Numerical methods

• Verfasst von: Rajasekar, S. [VerfasserIn]
• Titel: Numerical methods
• Titelzusatz: classical and advanced topics
• Verf.angabe: Shanmuganathan Rajasekar
• Ausgabe: First edition
• Verlagsort: Boca Raton ; London ; New York
• Verlag: CRC Press, Taylor & Francis Group
• Jahr: 2024
• Umfang: 1 Online-Ressource (xv, 541 Seiten)
• Fussnoten: Description based on publisher supplied metadata and other sources
• ISBN: 978-1-04-002163-7
• Datenträger: Online-Ressource
• Sprache: eng
• Bibliogr. Hinweis: Erscheint auch als : Druck-Ausgabe
• K10plus-PPN: 1886203695
• K10plus-PPN:
  Universitätsbibliothek
• Lokale URL UB: Zum Volltext

Abstract

This book presents a pedagogical treatment of a range of numerical methods to suit the needs of undergraduate and postgraduate students, and teachers and researchers in physics, mathematics, and engineering. For each method, the derivation of the formula, error analysis, case studies, applications in science and engineering are covered.

Abstract

Cover -- Half Title -- Title Page -- Copyright Page -- Dedication -- Contents -- Preface -- About the Author -- 1. Preliminaries -- 1.1. Introduction -- 1.2. Binary Number System -- 1.3. Floating Point Arithmetic and Significant Digits -- 1.4. Type of Errors -- 1.5. Periodic and Differentiable Functions and Series -- 1.6. Rolle's, Intermediate-Value and Extreme-Value Theorems -- 1.7. Iterations and a Root of an Equation -- 1.8. Concluding Remarks -- 1.9. Bibliography -- 1.10. Problems -- 2. Solutions of Polynomial and Reciprocal Equations -- 2.1. Introduction -- 2.2. Determination of the Region Enclosing all the Roots -- 2.3. Descartes' Rule for Sign of Real Roots -- 2.4. Determination of Exact Number of Real Roots − Sturm's Theorem -- 2.5. Roots of the Quadratic Equation -- 2.6. Solutions of the General Cubic Equation -- 2.7. Roots of Some Special Cubic Equations -- 2.8. Gräffe's Root Square Method -- 2.9. Laguere's Method -- 2.10. Reciprocal Equations -- 2.11. Concluding Remarks -- 2.12. Bibliography -- 2.13. Problems -- 3. Solution of General Nonlinear Equations -- 3.1. Introduction -- 3.2. Bisection Method -- 3.3. Method of False Position -- 3.4. SecantMethod -- 3.5. Newton-Raphson Method -- 3.6. Muller Method -- 3.7. Chebyshev Method -- 3.8. Comparison of Iterative Methods -- 3.9. Concluding Remarks -- 3.10. Bibliography -- 3.11. Problems -- 4. Solution of Linear Systems AX = B -- 4.1. Introduction -- 4.2. Cramer's Rule -- 4.3. Upper- and Lower-Triangular Systems -- 4.4. Gauss Elimination Method -- 4.5. Gauss-Jordan Elimination Method -- 4.6. Inverse of a Matrix by the Gauss-Jordan Method -- 4.7. Triangular Factorization or Decomposition Method -- 4.8. Tridiagonal Systems -- 4.9. Counting Arithmetic Operations -- 4.10. Iterative Methods -- 4.11. System AX = B with A being Vandermonde Matrix -- 4.12. Ill-Conditioned Systems.