Syllabus
1. Complex numbers; exponential, trigonometric and hyperbolic functions; logarithms.
2. Scalars, vectors and tensors; linear algebraic equations, matrices and determinants.
3. Derivatives, partial derivatives, differentials; extremes of functions, Lagrange multipliers. Functions and limits.
4. Integrals and their evaluation, line and surface integrals; change of variables, Jacobians; differentiation of integrals, Leibnitz theorem.
5. Differential operators; Green, Stokes and Gauss theorems, transformation of coordinates, tensor analysis.
6. Fourier series; Legendre polynomials and spherical harmonic functions; Fourier and Laplace transform; distributions; convolution.
7. Ordinary differential equations and methods of their solution.
Annotation
The course is offered to the PhD students who did not attend the basic lectures in mathematics at the Faculty of
Mathematics and Physics. The goal of the course is to deepen the knowledge of the mathematical methods used in geophysical research and to gain practice in using them.