Introduction to methods of approximation in physics and astronomy. (2017)

• Record Type: Book
• Further Information: Note: Maurice H.P.M. van Putten.
• Authors: Van Putten, Maurice H. P. M
• Contents: Preface Part I Preliminaries 1. Complex numbers 1.1 Quotients of complex numbers 1.2 Roots of complex numbers 1.3 Sequences and Euler's constant 1.4 Power series and radius of convergence 1.5 Minkowski spacetime 1.6 The logarithm and winding number 1.7 Branch cuts for z 1.8 Branch cuts for z 1/p 1.9 Exercises 2. Complex function theory 2.1 Analytic functions 2.2 Cauchy's Integral Formula 2.3 Evaluation of a real integral 2.4 Residue theorem 2.5 Morera's theorem 2.6 Liouville's theorem 2.7 Poisson kernel 2.8 Flux and circulation 2.9 Examples of potential flows 2.10Exercises 3. Vectors and linear algebra 3.1 Introduction 3.2 Inner and outer products 3.3 Angular momentum vector 3.4 Elementary transformations in the plane 3.5 Matrix algebra 3.6 Eigenvalue problems 3.7 Unitary matrices and invariants 3.8 Hermitian structure of Minkowski spacetime 3.9 Eigenvectors of Hermitian matrices 3.10QR factorization 3.11Exercises 4. Linear partial differential equations 4.1 Hyperbolic equations 4.2 Diffusion equation 4.3 Elliptic equations 4.4 Characteristic of hyperbolic systems 4.5 Weyl equation 4.6 Exercises Part II Methods of approximation 5. Projections and minimal distances 5.1 Vectors and distances 5.2 Projections of vectors 5.3 Snell's law and Fermat's principle 5.4 Fitting data by least squares 5.5 Gauss-Legendre quadrature 5.6 Exercises 6. Spectral methods and signal analysis 6.1 Basis functions 6.2 Expansion in Legendre polynomials 6.3 Fourier expansion 6.4 The Fourier transform 6.5 Fourier series 6.6 Chebychev polynomials 6.7 Weierstrass approximation theorem 6.8 Detector signals in the presence of noise 6.9 Signal detection by FFT using Maxima 6.10GPU-Butterfly filter in (f, f) 6.11Exercises 7. Root finding 7.1 Solving for √2 and π 7.2 Convergence in Newton's method 7.3 Contraction mapping 7.4 Newton's method in two dimensions 7.5 Basins of attraction 7.6 Root finding in higher dimensions 7.7 Exercises 8. Finite differencing: differentiation and integration 8.1 Vector fields 8.2 Gradient operator 8.3 Integration of ODE's 8.4 Numerical integration of ODE's 8.5 Examples of ordinary differential equations 8.6 Exercises 9. Perturbation theory, scaling and turbulence 9.1 Roots of a cubic equation 9.2 Damped pendulum 9.3 Orbital motion 9.4 Inertial and viscous fluid motion 9.5 Kolmogorov scaling of homogeneous turbulence 9.6 Exercises Part III Selected topics 10. Thermodynamics of N-body systems 10.1 The action principle 10.2 Momentum in Euler-Lagragne equations 10.3 Legendre transformation 10.4 Hamiltonian formulation 10.5 Globular clusters 10.6 Coefficients of relaxation 10.7 Exercises 11. Accretion flows onto black holes 11.1 Bondi accretioin 11.2 Hoyle-Lyttleton accretion 11.3 Accretion disks 11.4 Gravitational wave emission 11.5 Mass transfer in binaries 11.6 Exercises 12. Rindler observers in astrophysics and cosmology 12.1 The moving mirror problem 12.2 Implications for dark matter 12.3 Exercises A. Some units and constant B. Г(z) and Ϛ(z) functions.
• Publisher Details: Singapore : Springer
• Publication Date: 2017
• Extent: 1 online resource (xiii, 345 pages), illustrations (some color)
• Subjects: 530.15; Mathematical physics; Astronomy -- Mathematics; Approximation theory; Approximation theory; Astronomy -- Mathematics; Mathematical physics; Physics; Mathematical Methods in Physics; Astronomy, Observations and Techniques; Numerical and Computational Physics, Simulation; Astrophysics and Astroparticles; Electronic books; Observations
• Languages: English
• ISBNs: 9789811029325; 9811029326; 9811029318; 9789811029318
• Related ISBNs: 9789811029318
• Notes: Note: Includes bibliographical references and index.; Note: Online resource; title from PDF title page (SpringerLink, viewed April 19, 2017).
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.