{ "item_title" : "Introduction to Methods of Approximation in Physics and Astronomy", "item_author" : [" Maurice H. P. M. Van Putten "], "item_description" : "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 constant1.4 Power series and radius of convergence1.5 Minkowski spacetime 1.6 The logarithm and winding number1.7 Branch cuts for z 1.8 Branch cuts for z 1/p 1.9 Exercises2. Complex function theory 2.1 Analytic functions2.2 Cauchy's Integral Formula2.3 Evaluation of a real integral2.4 Residue theorem2.5 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 Introduction3.2 Inner and outer products 3.3 Angular momentum vector 3.4 Elementary transformations in the plane 3.5 Matrix algebra3.6 Eigenvalue problems 3.7 Unitary matrices and invariants3.8 Hermitian structure of Minkowski spacetime 3.9 Eigenvectors of Hermitian matrices3.10QR factorization 3.11Exercises4. Linear partial differential equations 4.1 Hyperbolic equations 4.2 Diffusion equation 4.3 Elliptic equations 4.4 Characteristic of hyperbolic systems4.5 Weyl equation 4.6 ExercisesPart II Methods of approximation 5. Projections and minimal distances 5.1 Vectors and distances5.2 Projections of vectors5.3 Snell's law and Fermat's principle 5.4 Fitting data by least squares5.5 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 finding7.1 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's8.5 Examples of ordinary differential equations 8.6 Exercises9. Perturbation theory, scaling and turbulence 9.1 Roots of a cubic equation9.2 Damped pendulum9.3 Orbital motion 9.4 Inertial and viscous fluid motion 9.5 Kolmogorov scaling of homogeneous turbulence 9.6 ExercisesPart 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 ExercisesA. Some units and consta", "item_img_path" : "https://covers3.booksamillion.com/covers/bam/9/81/102/931/9811029318_b.jpg", "price_data" : { "retail_price" : "79.99", "online_price" : "79.99", "our_price" : "79.99", "club_price" : "79.99", "savings_pct" : "0", "savings_amt" : "0.00", "club_savings_pct" : "0", "club_savings_amt" : "0.00", "discount_pct" : "10", "store_price" : "" } }

Overview

Customers Also Bought

Details