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.

1. G. N. Berman: A problem book in mathematical analysis, Moscow : Mir Publishers, 1980.
2. E. Kreyszig: Advanced Engineering Mathematics, 9th ed., Hoboken, NJ : J. Wiley & Sons, cop. 2006.
3. P. Mizori-Oblak: Matematika za študente tehnike in naravoslovja. Del 1, 6. izd., Ljubljana : Fakulteta za strojništvo, cop. 1997, 2001.
4. P. Mizori-Oblak: Matematika za študente tehnike in naravoslovja. Del 2, 6. izd., Ljubljana : Fakulteta za strojništvo, cop. 1997.
5. M. H. Protter, C. B. Morrey: Intermediate calculus, 2nd ed., New York, : Springer, 1985.
6. K. A. Ross: Elementary analysis : the theory of calculus, 2nd ed., New York : Springer, cop. 2013.
7. J. Stewart: Calculus, 6th ed., Belmont : Brooks/Cole, cop. 2009.
8. S. Strle: Analiza 1 : za študente Finančne matematike, DMFA – založništvo, Ljubljana, 2021.
9. G. Tomšič, B. Orel, N. Mramor Kosta: Matematika I, 4. izd., Ljubljana : Fakulteta za elektrotehniko : Fakulteta za računalništvo in informatiko, 2004.
10. G. Tomšič, B. Orel, N. Mramor Kosta: Matematika II, 4. izd., Ljubljana : Fakulteta za elektrotehniko, 2005.
11. I. Vidav: Višja matematika I, 10., 11. in 12., nespremenjena izd. - Ljubljana : DMFA - založništvo, 1990, 1994, 2008.
12. E. Zakrajšek: Analiza III, 3. popravljena izd. - Ljubljana : DMFA - založništvo, 2002.

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]