Analysis 2

Integral: indefinite integral, integration rules, definite integral, relation between the definite and indefinite integral, improper integrals, applications of integration.

Basics of curves and surfaces: descriptions of curves and surfaces (explicit, implicit, parametric, polar coordinates), tangent to a curve, drawing of curves, arc lenght.

Number and function series: convergence: series of real and complex numbers, absolute and conditional convergence, convergence tests, alternating series, series of functions, uniform convergence, differentiation and integration of series of functions, power series, Taylor series.

Elementary differential equations: differential equations of first order (separable, exact, linear), linear differential equations of higher order.

Systems of differential equations: existence and uniqueness of solutions, structure of the space of solutions, linear systems with constant coefficients.

Ivan Vidav: Višja matematika I, Ljubljana: DMFA-založništvo, 1994.

Gabrijel Tomšič, Bojan Orel, Neža Mramor Kosta: Matematika I, Ljubljana: Založba FE in FRI, 2001.

Neža Mramor Kosta, Borut Jurčič Zlobec: Zbirka nalog iz matematike I, Ljubljana: Založba FE in FRI, 2001.

Pavlina Mizori-Oblak: Matematika za študente tehnike in naravoslovja, Del 1. Ljubljana: Fakulteta za strojništvo, 1991.

James Stuart: Calculus, Brooks/Cole Publishing Company, 1999.

M. H. Protter, C. B. Morrey, Intermediate Calculus. Springer-Verlag, New York-Heidelberg, 1985.

W. Rudin, Principles of mathematical analysis. McGraw-Hill, Auckland, 1976.

Student learns the basic concepts of mathematical analysis such as integral of real functions of one real variable, numerical and function series, Taylor series, and learns the basic metods for solving differential equations and systems of linear differential equations. Analysis 2 is one of the fundamental courses of the study of mathematics and computer science.

Knowledge and understanding: Knowledge and understanding of basic notions, definitions and theorems.

Application: Analysis 2 is one of the fundamental courses of the program. Understanding of the material of this course is indispensable for many other mathematics and computer science courses of the program.

Reflection: Understanding the theory from the applications.

Transferable skills: Skills in using the literature and other sources, the ability to identify and solve the problem, critical analysis.

Lectures and tutorial sessions, homework.

Two midterm exercise-based exams or final exercise-based exam.

Oral exam / Theoretical knowledge exam.

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

Janez Mrčun:
MOERDIJK, Ieke, MRČUN, Janez. On the developatibility of Lie subalgebroids. Advances in mathematics, ISSN 0001-8708, 2007, vol. 210, no. 1, str.1-21. [COBISS-SI-ID 14209881]
MRČUN, Janez. On isomorphisms of algebras of smooth functions. Proceedings of the American Mathematical Society, ISSN 0002-9939, 2005, vol. 133, no. 10, str. 3109-3113. [COBISS-SI-ID 13782361]
MOERDIJK, Ieke, MRČUN, Janez. On integrability of infinitesimal actions. American journal of mathematics, ISSN 0002-9327, 2002, vol. 124, no. 3, str. 567-593. [COBISS-SI-ID 11700057]
Sašo Strle:
RUBERMAN, Daniel, STRLE, Sašo. Concordance properties of parallel links. Indiana University mathematics journal, ISSN 0022-2518, 2013, vol. 62, no. 3, str. 799-814. [COBISS-SI-ID 16946265]
OWENS, Brendan, STRLE, Sašo. Dehn surgeries and negative-definite four-manifolds. Selecta mathematica. New series, ISSN 1022-1824, 2012, vol. 18, iss. 4, str. 839-854. [COBISS-SI-ID 16808025]
CHA, Jae Choon, KIM, Taehee, RUBERMAN, Daniel, STRLE, Sašo. Smooth concordance of links topologically concordant to the Hopf link. Bulletin of the London Mathematical Society, ISSN 0024-6093, 2012, vol. 44, iss. 3, str. 443-450. [COBISS-SI-ID 16807769]
Bojan Magajna:
–MAGAJNA, Bojan. Maps with the unique extension property and C∗-extreme points. Complex analysis and operator theory, ISSN 1661-8254, Nov. 2018, vol. 12, iss. 8, str. 1903-1927. [COBISS-SI-ID 18488409]
–MAGAJNA, Bojan. On the range inclusion for normal derivations on C∗-algebras. Proceedings of the Edinburgh Mathematical Society, ISSN 0013-0915, Feb. 2018, vol. 61, iss. 1, str. 1-11. [COBISS-SI-ID 18326873]
–MAGAJNA, Bojan. C∗-convex sets and completely positive maps. Integral equations and operator theory, ISSN 0378-620X, 2016, vol. 85, iss. 1, str. 37-62. [COBISS-SI-ID 17824601]