### Mathematical Analysis 1

#### Learning Outcomes

1. define and explain basic notions of discrete mathematics
2. apply basic counting methods in combinatorics
3. explain and relate fundamental notions and results of differential calculus
4. demonstrate and apply methods and techniques of differential calculus
5. describe and relate fundamental notions and results of integral calculus
6. demonstrate and apply techniques of integral calculus
7. demonstrate ability for mathematical modeling and problem solving
8. use critical thinking
9. demonstrate ability for mathematical expression and logic thinking
10. use methods of mathematical analysis in engineering

#### Forms of Teaching

Lectures

Lectures are held in two cycles, 6 hours per week.

Exercises

Excercises are held two hours per week.

Partial e-learning

Teaching materials and homeworks are accessible on course webpage.

Continuous Assessment Exam
Homeworks 50 % 0 % 0 % 0 %
Attendance 50 % 0 % 0 % 0 %
Mid Term Exam: Written 0 % 50 % 0 %
Final Exam: Written 0 % 50 %
Exam: Written 0 % 100 %
##### Comment:

Regular attendance of lectures and doing homework are conditions for taking exam.

#### Week by Week Schedule

1. 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.
2. Real functions; Injection, surjection, bijection; Composition; Inverse function; Bijective functions; Equipotent sets; Cardinal number, countable and uncountable sets; Binary relations; Equivalence relation; Quotient set.
3. 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.
4. Elementary functions, properties and basic relations, graphs; Graph transformations, translation, symmetry, rotation; Parametric functions; Polar equations of the plane curves.
5. Sequences, subsequences, accumulation points; Limit, convergence of a sequence; Monotone sequences, some notable limits.
6. Limit of a function, properties and operations with limits; One-sided limits; Limits of indeterminate forms; Continuity of functions; Properties of function on interval.
7. Derivative of a function, geometrical and physical interpretation, differentiation rules; Derivative of composition and inverse function; Higher order derivatives; Differentiation of elementary functions.
8. Midterm exam.
9. 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.
10. 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.
11. Asymptotes; Qualitative graph of a function; Differential of an arc; Curvature; Evolute; Area under a curve, definite integral, Newton-Leibniz formula.
12. Methods of integration, substitution, integration by parts; Integration of rational functions; Integration of trigonometric functions.
13. Improrer integrals; Area of planar sets.
14. 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.
15. Final exam.

#### Study Programmes

Electrical Engineering and Information Technology and Computing (study)
(1. semester)

#### Literature

(.), 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.,

#### General

ID 183352
Winter semester
8 ECTS
L1 English Level
L2 e-Learning
90 Lectures
30 Exercises
0 Laboratory exercises
0 Project laboratory