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

By:

Whelan, Colm T [VerfasserIn]

Resource type: Ressourcentyp: Buch (Online)Book (Online)Language: English Series: Synthesis Lectures on Engineering, Science, and TechnologyPublisher: [Williston, VT] : Morgan & Claypool, [2020]Description: 1 Online-RessourceISBN:

1681738732
9781681738734

Subject(s):

Sequences (Mathematics)

Additional physical formats: 9781681738741. | 9781681738727. | Erscheint auch als: An introduction to numerical methods for the physical sciences. Druck-Ausgabe San Rafael : Morgan & Claypool Publishers, 2020. xvii, 148 SeitenDDC classification:

515/.24

LOC classification:

QA292

Online resources:

Zugang im Netz des KIT

Summary: Intro -- Preface -- Preliminaries -- Numbers and Errors -- Algorithms -- Programming Languages -- Some Elementary Results -- Taylor's Series -- Extrema -- Power Series -- Numerical Differentiation and Integration -- Derivatives -- Quadrature -- Singular Integrands, Infinite Integrals -- Finding Roots -- The Numerical Solution of Ordinary Differential Equations -- Trigonometric Functions -- Analytic Solutions -- Numerical Methods -- Euler Approximation -- Runge-Kutta Method -- Numerov Method -- Case Study: Damped and Driven Oscillations -- Linear and Nonlinear Ordinary Differential EquationsSummary: Least Squares Approximation -- Case Study: The Quantum Oscillator -- Numerical Solution of the One Dimensional Schrödinger Equation -- Numerical Solution for the Oscillator -- Variational Principles -- Rayleigh-Ritz Theorem -- The Euler-Lagrange Equations -- Constrained Variations -- Sturm-Liouville Revisited -- Case Study: The Ground State of Atoms -- Hydrogenic Ions -- Two Electron Ions -- The Hartree Approach -- Vector Spaces -- Analytic Solution to the Quantum Oscillator -- First-Order Perturbation Theory -- Bibliography -- Author's Biography -- Index -- Blank PageSummary: The Physical Pendulum -- Small Oscillations -- Differences Between Linear and Nonlinear Pendulum -- Chaos -- Numerical Linear Algebra -- System of Linear Equations -- LU Factorization -- QR Factorization -- Systems of Linear Equations -- Eigenvalues -- Linear Least Squares -- Polynomial Approximations -- Interpolation -- Error Estimation -- Orthogonal Polynomials -- Legendre Equation -- Infinite Dimensional Vector Spaces -- Zeros of Orthogonal Polynomials -- Quadrature -- Simpson Revisited -- Weights and Nodes -- Gaussian Quadrature -- Sturm-Liouville Theory -- EigenvaluesSummary: 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 physicsPPN: PPN: 1755157126Package identifier: Produktsigel: BSZ-4-NLEBK-KAUB | ZDB-4-NLEBK

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