I'm reviewing this integral calculus book for Amazon. I had some difficulty understanding it at first but, after reading through the book again and following the examples, it became clear how to use this book. The introduction of Ricardo Asin's integral calculus textbook is quite informative and lucid. If you're looking for a good alternative to Milne's textbook then I would certainly recommend this one. All of the rules that are taught in Milne's text are also taught here with some examples thrown in as well to provide some clarity on just what is being done at each step along the way which proved quite useful when I was having trouble grasping certain concepts from Milne's text. The book does not provide answers to the problems that are provided nor does it provide solutions. The book is organized into three parts. The first part teaches you what an integral is, how to calculate an integral, properties of integrals, and elementary techniques for finding the area under a curve. It also includes some examples of integrals. Much of this part is taught through very informal presentations, which I found very helpful since I didn't have much background in calculus at all to begin with. The second part teaches you how to find the antiderivative of special functions, which was helpful since I needed to know how to find the antiderivative for problems in physics class. The third part teaches you how to evaluate definite integrals using elementary methods. This includes calculating the length of a curve using Riemann sums. This book was written with students who are taking an introductory calculus course in mind. Other texts are more rigorous and mathematical but this book is very easy for anyone with absolutely no background in calculus to use right away. The informal explanations make it quite readable and understandable which I found very helpful when I first purchased it. The examples given in the book are very clear and well explained and provide a lot of insight into how to solve problems and integrate functions. The biggest problem that I found with this text is the lack of answers to many of the problems provided. This yielded quite a bit of frustration on my part when I was working through the textbook for the first time since I sometimes wouldn't know why my answer to a particular problem was wrong. I would recommend this book if you're looking for an alternative to Milne's calculus text or if you're having trouble with any concepts in Milne because this does provide some helpful explanations and examples that help you grasp these concepts more easily than they would be otherwise. This is an excellent book if you are trying to learn calculus or you aren't sure where your calculus knowledge is coming from. If you do not have any background in differential equations or complex numbers then I would recommend that you look into some other resources to help with these concepts. I would definitely recommend this book for an advanced level calculus course. This book teaches the same material as Milne t his is just one of many different options, so it's difficult to say which one is better than the other. However, I think that the format of Asin's book is easier to use for someone who has no background in calculus, so if you want a good alternative this may be a good place to start.
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