Analysis 3

Completed courses Analysis 1 and Analysis 2.

Parametric integral, gamma and beta functions.

Double and triple integral with most common applications.

Curves and surfaces in space, tangent to a curve, normal to a surface.

Fundamentals of metric spaces. Fixed point theorem.

Space R^n: metric, open and closed sets, sequences, compactness, existence of global extrema.

Holomorphic functions. Integral of a holomorphic function. Cauchy theorem. Series expansion of a holomorphic function.

Simple differential equations.

Linear differential equations. Systems of linear differential equations of the first order.

I. Vidav: Matematika III, DZS, Ljubljana, 1976.
M. H. Protter, C. B. Morrey: Intermediate Calculus, New York, Springer, 1985.
E. Kreyszig: Advanced Engineering Mathematics, Huboken, J.Wiley, 2006.
S. Lang: Calculus of Several Variables, 3rd edition, Springer, New York, 1996.
I. N. Sneddon: Elements of Partial Differential Equations, McGraw-Hill, New York-Toronto-London,1957.
G. Tomšič, T. Slivnik: Matematika III, Založba FE in FRI, Ljubljana, 2001.
P. Mizori-Oblak: Matematika za študente tehnike in naravoslovja II, Fakulteta za strojništvo, Ljubljana, 2003.
P. DuChateau, D. W. Zachman: Schaum's Outline of Theory and Problems of Partial Differerential Equations, McGraw-Hill, New York, 1986.

Extension of the basic knowledge of analysis, understanding of complex concepts and principles and their application in mathematics, natural science, engineering, and other disciplines.

Knowledge and understanding: Knowledge and understanding of concepts of differential and integral calculus of several variables and partial differential equations.

Application: The course is the continuation of Analysis 1 and Analysis 2. The material is later used in most of the professional courses.

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

Transferable skills: The ability of clear definition of problems in mathematical language and the choice of appropriate methods. Ability to use domestic and foreign literature.

Lectures, exercises, consultations

Type (examination, oral, coursework, project):

2 midterm exams instead of written exam, written exam

theoretical knowledge exam

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

Barbara Drinovec Drnovšek:
– DRINOVEC-DRNOVŠEK, Barbara. Proper discs in Stein manifolds avoiding complete pluripolar sets. Mathematical research letters, ISSN 1073-2780, 2004, vol. 11, no. 5-6, str. 575-581 [COBISS-SI-ID 13311065]
– DRINOVEC-DRNOVŠEK, Barbara, FORSTNERIČ, Franc. Approximation of holomorphic mappings on strongly pseudoconvex domains. Forum mathematicum, ISSN 0933-7741, 2008, vol. 20, iss. 5, str. 817-840 [COBISS-SI-ID 15078745]
– 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]

Franc Forstnerič:
– FORSTNERIČ, Franc, WOLD, Erlend Fornæss. Fibrations and Stein neighborhoods. Proceedings of the American Mathematical Society, ISSN 0002-9939, 2010, vol. 138, no. 6, str. 2037-2042 [COBISS-SI-ID 15876441]
– 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]

Pavle Saksida:
– 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]
– SAKSIDA, Pavle. Maxwell-Bloch equations, C Neumann system and Kaluza-Klein theory. Journal of physics. A, Mathematical and general, ISSN 0305-4470, 2005, vol. 38, no. 48, str. 10321-10344 [COBISS-SI-ID 13802073]
– SAKSIDA, Pavle. Lattices of Neumann oscillators and Maxwell-Bloch equations. Nonlinearity, ISSN 0951-7715, 2006, vol. 19, no. 3, str. 747-768 [COBISS-SI-ID 13932377]