Numerical Analysis with Algorithms and Programming

Santanu Saha Ray

Numerical Analysis with Algorithms and Programming

買這商品的人也買了...

相關主題

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)

《數值分析與演算法程式設計》是第一本全面介紹數值方法、其演算法和相應電腦程式的教科書。它提供了許多科學和工程中高效數值解決問題的技術。

除了大量的實例、章末練習和Mathematica®程式外，本書還包括了數值計算的標準演算法：

- 非線性方程的根尋找
- 通過較簡單的計算構建塊（如多項式和樣條）對函數進行插值和逼近
- 線性方程組的求解和三角化
- 函數逼近和最小二乘逼近
- 數值微分和差分
- 數值積分和求積
- 常微分方程（ODEs）和邊值問題的數值解
- 偏微分方程（PDEs）的數值解

本書通過深入研究演算法，培養學生對數值演算法的理解和方法的適用性。通過仔細學習這些方法，學生將發現各種方法如何為大規模系統提供準確性、效率性、可擴展性和穩定性。

類似商品