An introduction to numerical methods for the physical sciences /

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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Bibliographic Details
Online Access: Full Text (via Morgan & Claypool)
Main Author: Whelan, Colm T. (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:
Sequences (Mathematics)
Table of 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.

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