COURSE AIMS AND OBJECTIVES: In this course, students are introduced to some of the fundamental concepts of mathematical analysis, such as real numbers, sequences, convergence of sequences, series, convergence of series, limits of functions, and continuity of functions.
COURSE DESCRIPTION AND SYLLABUS:
1) Real numbers. The axioms of the field R, supremum and infimum of a set, completeness.
2) Sequences. Definition of a sequence and subsequence, monotonicity, boundedness, monotone subsequence, various examples of sequences. Convergence, basic rules, the relationship between convergence, boundedness, and monotonicity, Cauchy sequence, limit superior and limit inferior, Bolzano-Weierstrass theorem for sequences.
3) Series. Series, convergence, absolute convergence, tests for convergence of series, geometric series.
4) Continuity. Limit of a function and basic rules. Continuity of a function and operations with continuous functions. Examples.
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Matematička analiza 1 & 2, B. Guljaš, Skripta, 2018.
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Calculus I, J. E. Marsden, A. Weinstein, Springer, New York, 1985.
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Calculus: One and Several Variables, S. L. Salas, G. J. Etgen, E. Hille, Wiley, Hoboken, 2006.
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Pristupačnost
