Mathematical Methods in Maritime Studies and Transport
Syllabus
Vector space, basis, dimension, subspaces. Linear mappings and matrices, change of basis, similarity, eigenvalues, triangular form, Jordan canonical form. Euclidean and unitary spaces: inner product, orthonormal basis, normal, unitaty and self-adjoint matrices, polar decomposition, singular value decomposition, rotations of Euclidean space. Linear differential equations and systems of linear differential equations. Partial differential equations of 1st order, classification of partial differential equations of 2nd order, Fourier method, Fourier and Laplace transform, applications of partial differential equations.
Goals and competencies
To expand knowledge and understanding of linear algebra, linear ordinary differential equations and partial differential equations.
Basic literature
- T.S. Shores, Applied linear algebra and matrix analysis, Springer, 2007.
- P. Halmos, Finite dimensional vector spaces, Springer, 1974.
- S. Lipschutz, M.L. Lipson, Schaum's outline of theory and problems of linear algebra, 4th ed., McGraw-Hill, 2009.
- I. Vidav, Višja matematika II, DZS, 1979.
- S. Kurepa, Uvod u linearnu algebru, Školska knjiga Zagreb, 1982.
- E. Zakrajšek, Analiza III, DMFA, 1998.
- E. Zakrajšek, Analiza IV, DMFA, 1998
- J.D. Logan, Applied partial differential equations, 2nd ed., Springer, 2004.
- Y. Pinchover, J. Rubinstein, An introduction to partial differential equations, Cambridge University Press, 2006.
- E. Kreyszig, Advanced engineering mathematics, John Wiley&Sons, 1993.