solutions are x=((v cos A)/k)(1-e^(-kt)) and y=-gt/k+((v sin A)/k+g/k^2)(1-e^(-kt)). These formulae allow us to make some qualitative comparisons with ordinary parabolic motion. Also, an interesting special case is pure vertical motion where we have my''=mg-Ky' so y'=-(mg/K)(1-e^(-Kt/m)) and so the limit velocity of a freely falling body is -mg/K. Another application is pendulum motion. We wish to find s(t), the elevation of the pendulum measured along its arc. The force involved is the component of gravity that pulls in the direction of the tangent; this is -gm(sin A), where A is the swing angle, so F=ma says ms''=-gm(sin A). But sin A=opp./hyp.=(horizontal displacement)/(length of pendulum L). Now here's the trick: horizontal displacement is kind of equal to displacement along the arc, i.e. s(t), at least for small A, so we get s''=-(gm/L)s, so a solution is s(t)=C*sin(sqrt(gm/L)t). Another application is escape velocity. The quantity (mv^2)/2-G(Mm/d) is seen to be constant ("conservation of energy") by differentiation, and if we have just enough initial velocity to escape to d=infinity we will get there with zero velocity v=0; plugging in these conditions we see that the constant is zero, so we can solve for initial velocity, which will be sqrt(2GM/R). | | Calculus: An Intuitive and Physical Approach (Second Edition) by Dover Publications Ok class, Calculus is hard if you didn't already know it! | | In general I like the book. But to offend the author think he must save you by saying this part is hard, I'll give you more details later. I found I skipped some part becuase of to much blah, blah. If you never have taken Calculus it's just as good as any text. It won't make learning calculus any easier. For a reference piece it's a good addition to your collection. | | Calculus: An Intuitive and Physical Approach (Second Edition) by Dover Publications Do you really wanna know what Calculus is, get this book then ... | I just want to learn Calculus in an application point of view from my school. During the time, when preparing for the college Entrance Examination, the solution suddenly contains Integral Calculus without me knowing the reason on why they have used that.
I picked up some book to equip myself with Calculus and all the book starts with limits with its formal definition, which leave me spellbound ...I will ponder over the same for some days to get what they mean exactly and leave it for later, but this book touched the concept of limits only in the 800 and odd pages. Till then you will be learning Calculus and applying it INTUITIVELY ...
This is THE book for person who would like to learn Calculus ...great work Kline ... | | Calculus: An Intuitive and Physical Approach (Second Edition) by Dover Publications Where do I start? | | I wish I could give this book 10 stars. I made a "D" in my college Calculus class. It wasn't that I didn't understand how to do problems or didn't try, it was that I didn't know WHEN to apply what I knew to certain problem sets. This is your answer. Kline explains in detail (without getting too deep) WHY, WHY we use limits, WHY we differentiate, answers my Peruvian Calculus teacher never answered. I can't even begin to tell you how excellent this book is! The problem sets are intuitive, based in reality, and are applicable to me! After doing problems in this book and making it to where we left off in Calc I, I bought my old Calc book that we used in class. No wonder! I wish that more textbook authors took the time and made the effort to make sure that their materials is as clear and concise as Kline has. His explanations are obvious, he doesn't skip steps, and he works with simple numbers (base 10s) so that you understand WHY and HOW. His problems get progressively more difficult, which is awesome, because it gives you the confidence that you know what you are doing once you have finished the problem. If you have a hard time with Calculus or you just want something to do, BUY THIS BOOK. It is an excellent resource and an excellent textbook. | | Calculus: An Intuitive and Physical Approach (Second Edition) by Dover Publications Product Description | Application-oriented introduction relates the subject as closely as possible to science. In-depth explorations of the derivative, the differentiation and integration of the powers of x, theorems on differentiation and antidifferentiation, the chain rule and examinations of trigonometric functions, logarithmic and exponential functions, techniques of integration, polar coordinates, much more. Examples. 1967 edition. Solution guide available upon request.
|
No item elements found in rss feed.
|
