UID:
almahu_9949385733502882
Umfang:
1 online resource (xv, 381 pages) :
,
illustrations
Ausgabe:
First edition.
ISBN:
9781003201694
,
1003201695
,
9781000596540
,
1000596540
,
9781000596571
,
1000596575
Inhalt:
"This textbook is written for the first introductory course on scientific computing. It covers elementary numerical methods for linear systems, root finding, interpolation, numerical integration, numerical differentiation, least squares problems, initial value problems and boundary value problems. It includes short Matlab and Python tutorials to quickly get students started on programming. It makes the connection between elementary numerical methods with advanced topics such as machine learning and parallel computing. This textbook gives a comprehensive and in-depth treatment of elementary numerical methods. It balances the development, implementation, analysis and application of a fundamental numerical method by addressing the following questions. Where is the method applied? How is the method developed? How is the method implemented? How well does the method work? The material in the textbook is made as self-contained and easy-to-follow as possible with reviews and remarks. The writing is kept concise and precise. Examples, figures, paper-and-pen exercises and programming problems are deigned to reinforce understanding of numerical methods and problem-solving skills"--
Anmerkung:
Includes index.
,
Cover -- Half Title -- Title Page -- Copyright Page -- Dedication -- Contents -- Preface -- Author -- 1. An Overview of Scientific Computing -- 1.1. What Is Scientific Computing? -- 1.2. Errors in Scientific Computing -- 1.2.1. Absolute and Relative Errors -- 1.2.2. Upper Bounds -- 1.2.3. Sources of Errors -- 1.3. Algorithm Properties -- 1.4. Exercises -- 2. Taylor's Theorem -- 2.1. Polynomials -- 2.1.1. Polynomial Evaluation -- 2.2. Taylor's Theorem -- 2.2.1. Taylor Polynomials -- 2.2.2. Taylor Series -- 2.2.3. Taylor's Theorem -- 2.3. Alternating Series Theorem -- 2.4. Exercises
,
2.5. Programming Problems -- 3. Roundoff Errors and Error Propagation -- 3.1. Numbers -- 3.1.1. Integers -- 3.2. Floating-Point Numbers -- 3.2.1. Scientific Notation and Rounding -- 3.2.2. DP Floating-Point Representation -- 3.3. Error Propagation -- 3.3.1. Catastrophic Cancellation -- 3.3.2. Algorithm Stability -- 3.4. Exercises -- 3.5. Programming Problems -- 4. Direct Methods for Linear Systems -- 4.1. Matrices and Vectors -- 4.2. Triangular Systems -- 4.3. GE and A=LU -- 4.3.1. Elementary Matrices -- 4.3.2. A=LU -- 4.3.3. Solving Ax = b by A=LU -- 4.4. GEPP and PA=LU -- 4.4.1. GEPP
,
4.4.2. PA=LU -- 4.4.3. Solving Ax = b by PA=LU -- 4.5. Tridiagonal Systems -- 4.6. Conditioning of Linear Systems -- 4.6.1. Vector and Matrix Norms -- 4.6.2. Condition Numbers -- 4.6.3. Error and Residual Vectors -- 4.7. Software -- 4.8. Exercises -- 4.9. Programming Problems -- 5. Root Finding for Nonlinear Equations -- 5.1. Roots and Fixed Points -- 5.2. The Bisection Method -- 5.3. Newton's Method -- 5.3.1. Convergence Analysis of Newton's Method -- 5.3.2. Practical Issues of Newton's Method -- 5.4. Secant Method -- 5.5. Fixed-Point Iteration
,
5.6. Newton's Method for Systems of Nonlinear Equations -- 5.6.1. Taylor's Theorem for Multivariate Functions -- 5.6.2. Newton's Method for Nonlinear Systems -- 5.7. Unconstrained Optimization -- 5.8. Software -- 5.9. Exercises -- 5.10. Programming Problems -- 6. Interpolation -- 6.1. Terminology of Interpolation -- 6.2. Polynomial Space -- 6.2.1. Chebyshev Basis -- 6.2.2. Legendre Basis -- 6.3. Monomial Interpolation -- 6.4. Lagrange Interpolation -- 6.5. Newton's Interpolation -- 6.6. Interpolation Error -- 6.6.1. Error in Polynomial Interpolation -- 6.6.2. Behavior of Interpolation Error
,
6.6.2.1. Equally-Spaced Nodes -- 6.6.2.2. Chebyshev Nodes -- 6.7. Spline Interpolation -- 6.7.1. Piecewise Linear Interpolation -- 6.7.2. Cubic Spline -- 6.7.3. Cubic Spline Interpolation -- 6.8. Discrete Fourier Transform (DFT) -- 6.9. Exercises -- 6.10. Programming Problems -- 7. Numerical Integration -- 7.1. Definite Integrals -- 7.2. Numerical Integration -- 7.2.1. Change of Intervals -- 7.3. The Midpoint Rule -- 7.3.1. Degree of Precision (DOP) -- 7.3.2. Error of the Midpoint Rule -- 7.4. The Trapezoidal Rule -- 7.5. Simpson's Rule -- 7.6. Newton-Cotes Rules -- 7.7. Gaussian Quadrature Rules
Weitere Ausg.:
Print version: Xu, Sheng, 1973- Introduction to scientific computing with Matlab and Python tutorials Boca Raton : CRC Press/Chapman & Hall, 2022 ISBN 9781032063157
Sprache:
Englisch
Schlagwort(e):
Electronic books.
;
Electronic books.
DOI:
10.1201/9781003201694
URL:
https://www.taylorfrancis.com/books/9781003201694
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