Numerical Analysis

The book "Numerical Analysis" by Richard L. Burden, J. Douglas Faires, and Annette M. Burden is a comprehensive textbook that introduces students to the theory and application of modern numerical approximation techniques. Here is a detailed overview of the book:

Key Themes

1. Introduction to Numerical Analysis: The book provides an accessible treatment of numerical analysis, requiring only a calculus prerequisite. It explains how, why, and when approximation techniques can be expected to work and why they might fail in certain situations.
2. Theory and Application: The authors cover a wide range of topics, including the mathematical aspects of numerical problem solving, measurement of error, and scientific computing. The book is designed to serve both undergraduate and beginning graduate students in various disciplines such as mathematics, computing, engineering, and physical sciences.
3. Practical Applications: The text includes numerous examples and exercises that develop students' intuition and demonstrate the practical applications of numerical analysis to everyday problems. This practical focus helps students understand the relevance of numerical methods in real-world scenarios.
4. Updated Editions: The book has been revised multiple times, with significant changes in each edition. For example, the 10th edition includes new techniques to keep the treatment current, additional steps in examples to show computations required for iteration processes, and split chapter exercises into computational, applied, and theoretical sections to give instructors more flexibility in assigning homework.

Plot Summary

The book does not have a traditional plot summary as it is a textbook. However, it can be summarized as follows:

• Chapters and Topics: The book typically covers a broad range of topics in numerical analysis, including interpolation, differentiation, integration, solution of equations, and optimization techniques.
• Examples and Exercises: Each chapter is filled with examples and exercises that illustrate the theoretical concepts. These examples are designed to help students understand the practical applications of numerical methods.
• Pedagogical Approach: The authors aim to provide a clear and concise introduction to the subject, making it accessible to students with minimal mathematical background.

Critical Reception

The book has received positive reviews for its clear and thorough introduction to the theoretical aspects of numerical analysis. Here are some key points from critical reception:

1. Theoretical Focus: The book is praised for its focus on the theoretical aspects of numerical analysis, providing a solid foundation for understanding the subject.
2. Practical Use: While it is noted that the book needs to be complemented with a more hands-on, how-to-do-it book of numerical methods for practical use, it is recognized as a readable text on the underlying theoretical aspects.
3. Layout Issues: Some reviewers have mentioned difficulties with the layout style, which can make it challenging to distinguish between main text, supplementary text, definitions, theorems, and examples.

Overall, "Numerical Analysis" by Richard L. Burden, J. Douglas Faires, and Annette M. Burden is a well-respected textbook that provides a comprehensive introduction to the theory and application of numerical approximation techniques. Its practical focus and clear explanations make it a valuable resource for students in various disciplines.