Numerical Analysis with Algorithms and Programming
暫譯: 數值分析與演算法及程式設計

Santanu Saha Ray

Numerical Analysis with Algorithms and Programming

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商品描述

Numerical Analysis with Algorithms and Programming is the first comprehensive textbook to provide detailed coverage of numerical methods, their algorithms, and corresponding computer programs. It presents many techniques for the efficient numerical solution of problems in science and engineering.

Along with numerous worked-out examples, end-of-chapter exercises, and Mathematica® programs, the book includes the standard algorithms for numerical computation:

  • Root finding for nonlinear equations
  • Interpolation and approximation of functions by simpler computational building blocks, such as polynomials and splines
  • The solution of systems of linear equations and triangularization
  • Approximation of functions and least square approximation
  • Numerical differentiation and divided differences
  • Numerical quadrature and integration
  • Numerical solutions of ordinary differential equations (ODEs) and boundary value problems
  • Numerical solution of partial differential equations (PDEs)

The text develops students’ understanding of the construction of numerical algorithms and the applicability of the methods. By thoroughly studying the algorithms, students will discover how various methods provide accuracy, efficiency, scalability, and stability for large-scale systems.

商品描述(中文翻譯)

《數值分析與演算法及程式設計》是第一本全面的教科書，詳細介紹了數值方法、其演算法及相應的電腦程式。它提供了許多有效解決科學和工程問題的數值技術。

除了眾多的範例、章末練習和 Mathematica® 程式外，本書還包括數值計算的標準演算法：

- 非線性方程的根尋找
- 通過更簡單的計算構建塊（如多項式和樣條）進行函數的插值和近似
- 線性方程組的解及三角化
- 函數的近似和最小二乘近似
- 數值微分和劃分差
- 數值積分和求積
- 常微分方程（ODE）和邊值問題的數值解
- 偏微分方程（PDE）的數值解

本書幫助學生理解數值演算法的構建及其方法的適用性。通過深入研究這些演算法，學生將發現各種方法如何為大規模系統提供準確性、效率、可擴展性和穩定性。

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