1. Systems of linear equations, the Gauss algorithm, determinants, Cramer's rule. (14 + 0 + 11 hours)
2. Basic linear algebra: vectors, basis, coordinatisation (continued from Mathematics 1). (6 + 0 + 3 hours)
3. Multivariable functions. Partial derivatives (definition and geometric interpretation). (3 + 0 + 2 hours)
4. Gradient. Directional derivative. Higherorder partial derivatives. (2 + 0 + 1 hours)
5. Implicitely represented functions. Surfaces in space (equation of the tangential plane and normal line). Curves in space (equation of the tangential line and normal plane). (3 + 0 + 2 hours)
6. Analysing of twovariable functions. Extrema of two and threevariable functions. (1 + 0 + 3 hours)
7. Conditional extrema. Lagrange multipliers. Applications to optimization problems. (2 + 0 + 2 hours)
8. Riemann integrals of two and threevariable functions. Fubini theorem for two and threevariable functions. Change of variables in double and triple integrals. (2 + 0 + 1 hours)
9. Integration in polar, cylindric and spheric coordinates. Applications of double and triple integrals (barycenter, moment of inertia). (2 + 0 + 2 hours)
10. Line integrals of first and second sort. Vector fields. Rotation and divergence. Conservative vector fields. Examples from mechanics. (5 + 0 + 2 hours)
11. The notion of a differential equation. Types of differential equations. The order of a differential equation. Linear ordinary differential equations of first order (definition and solution). (3 + 0 + 2 hours)
12. Nonlinear first order ordinary differential equations (Bernoulli equation, Ricatti equatios, separable equations, logistic equation with applications, exact equations, Euler multiplier). (3 + 0 + 5 hours)
13. Linear second order ordinary differential equations reda (fundamental set, Wronskian, method of indeterminate coefficients for determining a particular solution, method of variation of constants). (4 + 0 + 4 hours)
14. Sequences and series: Definition and basic properties, convergence, convergence criteria. (3 + 0 + 2 hours)
15. Applications of higherorder derivatives to approximations of functions with polynomials. Approximation with Taylor polynomials. Approximate calculations and estimate of the error of approximatin by a Taylor polynomial of degree n. Taylor series. (3 + 0 + 2 hours)
16. Fourier series (definition and basic properties). (4 + 0 + 1 hours)
LEARNING OUTCOMES:
 to solve systems of linear equations with various methods
 to explain and to understand basic matrix algebra and basic knowledge about abstract vector spaces
 to explain and to understand fundamentals of multivariable calculus
 to explain and to understand advanced multivariable calculus notions  gradient, divergence, rotation, differentials, line integrals
 to explain and to understand the notion of ordinary differential equations and ability to solve basic types of ordinary differential equations
 to explain and to understand the definitions and basic properties of sequences, series and function series
 to explain and to understand basics of Fourier analysis

 M. Alić: Obične diferencijalne jednadžbe, PMFMatematički odjel, Zagreb, 1994.
 B. P. Demidovič: Zadaci i riješeni primjeri iz više matematike, Tehnička knjiga, Zagreb, 1978.
 S. Kurepa: Matematička analiza III, Tehnička knjiga, Zagreb, 1975.
 F. Ayres, E.Mendelson: Differential and Integral Calculus, Schaum's Outline Series, New York, 1990.
