Course title

Mathematical Analysis 1

Lecture type

Obligatory

Course code

183352

Semester

1

ECTS

8

Lecturers and associates

• Full Professor PhD Ilko Brnetić
• Assistant Professor PhD Mario Bukal
• Associate Professor PhD Tomislav Burić
• Assistant Professor PhD Lana Horvat Dmitrović
• Full Professor PhD Mervan Pašić
• Associate Professor PhD Josipa Pina Milišić
• Assistant Professor PhD Ana Žgaljić Keko
• Full Professor PhD Darko Žubrinić

Course objectives

Integers and rational numbers. Set of real numbers; Order in set of real numbers, absolute value, inequalities, infimum and supremum; Complex numbers, arithmetic operations, trigonometric form, powers and roots of complex numbers; Sets. Subsets. Set algebra. Direct product of sets; Integers. Mathematical induction.
Real functions. Injection, surjection, bijection. Composition. Inverse function; Bijective functions. Equipotent sets. Cardinal number, countable and uncountable sets; Binary relations. Equivalence relation. Quotient set.
Permutations, variations and combinations (without or with repetitions); Binomial and multinomial theorem. Inclusion-Exclusion principle; Pigeonhole principle; Generating functions. Operations with generating functions. Applications in enumerative combinatorics.
Elementary functions, properties and basic relations, graphs; Graph transformations, translation, symmetry, rotation; Parametric functions. Polar equations of the plane curves.
Sequences, subsequences, accumulation points. Limit, convergence of a sequence; Monotone sequences, some notable limits.
Limit of a function, properties and operations with limits; One-sided limits. Limits of indeterminate forms; Continuity of functions. Properties of function on interval.
Derivative of a function, geometrical and physical interpretation, differentiation rules; Derivative of composition and inverse function. Higher order derivatives; Differentiation of elementary functions.
Midterm exam.
Differentiation of implicit and parametric functions; Basic theorems of differential calculus, Lagrange mean value theorem; Taylor's theorem, Taylor's polynomial; L'Hospital's rule. Limits of indeterminante forms.
Tangent and normal lines to the graph of function. Increasing and decreasing functions; Convexity and concavity of a function. Finding extrema of a function, necessary and sufficient conditions.
Asymptotes. Qualitative graph of a function; Differential of an arc. Curvature. Evolute; Area under a curve, definite integral, Newton-Leibniz formula.
Methods of integration, substitution, integration by parts; Integration of rational functions; Integration of trigonometric functions.
Improrer integrals; Area of planar sets.
Arc length of curves; Volume of solid of revolution; Area of sets and length of curves in polar coordinates; Surface of solid of revolution; Application of integrals in physics.
Final exam.

Prerequisites for:

1. Physics 2
2. Electrical Circuits
3. Interactive Computer Graphics
4. Electroacoustics
5. Alarm Systems
6. Fundamentals of Intelligent Control Systems
7. Robotics Practicum
8. Software Design Project
9. Mathematics 3 - EE
10. Mathematics 3 - C
11. DisCont mathematics 1
12. DisCont mathematics 2
13. Electromechanics
14. Mathematical Modeling of Computer
15. Transmission of Audio
16. Sound and Environment
17. Technology in Medicine
18. Electronics 1R
19. Physics 2R

Required reading

(.), P. Javor, Matematička analiza 1, Element, 1999.,(.), A. Aglić Aljinović i ostali, Matematika 1, Element, 2015.,(.), J. Stewart, Single Variable Calculus, 8th edition, Cengage Learning, Boston, USA, 2016.,(.), M. Pašić, Matematička analiza 1, Merkur ABD, 2004.,(.), B.P. Demidovič, Zadaci i riješeni primjeri iz matematičke analize za tehničke fakultete, Danjar, Zagreb, 1995.,(.), B.E. Blank, S.G. Krantz, Single Variable Calculus, John Wiley and Sons, 2011.,