# Computing

## Mathematical Analysis 1

- Class 90
- Practice 30
- Independent work 120

### 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:

- Physics 2
- Electrical Circuits
- Interactive Computer Graphics
- Electroacoustics
- Alarm Systems
- Fundamentals of Intelligent Control Systems
- Robotics Practicum
- Software Design Project
- Mathematics 3 - EE
- Mathematics 3 - C
- DisCont mathematics 1
- DisCont mathematics 2
- Electromechanics
- Mathematical Modeling of Computer
- Transmission of Audio
- Sound and Environment
- Technology in Medicine
- Electronics 1R
- 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.,

#### Online education during epidemiological measures

- Study program duration
- 6 semesters (3 years)
- Semester duration
- 15 weeks of active teaching + 5 examination weeks
- Total number of ECTS points
- 180
- Title
- Bacc.ing.comp (Bachelor of Science in Computing)

**Academic calendar**

#### Minimal learning outcomes

- Define and explain basic notions of discrete mathematics
- Apply basic counting methods in combinatorics
- Explain and relate fundamental notions and results of differential calculus
- Demonstrate and apply methods and techniques of differential calculus
- Describe and relate fundamental notions and results of integral calculus
- Demonstrate and apply techniques of integral calculus
- Demonstrate ability for mathematical modeling and problem solving
- Use critical thinking
- Demonstrate ability for mathematical expression and logic thinking Use methods of mathematical analysis in engineering