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Mathematics 1

 Code: 38176 ECTS: 8.0 Lecturers in charge: doc. dr. sc. Franka Miriam Brückler - Lectures Lecturers: Sonja Žunar - Exercises Take exam: Studomat

1. komponenta

Lecture typeTotal
Lectures 60
Exercises 45
Description:
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. Higher-order derivatives. (5 + 0 + 1 hours)
5. Differential calculus: basic properties of derivatives and tabular differentiation. (4 + 0 + 5 hours)
6. Optimization problems for one-variable functions. Extrema of functions. The second-derivative 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: Leibniz-Newton 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 one-variable 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
Literature:
1. B.P. Demidovič: Zadaci i riješeni primjeri iz više matematike, Tehnička knjiga, Zagreb, 1978.
2. S. Kurepa: Matematička analiza I, Tehnička knjiga, Zagreb, 1975.
3. S. Kurepa: Uvod u linearnu algebru, Školska knjiga, Zagreb, 1975.
4. F. Ayres, E. Mendelson: Differential and Integral Calculus, Schaum's Outline Series, New York, 1990.
 1. semester Mandatory course - Mandatory studij - Chemistry
Consultations schedule: