Mathematical methods for geophysics and space physics (Q2808360)

The monograph is devoted to mathematical methods which are used in geophysics and space physics. It is addressed to graduate students in geophysics.NEWLINENEWLINEThe monograph consists of five chapters:{\parindent=6mm \begin{itemize}\item[1.] Mathematical Preliminaries; \item[2.] Ordinary Differential Equations; \item[3.] Evaluation of Integrals and Integral Transform Methods; \item[4.] Partial Differential Equations of Mathematical Geophysics; \item[5.] Probability, Statistics and Computational Methods. NEWLINENEWLINE\end{itemize}} In the first chapter reviews of many mathematical preliminaries are given. Vectors, indicial or ``Einstein'' notation, vector operators, cylindrical and spherical geometry, and the theorems of Gauss, Green, and Stokes are presented here. Also the author introduces matrices and tensors, which are matrices whose physical properties remain unchanged under a rotation and preserve other physical principles. A very brief description of the eigenvalue problem is given. Introduced the concept of generalized functions.NEWLINENEWLINEThe chapter two is devoted to methods for solution of ordinary differential equations. Considered one-order and second-order ordinary differential equations in the different geometrical variables. Introduced the concept of Green's functions. Provided brief surveys of turbulence problem and fractals.NEWLINENEWLINEIn the third chapter, the author introduces the evaluation of integrals, including the complex analysis and elementary contour integration, consider integral transforms, including Fourier transform and fast Fourier transform.NEWLINENEWLINEIn chapter four the fundamental partial differential equations of mathematical physics are introduced. For solution of these equations are used integral transform methods, eigenfunctions, eigenvalues and Green's functions. Solutions of diffusion equation and wave equation are given in three dimensions. The chapter embeds practical examples of real-world problems with theory.NEWLINENEWLINEThe fifth chapter surveys two important topics. First topic is devoted to probability and statistics, including the binomial, Poisson and Gaussian distributions, as well as the central limit theorem. The second topic is devoted to numerical methods of solving ordinary and partial differential equations.NEWLINENEWLINEEach chapter is ended with list of interesting exercises, some of them are touch the geophysics problems.