Completed courses Analysis 1 and Analysis 2.
Analysis 3
2018/2019
Programme:
Interdisciplinary University Study Programme Computer Science and Mathematics
Year:
2 year
Semester:
first
Kind:
mandatory
ECTS:
5
Language:
slovenian
Course director:
Lecturer (contact person):
Hours per week – 1. semester:
Lectures
2
Seminar
0
Tutorial
2
Lab
0
Content (Syllabus outline)
Multiple integrals: integrals with a parameter, double and multiple integrals, length of a curve, area of a surface.
Systems of differential equations: existence and uniqueness of solutions, structure of the space of solutions, systems with constant coefficients, phase space, stationary points, stability.
Functions of a complex variable: elementary functions of a complex variable, the Cauchy theorem, residues and evaluation of integrals, transformations of the complex plane.
Readings
Ivan Vidav: Višja matematika 2, Državna založba Slovenije, Ljubljana, 1979, 591 str.
Erwin Kreyszig: Advanced engineering mathematics, 9th ed., J.Wiley, Hoboken, 2006.
Gabrijel Tomšič, Tomaž Slivnik: Matematika III, Založba FE in FRI, Ljubljana, 2001, 175 str.
Tomo Žitko: Zbirka nalog iz matematike III, Založba FE in FRI, Ljubljana, 2002, 92 str.
Serge Lang: Calculus of several variables, Springer-Verlag, 1995.
Objectives and competences
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.
Intended learning outcomes
Knowledge and understanding:
Understanding of certain advanced topics of mathematical analysis.
Learning and teaching methods
Lectures, classes, homework, consultations.
Assessment
Type (examination, oral, coursework, project):
Lecturer's references
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]
