Numerical Mathematics (Texts in Applied Mathematics Book 37) by Alfio Quarteroni (PDF)

Description

The purpose of this book is to provide the mathematical foundations of numerical methods, to analyze their basic theoretical properties and to demonstrate their performances on examples and counterexamples. Within any specific class of problems, the most appropriate scientific computing algorithms are reviewed, their theoretical analyses are carried out and the expected results are verified using the MATLAB software environment. Each chapter contains examples, exercises and applications of the theory discussed to the solution of real-life problems. While addressed to senior undergraduates and graduates in engineering, mathematics, physics and computer sciences, this text is also valuable for researchers and users of scientific computing in a large variety of professional fields.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐I’ve been using this book in an intro to numerical math course at the graduate level. It is the only textbook for the course, and it leaves some to be desired. A number of the sections are very clear and well-written, and it makes understanding the material a breeze. However, there are as many sections that seem to have been thrown together and only provide a cursory glance at the ideas involved, but lack examples and implementations. Those sections sometimes lack enough information to “fill in the gaps” as would be expected at the graduate level, so after reading it, the reader is left with a hazy “30,000 foot view” of the solution and very little else to grab on to. The notation is sometimes confusing and undefined. There is a particular example on splines that uses non-standard notation for characteristic functions, which left everyone in the course confused about what was even being asked. It also uses some strange methods in the Matlab code that require some tweaking if you aren’t careful. They were certainly written in a FORTRAN style. So I have a split opinion of this book. When its good, its really good, but when it misses the mark, it really misses the mark. So I give it 5 stars for when it works, and 1 for when it doesn’t, so my net score is 3 stars.

⭐1)I do not like that the book uses some technical terms without defining them first. There is one word: “stencil” which the book uses once and it appears in the index, but the authors never talk about the meaning of the term in numerical analysis. They assume you know already everything in some sections.2)In the section on finite differences formulas, which I used in my coursework, they even say “we easily get” and show the formula for the centered difference second derivative without explaining clearly how to get it. The book is advanced, and not intended for learning basic concepts in Numerical Analysis. For technical matlab programs, and as a reference it is ok.

⭐Too theoretical for a person moving into math, but extremely broad and in-depth.

⭐A hefty tome of numerical mathematical knowledge. Rather like religious text in some sense: comprehensive and final, but difficult notation makes it hard to decipher the meaning in places.

⭐Every page of this book is written like an extended mathematical proof. It can be daunting if you’re not accustomed to this type of text.

⭐The book satisfied the purpose and I couldnt have asked for anything else. It was the right edition and good quality.

⭐Prompt delivery, item as described

⭐Reference book rather than a textbook. But a good reference book.

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