An introduction to numerical methods for the physical sciences / Colm T. Whelan.
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 a...
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Full Text (via Morgan & Claypool) |
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| Main Author: | |
| Format: | eBook |
| Language: | English |
| Published: |
San Rafael, California (1537 Fourth Street, 1537 Fourth Street, San Rafael, CA 94901 USA) :
Morgan & Claypool Publishers,
[2020]
|
| Series: | Synthesis lectures on engineering, science, and technology ;
8. |
| Subjects: |
MARC
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| 100 | 1 | |a Whelan, Colm T., |e author. |0 http://id.loc.gov/authorities/names/n93067435 |1 http://isni.org/isni/0000000117133393. | |
| 245 | 1 | 3 | |a An introduction to numerical methods for the physical sciences / |c Colm T. Whelan. |
| 264 | 1 | |a San Rafael, California (1537 Fourth Street, 1537 Fourth Street, San Rafael, CA 94901 USA) : |b Morgan & Claypool Publishers, |c [2020] | |
| 300 | |a 1 PDF (xvii, 148 pages) : |b illustrations (some color) | ||
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| 490 | 1 | |a Synthesis lectures on engineering, science, and technology, |x 2690-0327 ; |v #8. | |
| 500 | |a Part of: Synthesis digital library of engineering and computer science. | ||
| 504 | |a Includes bibliographical references (pages 141-143) and index. | ||
| 505 | 0 | |a 1. Preliminaries -- 1.1. Numbers and errors -- 1.2. Algorithms -- 1.3. Programming languages. | |
| 505 | 8 | |a 2. Some elementary results -- 2.1. Taylor's series -- 2.2. Numerical differentiation and integration -- 2.3. Finding roots. | |
| 505 | 8 | |a 3. The numerical solution of ordinary differential equations -- 3.1. Trigonometric functions -- 3.2. Analytic solutions -- 3.3. Numerical methods. | |
| 505 | 8 | |a 4. Case study : damped and driven oscillations -- 4.1. Linear and nonlinear ordinary differential equations -- 4.2. The physical pendulum -- 4.3. Chaos. | |
| 505 | 8 | |a 5. Numerical linear algebra -- 5.1. System of linear equations -- 5.2. Lu factorization -- 5.3. QR factorization. | |
| 505 | 8 | |a 6. Polynomial approximations -- 6.1. Interpolation -- 6.2. Orthogonal polynomials -- 6.3. Infinite dimensional vector spaces -- 6.4. Quadrature. | |
| 505 | 8 | |a 7. Sturm-Liouville theory -- 7.1. Eigenvalues -- 7.2. Least squares approximation. | |
| 505 | 8 | |a 8. Case study : the quantum oscillator -- 8.1. Numerical solution of the one dimensional Schrödinger equation -- 8.2. Numerical solution for the oscillator. | |
| 505 | 8 | |a 9. Variational principles -- 9.1. Rayleigh-Ritz theorem -- 9.2. The Euler-Lagrange equations -- 9.3. Constrained variations -- 9.4. Sturm-Liouville revisited. | |
| 505 | 8 | |a 10. Case study : the ground state of atoms -- 10.1. Hydrogenic ions -- 10.2. Two electron ions -- 10.3. The Hartree approach. | |
| 520 | |a 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. | ||
| 588 | |a Title from PDF title page (viewed on July 30, 2020) | ||
| 650 | 0 | |a Sequences (Mathematics) |0 http://id.loc.gov/authorities/subjects/sh85120145. | |
| 776 | 0 | 8 | |i Print version: |z 9781681738741 |z 9781681738727. |
| 830 | 0 | |a Synthesis lectures on engineering, science, and technology ; |v 8. | |
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