Introduction: natural numbers and mathematical induction, real numbers, complex numbers, sequences, accumulation points and limits.
Series: series of real and complex numbers, absolute and conditional convergence, convergence tests, alternating series.
Functions of one variable: continuity and the limit, properties of continuous functions, elementary functions.
Derivatives of functions of one variable: definition of the derivative and its geometric meaning, differentiation rules, derivatives of elementary functions, properties of differentiable functions, applications of the derivative (drawing graphs, calculating limits, extrema), Taylor's theorem, Taylor's series.
Integral: indefinite integral, basic rules for calculating integrals, definite integral, connection between a definite and an indefinite integral, generalized integrals, application of integrals.
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.
The student learns about the basic concepts of mathematical analysis, such as the limit of a sequence, numerical series, continuity, the derivative of a function of one real variable, Taylor series, an integral of a function of one real variable. Analysis 1 is one of the fundamental courses within 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]
Oliver Dragičević:
DRAGIČEVIĆ, Oliver, VOLBERG, Alexander. Linear dimension-free estimates in the embedding theorem for Schrödinger operators. Journal of the London Mathematical Society, ISSN 0024-6107, 2012, vol. 85, p. 1, str. 191-222. [COBISS-SI-ID 16214873]
DRAGIČEVIĆ, Oliver, VOLBERG, Alexander. Bilinear embedding for real elliptic differential operators in divergence form with potentials. Journal of functional analysis, ISSN 0022-1236, 2011, vol. 261, iss. 10, str. 2816-2828. [COBISS-SI-ID 16051545]
DRAGIČEVIĆ, Oliver. Weighted estimates for powers of the Ahlfors-Beurling operator. Proceedings of the American Mathematical Society, ISSN 0002-9939, 2011, vol. 139, no. 6, str. 2113-2120. [COBISS-SI-ID 15876697]
