Introduction to Methods of Approximation in Physics and Astronomy - Brossura

Van Putten, Maurice H. P. M.

Brossura

ISBN 10: 9811029334 ISBN 13: 9789811029332

Casa editrice: Springer, 2017

Riassunto

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 consta

Dettagli dell'edizione

• Editore: Springer
• Data di pubblicazione: 2017
• Lingua: Inglese
• ISBN 10: 9811029334
• ISBN 13: 9789811029332
• Rilegatura: Paperback
• Contatto del produttore: non disponibile
• Persona responsabile: non disponibile