1. The number line. Approximating real numbers with decimal ones. Limiting processes. (3+0+0 hours)
2. Graphs and properties of elementary functions: polynomials, rational functions, trigonometric functions, exponential function, logarithmic function. (10 + 0 + 5 hours)
3. Graphs and properties of elementary functions: cyclometric functions, hyperbolic functions, general exponential function. (3 + 0 + 1 hours)
4. Derivative of a function and linearisation of nonlinear problems; the notion of a tangent and of speed in mechanics. Higherorder derivatives. (5 + 0 + 1 hours)
5. Differential calculus: basic properties of derivatives and tabular differentiation. (4 + 0 + 5 hours)
6. Optimization problems for onevariable functions. Extrema of functions. The secondderivative test. (6 + 0 + 5 hours)
7. Analyzing graphs of functions using derivatives: extrema, intervals of increase and decrease, graph sketching. (3 + 0 + 6 hours)
8. Analyzing graphs of functions using derivatives: extrema, intervals of increase and decrease, convexity and concaveness, asymptotic behaviour of functions. L'Hospital rule. (4 + 0 + 4 hours)
9. Indefinite integral: definition and basic properties, substitutions in integrals, partial integration, primitive function. (6 + 0 + 5 hours)
10. Definite integral: LeibnizNewton formula, applications of integrals. (6 + 0 + 5 hours)
11. Basic linear algebra: vectors, basis, coordinatisation, dot, cross and triple product of vectors in threedimensional space. (5 + 0 + 4 hours)
12. Analytic geometry of space: Equation of a plane in space, equation of a line in space. (5 + 0 + 4 hours)
LEARNING OUTCOMES:
 to understand fundamental notions about functions and their graphs
 to explain and to understand of elementary onevariable functions
 to explain and to understand the definition and geometric interpretation of limits of functions, and of the procedure of calcultation simpler limits
 to explain and to understand the definitions of a derivative of a function, ability of calculating and interpreting derivatives and applying them to analyzing functional graphs
 to explain and to understand the definitions and connections between various types of integrals and ability of calculating simpler integrals
 to explain and to understand classical vector algebra
 to explain and to understand basic analytical geometry of space

 B.P. Demidovič: Zadaci i riješeni primjeri iz više matematike, Tehnička knjiga, Zagreb, 1978.
 S. Kurepa: Matematička analiza I, Tehnička knjiga, Zagreb, 1975.
 S. Kurepa: Uvod u linearnu algebru, Školska knjiga, Zagreb, 1975.
 F. Ayres, E. Mendelson: Differential and Integral Calculus, Schaum's Outline Series, New York, 1990.
