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An Introduction to Numerical Mathematics
- 1st Edition - January 1, 1963
- Author: Eduard L. Stiefel
- Language: English
- eBook ISBN:9 7 8 - 1 - 4 8 3 2 - 2 5 4 1 - 8
An Introduction to Numerical Mathematics provides information pertinent to the fundamental aspects of numerical mathematics. This book covers a variety of topics, including linear… Read more
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Request a sales quoteAn Introduction to Numerical Mathematics provides information pertinent to the fundamental aspects of numerical mathematics. This book covers a variety of topics, including linear programming, linear and nonlinear algebra, polynomials, numerical differentiation, and approximations. Organized into seven chapters, this book begins with an overview of the solution of linear problems wherein numerical mathematics provides very effective algorithms consisting of finitely many computational steps. This text then examines the method for the direct solution of a definite problem. Other chapters consider the determination of frequencies in freely oscillating mechanical or electrical systems. This book discusses as well eigenvalue problems for oscillatory systems of finitely many degrees of freedom, which can be reduced to algebraic equations. The final chapter deals with the approximate representation of a function f(x) given by I-values as in the form of a table. This book is a valuable resource for physicists, mathematicians, theoreticians, engineers, and research workers.
Foreword to German EditionForeword to English EditionChapter I Linear Algebra 1.1 Linear Functions, Exchange 1.2 Inversion 1.3 Practical Solution of Linear EquationsChapter 2 Linear Programming 2.1 An Introductory Example 2.2 Solution of a Program with the Exchange Method 2.3 Geometric Interpretation of the Simplex Algorithm 2.4 Generalizations 2.5 Method of Dual Solution 2.6 Application to Game Theory 2.7 Chebyshev ApproximationChapter 3 Least-Squares Approximation and Definite Problems 3.1 The Method of Least-Squares 3.2 Definite Problems 3.3 Solution of Symmetric-Definite Equations 3.4 OrthogonalityChapter 4 Nonlinear Algebra 4.1 Linearization 4.2 The Correction Method of Newton 4.3 Recursion formulas, Convergence 4.4 Newton's Method for Several Unknowns 4.5 Polynomials 4.6 Direct Methods for the Solution of Algebraic EquationsChapter 5 Eigenvalue Problems 5.1 An Introductory Example 5.2 The Characteristic Polynomial 5.3 General Eigenvalue Problem, Iterative Methods 5.4 OutlooksChapter 6 Differential Equations 6.1 Numerical Differentiation 6.2 Numerical Integration 6.3 Differential Equations of the First Order 6.4 Systems of Differential Equations of the First Order 6.5 Boundary-Value Problems 6.6 Partial Differential EquationsChapter 7 Approximations 7.1 The Interpolating Polynomial 7.2 Systems of Polynomials 7.3 Interpolation Problems in the Complex PlaneAppendix I. Computational ExamplesAppendix II. TablesLiterature-ReferencesAdditional Literature-References in EnglishAuthor IndexSubject Index
- No. of pages: 296
- Language: English
- Edition: 1
- Published: January 1, 1963
- Imprint: Academic Press
- eBook ISBN: 9781483225418
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