Mathematical Analysis 1
- 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
Forms of Teaching
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.
|Type||Threshold||Percent of Grade||Threshold||Percent of Grade|
|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 %|
Regular attendance of lectures and doing homework are conditions for taking exam.
Week by Week Schedule
- 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.
Electrical Engineering and Information Technology and Computing (study)(1. semester)
(.), 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.,
L1 English Level
0 Laboratory exercises
0 Project laboratory
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