Analysis 3

Completed course Analysis 1.

Integrals with a parameter: continuity and differentiability.

Multiple integrals: definition and properties, change of variables, Fubini theorem. Length of a curve, area of a surface.

Functions of a complex variable: elementary functions of a complex variable, the Cauchy theorem, residues and evaluation of integrals, transformations of the complex plane.

1. M. Dobovišek: Matematika 2, Ljubljana : DMFA - založništvo, 2013.
2. M. Dobovišek: Rešene naloge iz analize II, Ljubljana : DMFA - založništvo, 2001, 2014, 2020.
3. E. Kreyszig: Advanced engineering mathematics, 7th ed. in 9th ed., Hoboken : J. Wiley & Sons, cop. 1993, 2006.
4. S. Lang: Calculus of several variables, 3rd ed., New York : Springer, cop. 1987.
5. G. Tomšič, T. Slivnik: Matematika III, Ljubljana : Fakulteta za elektrotehniko, 1996.
6. I. Vidav: Višja matematika. 2, Ljubljana : Državna založba Slovenije, 1975.
7. T. Žitko: Zbirka nalog iz matematike III, 8. izd., Ljubljana : Fakulteta za elektrotehniko, 2002.

By attending the course students get acquainted with some new notions and techniques of mathematical analysis, such as the double and the triple integrals, differential equations and complex analysis. These topics belong to the applied mathematics and are an essential component in the education of the students majoring in natural sciences or engineering. During the lectures and the classes students learn the mathematical rigor. They also acquire practical working knowledge of the topics, covered in the course.

Knowledge and understanding:
Understanding of certain advanced topics of mathematical analysis.

Lectures, classes, homework, consultations.

Two midterm exercise-based exams or final exercise-based exam.

Theoretical knowledge exam.

Grades: 6-10 (pass), 5 (fail) (according to the Statute of UL)

Pavle Saksida:
SAKSIDA, Pavle. On the nonlinear Fourier transform associated with periodic AKNS-ZS systems and its inverse. Journal of physics. A, Mathematical and theoretical, ISSN 1751-8113, 2013, vol. 46, no. 46, 465204 (22 str.). [COBISS-SI-ID 16833369]
SAKSIDA, Pavle. Integrable anharmonic oscillators on spheres and hyperbolic spaces. Nonlinearity, ISSN 0951-7715, 2001, vol. 14, no. 5, str. 977-994. [COBISS-SI-ID 10942809]
SAKSIDA, Pavle. Nahm's equations and generalizations Neumann system. Proceedings of the London Mathematical Society, ISSN 0024-6115, 1999, let. 78, št. 3, str. 701-720. [COBISS-SI-ID 8853849]
Aleš Vavpetič:
CENCELJ, Matija, DYDAK, Jerzy, VAVPETIČ, Aleš, VIRK, Žiga. A combinatorial approach to coarse geometry. Topology and its Applications, ISSN 0166-8641. [Print ed.], 2012, vol. 159, iss. 3, str. 646-658. [COBISS-SI-ID 16094809]
CENCELJ, Matija, DYDAK, Jerzy, MITRA, Atish, VAVPETIČ, Aleš. Hurewicz-Serre theorem in extension theory. Fundamenta mathematicae, ISSN 0016-2736, 2008, vol. 198, no. 2, str. 113-123. [COBISS-SI-ID 14551385]
CENCELJ, Matija, MRAMOR KOSTA, Neža, VAVPETIČ, Aleš. G-complexes with a compatible CW structure. Journal of mathematics of Kyoto University, ISSN 0023-608X, 2003, vol. 43, no. 3, str. 585-597. [COBISS-SI-ID 12807769]

Barbara Drinovec Drnovšek:
– 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, SIGURDSSON, Ragnar. A note on weighted homogeneous Siciak-Zaharyuta extremal functions. Indagationes mathematicae, ISSN 0019-3577, 2016, vol. 27, no. 1, str. 94-99. [COBISS-SI-ID 17434201]
–DRINOVEC-DRNOVŠEK, Barbara, FORSTNERIČ, Franc. Minimal hulls of compact sets in R3. Transactions of the American Mathematical Society, ISSN 0002-9947, 2016, vol. 368, no. 10, str. 7477-7506. [COBISS-SI-ID 17543769]