BME Mathematics A2. Oral exam. Spring 2017.
1. Functions of 2 real variables. Continuity, level curves, differentiation. Young theorem, total differential.
2. Functions of 2 real variables. Local extremum.
3. Functions of 2 real variables. Global, conditional extremum.
4. Functions of 2 real variables. Double integral (in Cartesian, polar coordinates).
5. Functions of 2 real variables. Applications of double integrals.
6. Functions of 3 real variables. Partial, directional derivatives.
7. Triple integral. Cylindrical, spherical coordinates.
8. Scalar and vector fields. Gradient, divergence, rotation.
9. Line integrals. Conservative vector fields, potential theory.
10. Gauss Ostrogradsky theorem.
11. Stokes theorem.
12. Power, Maclaurin series.
13. Fourier series.
14. Systems of linear equations, Gaussian elimination.
15. Determinants and Cramer's rule.
16. Vector spaces, inner product spaces, orthonormal basis, Gram-Schmidt process.
17. Rank of a matrix and its relation to the solvability of systems of linear equations.
18. Linear transformations, image and kernel spaces, dimension theorem.
19. Eigenvalues, eigenvectors; quadratic curves and surfaces.