Introduction: natural numbers and mathematical induction, real numbers, sequences and limits, compact subsets of Euclidean spaces.
Functions: the notion of a function of one and many variables, level curves and level surfaces, continuity and limit of a function, properties of continuous functions, elementary functions.
Derivative of a function of one variable: definition of the derivative and its geometric meaning, differentiation rules, derivatives of elementary functions, applications of the derivative (drawing graphs of functions, computations of limits, extrema), Taylor formula.
Derivative of a function of many variables: partial derivatives, gradient and directional derivative, total differential and tangent space, Taylor formula, local extrema and conditional extrema, the implicit function theorem.
Analysis 1
Ivan Vidav: Višja matematika I, Ljubljana: DMFA-založništvo, 1994.
Gabrijel Tomšič, Bojan Orel, Neža Mramor Kosta: Matematika I, Ljubljana: Založba FE in FRI, 2001.
Neža Mramor Kosta, Borut Jurčič Zlobec: Zbirka nalog iz matematike I, Ljubljana: Založba FE in FRI, 2001.
Pavlina Mizori-Oblak: Matematika za študente tehnike in naravoslovja, Del 1. Ljubljana: Fakulteta za strojništvo, 1991.
James Stuart: Calculus, Brooks/Cole Publishing Company, 1999.
M. H. Protter, C. B. Morrey, Intermediate Calculus. Springer-Verlag, New York-Heidelberg, 1985.
W. Rudin, Principles of mathematical analysis. McGraw-Hill, Auckland, 1976.
Student learns the basic concepts of mathematical analysis such as limit of a sequence and continuity and derivative of real functions of one ans well as many real variables. Analysis 1 is one of the fundamental courses of the study of mathematics and computer science.
Knowledge and understanding: Knowledge and understanding of basic notions, definitions and theorems.
Application: Analysis 1 is one of the fundamental courses of the program. Understanding of the material of this course is indispensable for many other mathematics and computer science courses of the program.
Reflection: Understanding the theory fromthe applications.
Transferable skills: Skills in using the literature and other sources, the ability to identify and solve the problem, critical analysis.
Lectures and tutorial sessions, homework.
2 midterm exams instead of written exam, written exam
Oral exam / theoretical test.
grading: 5 (fail), 6-10 (pass) (according to the Statute of UL)
Janez Mrčun:
MOERDIJK, Ieke, MRČUN, Janez. On the developatibility of Lie subalgebroids. Advances in mathematics, ISSN 0001-8708, 2007, vol. 210, no. 1, str.1-21. [COBISS-SI-ID 14209881]
MRČUN, Janez. On isomorphisms of algebras of smooth functions. Proceedings of the American Mathematical Society, ISSN 0002-9939, 2005, vol. 133, no. 10, str. 3109-3113. [COBISS-SI-ID 13782361]
MOERDIJK, Ieke, MRČUN, Janez. On integrability of infinitesimal actions. American journal of mathematics, ISSN 0002-9327, 2002, vol. 124, no. 3, str. 567-593. [COBISS-SI-ID 11700057]
Sašo Strle:
RUBERMAN, Daniel, STRLE, Sašo. Concordance properties of parallel links. Indiana University mathematics journal, ISSN 0022-2518, 2013, vol. 62, no. 3, str. 799-814. [COBISS-SI-ID 16946265]
OWENS, Brendan, STRLE, Sašo. Dehn surgeries and negative-definite four-manifolds. Selecta mathematica. New series, ISSN 1022-1824, 2012, vol. 18, iss. 4, str. 839-854. [COBISS-SI-ID 16808025]
CHA, Jae Choon, KIM, Taehee, RUBERMAN, Daniel, STRLE, Sašo. Smooth concordance of links topologically concordant to the Hopf link. Bulletin of the London Mathematical Society, ISSN 0024-6093, 2012, vol. 44, iss. 3, str. 443-450. [COBISS-SI-ID 16807769]
