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.
Curve integral, surface integral, arc length, area of a surface and other applications.
Fundamentals of vector analysis, Gauss and Stokes theorem.
Holomorphic functions. Integral of a holomorphic function. Cauchy theorem. Series expansion of a holomorphic function.
Simple partial differential equations. Wave equation. Heat equation.
Fundamentals of metric spaces. Fixed point theorem.

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

2 midterm exams instead of written exam, written exam
Oral exam
grading: 5 (fail), 6-10 (pass) (according to the Statute of UL)

Barbara Drinovec Drnovšek:
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, 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. 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]
Franc Forstnerič:
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]
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, 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]
Pavle Saksida:
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]
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. 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]