Numerical Analysis (Hardcover)

L. Ridgway Scott

  • 出版商: Princeton University
  • 出版日期: 2011-05-08
  • 售價: $1,950
  • 貴賓價: 9.8$1,911
  • 語言: 英文
  • 頁數: 344
  • 裝訂: Hardcover
  • ISBN: 0691146861
  • ISBN-13: 9780691146867
  • 相關分類: 數值分析 Numerical-analysis
  • 下單後立即進貨 (約5~7天)

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商品描述

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. It presents the mathematical foundations of numerical analysis. It explains the mathematical details behind simulation software. It introduces many advanced concepts in modern analysis. It is self-contained and mathematically rigorous. It contains problems and solutions in each chapter. This is an excellent follow-up course to "Principles of Mathematical Analysis" by Rudin.

商品描述(中文翻譯)

計算科學從根本上改變了技術問題的解決方式。現在,飛機、汽車甚至賽艇的設計都是通過計算模擬完成的。這種新方法的數學基礎是數值分析,它研究用實數定義的表達式的計算算法。本書強調計算背後的理論,提供了一個嚴謹且自成一體的數值分析入門,並介紹了支撐工業軟件的高級數學,其中包含大多數教科書所缺少的完整細節。本書採用探究式學習方法,以敘述風格撰寫,提供歷史背景,並在練習中包含許多證明和技術細節。學生將能夠超越對數值模擬的基本理解,深入了解該主題的基礎。他們將不再接受當前教科書中存在的數學漏洞。例如,本書涵蓋了基本迭代方法收斂的必要條件和充分條件,並且證明是以完全的一般性給出的,而不僅僅是基於特殊情況。本書適合本科數學專業的學生以及希望學習該主題基礎的計算科學家。它介紹了數值分析的數學基礎,解釋了模擬軟件背後的數學細節,引入了現代分析中的許多高級概念,並且自成一體且數學嚴謹。每章都包含問題和解答。這是Rudin的《數學分析原理》的一門很好的後續課程。