Central Library, Indian Institute of Technology Delhi
केंद्रीय पुस्तकालय, भारतीय प्रौद्योगिकी संस्थान दिल्ली

An introduction to numerical methods for the physical sciences / Colm T. Whelan.

By: Whelan, Colm T [author.]Material type: TextTextSeries: Synthesis digital library of engineering and computer science | Synthesis lectures on engineering, science, and technology ; #8.Publisher: San Rafael, California (1537 Fourth Street, 1537 Fourth Street, San Rafael, CA 94901 USA) : Morgan & Claypool Publishers, [2020]Description: 1 PDF (xvii, 148 pages) : illustrations (some color)Content type: text Media type: electronic Carrier type: online resourceISBN: 9781681738734Subject(s): Sequences (Mathematics) | differential equations | linear equations | polynomial approximations | variational principlesGenre/Form: Electronic books.Additional physical formats: Print version:: No titleDDC classification: 515/.24 LOC classification: QA292 | .W44 2020ebOnline resources: Abstract with links to full text | Abstract with links to resource Also available in print.
Contents:
1. Preliminaries -- 1.1. Numbers and errors -- 1.2. Algorithms -- 1.3. Programming languages
2. Some elementary results -- 2.1. Taylor's series -- 2.2. Numerical differentiation and integration -- 2.3. Finding roots
3. The numerical solution of ordinary differential equations -- 3.1. Trigonometric functions -- 3.2. Analytic solutions -- 3.3. Numerical methods
4. Case study : damped and driven oscillations -- 4.1. Linear and nonlinear ordinary differential equations -- 4.2. The physical pendulum -- 4.3. Chaos
5. Numerical linear algebra -- 5.1. System of linear equations -- 5.2. Lu factorization -- 5.3. QR factorization
6. Polynomial approximations -- 6.1. Interpolation -- 6.2. Orthogonal polynomials -- 6.3. Infinite dimensional vector spaces -- 6.4. Quadrature
7. Sturm-Liouville theory -- 7.1. Eigenvalues -- 7.2. Least squares approximation
8. Case study : the quantum oscillator -- 8.1. Numerical solution of the one dimensional Schrödinger equation -- 8.2. Numerical solution for the oscillator
9. Variational principles -- 9.1. Rayleigh-Ritz theorem -- 9.2. The Euler-Lagrange equations -- 9.3. Constrained variations -- 9.4. Sturm-Liouville revisited
10. Case study : the ground state of atoms -- 10.1. Hydrogenic ions -- 10.2. Two electron ions -- 10.3. The Hartree approach.
Summary: There is only a very limited number of physical systems that can be exactly described in terms of simple analytic functions. There are, however, a vast range of problems which are amenable to a computational approach. This book provides a concise, self-contained introduction to the basic numerical and analytic techniques, which form the foundations of the algorithms commonly employed to give a quantitative description of systems of genuine physical interest. The methods developed are applied to representative problems from classical and quantum physics.
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Mode of access: World Wide Web.

System requirements: Adobe Acrobat Reader.

Part of: Synthesis digital library of engineering and computer science.

Includes bibliographical references (pages 141-143) and index.

1. Preliminaries -- 1.1. Numbers and errors -- 1.2. Algorithms -- 1.3. Programming languages

2. Some elementary results -- 2.1. Taylor's series -- 2.2. Numerical differentiation and integration -- 2.3. Finding roots

3. The numerical solution of ordinary differential equations -- 3.1. Trigonometric functions -- 3.2. Analytic solutions -- 3.3. Numerical methods

4. Case study : damped and driven oscillations -- 4.1. Linear and nonlinear ordinary differential equations -- 4.2. The physical pendulum -- 4.3. Chaos

5. Numerical linear algebra -- 5.1. System of linear equations -- 5.2. Lu factorization -- 5.3. QR factorization

6. Polynomial approximations -- 6.1. Interpolation -- 6.2. Orthogonal polynomials -- 6.3. Infinite dimensional vector spaces -- 6.4. Quadrature

7. Sturm-Liouville theory -- 7.1. Eigenvalues -- 7.2. Least squares approximation

8. Case study : the quantum oscillator -- 8.1. Numerical solution of the one dimensional Schrödinger equation -- 8.2. Numerical solution for the oscillator

9. Variational principles -- 9.1. Rayleigh-Ritz theorem -- 9.2. The Euler-Lagrange equations -- 9.3. Constrained variations -- 9.4. Sturm-Liouville revisited

10. Case study : the ground state of atoms -- 10.1. Hydrogenic ions -- 10.2. Two electron ions -- 10.3. The Hartree approach.

Abstract freely available; full-text restricted to subscribers or individual document purchasers.

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There is only a very limited number of physical systems that can be exactly described in terms of simple analytic functions. There are, however, a vast range of problems which are amenable to a computational approach. This book provides a concise, self-contained introduction to the basic numerical and analytic techniques, which form the foundations of the algorithms commonly employed to give a quantitative description of systems of genuine physical interest. The methods developed are applied to representative problems from classical and quantum physics.

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