Subsets of Euclidean spaces. Differential calculus of several variables: partial derivatives, gradient and directional derivative, total differential and tangent space, Taylor's formula, local extrema and constrained extrema, implicit function theorem.
Basics of curves and surfaces: descriptions of curves and surfaces (explicit, implicit, parametric, polar coordinates), tangent to a curve, drawing of curves, arc length.
Function series: uniform convergence, differentiation and integration of series of functions, power series, Taylor series.
Elementary differential equations: differential equations of first order (separable, exact, linear), linear differential equations of higher order. Systems of differential equations: existence and uniqueness of solutions, structure of the space of solutions, linear systems with constant coefficients.
Analysis 2
- Ivan Vidav: Višja matematika I, Ljubljana: DMFA-založništvo, 1994.
- Sašo Strle: Analiza 1: za študente finančne matematike. DMFA - založništvo, 2021.
- Gabrijel Tomšič, Neža Mramor Kosta, Bojan Orel: Matematika II, Ljubljana: Založba FE in FRI, 2005.
- Neža Mramor Kosta, Borut Jurčič Zlobec: Zbirka nalog iz matematike II, Ljubljana: Založba FE in FRI, 2004.
- Pavlina Mizori-Oblak: Matematika za študente tehnike in naravoslovja, Del 2. Ljubljana: Fakulteta za strojništvo, 1997.
- James Stuart: Calculus, Brooks/Cole Publishing Company, 1999.
- Walter Rudin: Principles of mathematical analysis. McGraw-Hill, Auckland, 1976.
Student learns basic concepts of mathematical analysis such as functions of many real variables, function series, and the basic metods for solving differential equations and systems of linear differential equations. Analysis 2 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 2 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 from the 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.
Two midterm exercise-based exams or final exercise-based exam.
Oral exam / Theoretical knowledge exam.
6-10 (pass), 5 (fail) (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]
Barbara Drinovec Drnovšek:
DRINOVEC-DRNOVŠEK, Barbara, FORSTNERIČ, Franc. Minimal hulls of compact sets in R3R3. Transactions of the American Mathematical Society. 2016, vol. 368, no. 10, str. 7477-7506. [COBISS-SI-ID 17543769]
ALARCÓN, Antonio, DRINOVEC-DRNOVŠEK, Barbara, FORSTNERIČ, Franc, LÓPEZ, Francisco J. Minimal surfaces in minimally convex domains. Transactions of the American Mathematical Society, ISSN 0002-9947, Feb. 2019, vol. 371, no. 3, str. 1735-1770. [COBISS-SI-ID 18379865]
DRINOVEC-DRNOVŠEK, Barbara, SLAPAR, Marko. Proper holomorphic curves attached to domains. Complex variables and elliptic equations. 2020, vol. 65, no. 3, str. 489-497. [COBISS-SI-ID 18647129]
