Beside providing a foundation in modern numerical-approximation techniques, Burden and Faires' well-respected Numerical Analysis, Sixth Edition, explains how, why, and when the techniques can be expected to work. The authors use real-life problems from areas such as engineering, computer science, biology, and physics to show students how numerical methods are applied. more than 2,000 exercises are included, ranging from elementary applications of methods and algorithms to more rigorous generalizations and extensions of theory. Where appropriate, the text demonstrates how computer algebra systems can be of value in solving these problems. As with earlier editions, this text is designed to give students the preparation they need to pass the Actuaries' examination in Numerical Methods. To that end, the edition includes many more exercises of the type often found on the exam.
As with many textbooks on science, I use this book as a tool (in this case a borrowed tool), not reading the book from cover to cover, but rather using it to read up on whatever part of it I happen to need at the moment. I have certainly not read all parts of the book, but find those parts I have read a nice mathematically inclined description of the central conepts and methods of numerical analysis. The text's focus is very much on the what and why theoretical aspects of numerical analysis, rather than on the how-to aspects of numerical methods in practice.
The book does unfortunately suffer from a lay-out style that seems to have become popular with text books in the mathematical sciences the last fifteen or so years. While the pages certainly look, stylish, clean and modern, I find myself having difficulties trying to get an immediate overview of what is main text, suplementary text, definitions, theorems, examples etcetera.
Once we are past the lay-out issues, the text gives a thorough introduction to the mathematical aspects of numerical problem solving. Despite its thickness, the book does not waste space by endless babbling the way many American textbooks tend to do, but gives a fairly succinct account for its material, while giving ample space to pseudo-code descriptions of the numerical algorithms.
For practical use when working with numerical scienctific computing, this book does need to be complemented with a more hands-on, how-to-do-it book of numerical methods, but my impression currently is that it serves its purpose as a readable text on the underlying theoretical aspects.
Honestly, it is one of the better math textbooks that I have read. Unlike many others, it does try to simplify complicated concepts for the audience, which I definitely appreciate.
Am I insane or are some of the answers at the back of the textbook wrong. i checked quizlet and the answers there match mine but the textbook says otherwise...
Clear explanation with code for every single interpolation and quadrature! Super useful. My college class does not assign a textbook but I use this one to cover my blind spots.