Matematika II

Higher education teachers: Dolinar Gregor
Collaborators: Cafuta Kristijan, Perne Andrej, Stopar Nik, Žitko Tomislav

Subject description

Prerequisits:

• Enrolment into the programme. Completed exam Mathematics I.

Content (Syllabus outline):

Matrices (basic operations, matrix product, rank, determinant, eigenvalues, eigenvectors, linear transformations). Systems of linear equations (Gauss elimination, Cramer's rule). Vectors (basic operations, scalar product, vector product, scalar triple product, analytic geometry). Function series (power series, Taylor series, Fourier series). Functions of two and more variables (partial derivatives, chain rule, extrema, conditional extrema). Ordinary differential equations (ODE) of the first order (with separable variables, linear). ODE of higher orders (with constant coefficients, Euler's equation). Linear systems of ODEs, linearly independent solutions.

Objectives and competences:

• To present and upgrade basic mathematical concepts, procedures, and laws, and to deepen their understanding.
• To develop analytical thinking and careful and exact mathematical reasoning.
• To become familiar with the software for symbolic computations (e.g., Mathematica).

Intended learning outcomes:

• Knowledge and understanding of the basic concepts of calculus and linear algebra, including vectors, matrices, systems of linear equations, function series, and ordinary differential equations.
• The ability to analyse and mathematically interpret fundamental technical problems.
• The ability to use computer software for solving such problems.

Learning and teaching methods:

• Lectures, tutorials, laboratory tutorials and homework assignments.
• Collective analysis, interpretation, and solving of technical problems.

Study materials

• G. Tomšič, N. Mramor Kosta, B. Orel: Matematika II, Založba FE in FRI, Ljubljana, 2005
• E. Kreyszig: Advanced engineering mathematics, John Wiley & Sons, 2006
• George B. Thompson, jr., Maurice D. Weir, Joel Hass, Frank R. Giordano, Thomas' Calculus, Pearson, Addison Wesley, 2005.
• David C. Lay, Linear algebra and its applications, Pearson, Addison Wesley, 2011
• N. Mramor Kosta, B. Jurčič-Zlobec: Zbirka nalog iz Matematike II, Založba FE in FRI, Ljubljana, 2005
• G. Dolinar: Rešene naloge iz Matematike II za VSŠ, Založba FE in FRI, Ljubljana, 2005
• Spletna stranhttp://matematika.fe.uni-lj.si/