Analysis 2

Completed course Analysis 1.

Integral: indefinite integral, basic integration rules, definite integral of function of one variable, relation between definite and indefinite integral, improper integrals, applications

Plane curves: Representation of plane curves (explicit, implicit, parametric, polar), tangent, arc length, curvature, osculating circle.

Number and function series: number series , convergence, absolute and conditional convergence, Leibniz criterion, uniform convergence of function series, derivation and integration of function series, power series, Taylor series, Fourier series.

I.Vidav: Višja Matematika I, DMFA-založništvo, Ljubljana, 1994.
M. H. Protter, C. B. Morrey: Intermediate calculus, New York, Springer, 1985.
E. Kreyszig: Advanced Engineering Mathematics, Huboken, J. Wiley, 2006.
J. Stuart: Calculus, 5th edition, Brooks/Cole, Pacific Grove, 2003
E. Zakrajšek: Analiza III, DMFA-založništvo, Ljubljana, 2002.
G. Tomšič, B. Orel, N. Mramor Kosta: Matematika I, Založba FE in FRI, Ljubljana, 2004.
G. Tomšič, N. Mramor Kosta, B. Orel: Matematika II, Založba FE in FRI, Ljubljana, 2005.
G. N. Berman: A Problem Book in Mathematical Analysis, Moskva, Mir Publ., 1980.
P. Mizori-Oblak: Matematika za študente tehnike in naravoslovja I, Fakulteta za strojništvo, Ljubljana, 2001.
P. Mizori-Oblak: Matematika za študente tehnike in naravoslovja II, Fakulteta za strojništvo, Ljubljana, 2003.

Students learn new definitions and techniques in mathematical analysis and differential geometry together with the applications in mathematics, natural science, engineering and other fields of science.

Knowledge and understanding: Knowledge and understanding of additional concepts of integral calculus, number and function series.

Application: The course is a continuation of Analysis 1. This is a basic mathematical course that introduces terms that are used in the subsequent mathematical courses.

Reflection: Integration of the acquired knowledge and its application in other areas.

Transferable skills: The ability to formulate a problem in mathematical language, choose an appropriate method, and solve the problem individually.

Lectures, exercises, homework, consultations

Type (examination, oral, coursework, project):

2 midterm exams instead of problem-based exam, problem-based exam

theoretical knowledge exam

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

Barbara Drinovec Drnovšek:
– DRINOVEC-DRNOVŠEK, Barbara. Discs in Stein manifolds containing given discrete sets. Mathematische Zeitschrift, ISSN 0025-5874, 2002, vol. 239, no. 4, str. 683-702 [COBISS-SI-ID 11567449]
– DRINOVEC-DRNOVŠEK, Barbara. Proper holomorphic discs avoiding closed convex sets. Mathematische Zeitschrift, ISSN 0025-5874, 2002, vol. 241, no. 3, str. 593-596 [COBISS-SI-ID 12076377]
– DRINOVEC-DRNOVŠEK, Barbara, FORSTNERIČ, Franc. Strongly pseudoconvex domains as subvarieties of complex manifolds. American journal of mathematics, ISSN 0002-9327, 2010, vol. 132, no. 2, str. 331-360 [COBISS-SI-ID 15549529]
– DRINOVEC-DRNOVŠEK, Barbara, STRLE, Sašo. Naloge iz analize 1 : z odgovori, nasveti in rešitvami, (Izbrana poglavja iz matematike in računalništva, 46). 1. natis. Ljubljana: DMFA - založništvo, 2010. 285 str., ilustr. ISBN 978-961-212-219-5 [COBISS-SI-ID 250561280]

Roman Drnovšek:
– DRNOVŠEK, Roman. Invariant subspaces for operator semigroups with commutators of rank at most one. Journal of functional analysis, ISSN 0022-1236, 2009, vol. 256, iss. 12, str. 4187-4196 [COBISS-SI-ID 15167321]

– DRNOVŠEK, Roman. An infinite-dimensional generalization of Zenger's lemma. Journal of mathematical analysis and applications, ISSN 0022-247X, 2012, vol. 388, iss. 2, str. 1233-1238 [COBISS-SI-ID 16214617]

– DRNOVŠEK, Roman. Triangularizability of trace-class operators with increasing spectrum. Journal of mathematical analysis and applications, ISSN 0022-247X, 2017, vol. 447, iss. 2, str. 1102-1115 [COBISS-SI-ID 17797721]

Franc Forstnerič:
– FORSTNERIČ, Franc. Runge approximation on convex sets implies the Oka property. Annals of mathematics, ISSN 0003-486X, 2006, vol. 163, no. 2, str. 689-707 [COBISS-SI-ID 13908825]
– FORSTNERIČ, Franc. Stein manifolds and holomorphic mappings : the homotopy principle in complex analysis, (Ergebnisse der Mathematik und ihrer Grenzgebiete, Folge 3, vol. 56). Heidelberg [etc.]: Springer, cop. 2011. X, 489 str., ilustr. ISBN 978-3-642-22249-8. ISBN 978-3-642-22250-4 [COBISS-SI-ID 16008025]
– FORSTNERIČ, Franc. Holomorphic families of long c [sup] 2's. Proceedings of the American Mathematical Society, ISSN 0002-9939, 2012, vol. 140, no. 7, str. 2383-2389 [COBISS-SI-ID 16435289]

Sašo Strle:
– OWENS, Brendan, STRLE, Sašo. A characterisation of the n<1>[oplus]<3> form and applications to rational homology spheres. Mathematical research letters, ISSN 1073-2780, 2006, vol. 13, iss. 2, str. 259-271 [COBISS-SI-ID 13873241]
– GRIGSBY, J. Elisenda, RUBERMAN, Daniel, STRLE, Sašo. Knot concordance and Heegaard Floer homology invariants in branched covers. Geometry & topology, ISSN 1364-0380, 2008, vol. 12, iss. 4, str. 2249-2275 [COBISS-SI-ID 14892121]
– OWENS, Brendan, STRLE, Sašo. A characterization of the Z [sup] n [oplus] Z([delta]) lattice and definite nonunimodular intersection forms. American journal of mathematics, ISSN 0002-9327, 2012, vol. 134, no. 4, str. 891-913 [COBISS-SI-ID 16408153]
– DRINOVEC-DRNOVŠEK, Barbara, STRLE, Sašo. Naloge iz analize 1 : z odgovori, nasveti in rešitvami, (Izbrana poglavja iz matematike in računalništva, 46). 1. natis. Ljubljana: DMFA - založništvo, 2010. 285 str., ilustr. ISBN 978-961-212-219-5 [COBISS-SI-ID 250561280]