Numerical Analysis by Larkin Ridgway Scott (PDF)

Description

Computational science is fundamentally changing how technological questions are addressed. The design of aircraft, automobiles, and even racing sailboats is now done by computational simulation. The mathematical foundation of this new approach is numerical analysis, which studies algorithms for computing expressions defined with real numbers. Emphasizing the theory behind the computation, this book provides a rigorous and self-contained introduction to numerical analysis and presents the advanced mathematics that underpin industrial software, including complete details that are missing from most textbooks. Using an inquiry-based learning approach, Numerical Analysis is written in a narrative style, provides historical background, and includes many of the proofs and technical details in exercises. Students will be able to go beyond an elementary understanding of numerical simulation and develop deep insights into the foundations of the subject. They will no longer have to accept the mathematical gaps that exist in current textbooks. For example, both necessary and sufficient conditions for convergence of basic iterative methods are covered, and proofs are given in full generality, not just based on special cases. The book is accessible to undergraduate mathematics majors as well as computational scientists wanting to learn the foundations of the subject. Presents the mathematical foundations of numerical analysis Explains the mathematical details behind simulation software Introduces many advanced concepts in modern analysis Self-contained and mathematically rigorous Contains problems and solutions in each chapter Excellent follow-up course to Principles of Mathematical Analysis by Rudin

User’s Reviews

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

⭐I bought this book to use in the author’s class at UChicago. I would recommend finding a different book as an introduction to numerical analysis.While it is a very thorough mathematical treatment, and lots of proof exercises, it has virtually no “pencil-pushing” exercises, making it hard to ground and retain the knowledge earned. The book also contains dozens of typos.

⭐An outstanding resource. Provide an almost readable way to understand how numerical methods can be analyzed using mathematics.

⭐I bought this book to lighten my back pack, since I have a copy of the paper version. I think that this is a wonderful book, but the publisher did not do a good job of producing the Kindle edition. If for example you look at Chapter 6, you will see that the norm symbols are just omitted; you can just guess what the results might mean. Since I did not need to look up something in the book until I had it a few weeks, I cannot return it, even though it is clearly defective. I am not a happy camper.

⭐Kindle edition is riddled with errors. You are better off purchasing the text or going and getting the PDF version for free.

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