Introduction: numbers, sequences, cluster and limit points, compact, open and closed subsets of Euclidean spaces, recursive sequences.
Functions: functions of one and several variables, level curves, level surfaces, basic properties, continuity, limit values, properties of continuos functions.
Differential calculus of one variable: definition and geometric property, differentiation rules, derivatives of elementary functions, applications in analysing functions: graphs, limits, extremal points, Taylor formula, indefinite integral, simple first order differential equations.
Differential calculus of several variables. partial derivatives, gradient and directional derivatives, differentiability, Taylor formula, free and constrained extrema,implicit function theorem.
Analysis 1
I. Vidav: Višja Matematika I, DMFA-založništvo, Ljubljana, 1994.
J. Stuart: Calculus, 5th edition, Brooks/Cole, Pacific Grove, 2003.
K. A. Ross: Elementary analysis: The theory of calculus, New York-Heidelberg, 2003.
S. Lang: Calculus of Several Variables, 3rd edition, Springer, New York, 1996.
G. N. Berman: A problem book in mathematical analysis, Moskva, Mir Publ. , 1980.
G. Tomšič, B. Orel, N. Mramor Kosta: Matematika I, Založba FE in FRI, Ljubljana, 2004.
G. Tomšič, B. Orel, N. Mramor Kosta: Matematika II, Založba FE in FRI, Ljubljana, 2005.
P. Mizori-Oblak: Matematika za študente tehnike in naravoslovja I, Fakulteta za strojništvo, Ljubljana, 2001.
P. Mizori-Oblak: Matematika za študente tehnike in naravoslovja I, Fakulteta za strojništvo, Ljubljana, 2003.
Students learn the basic concepts and techniques of mathematical analysis, such as function, limit, continuity and derivative. Analysis 1 is a fundamental course for other mathematical and special courses in study of mathematics, natural science, technical science and other fields of science.
Knowledge and understanding: Understanding of real functions of one and several variables and of differential calculus.
Application: Analysis 1 is a fundamental course in natural science, technical science, social science and other fields of science.
Reflection: Understanding of the theory from the examples and applications.
Transferable skills: The ability to formulate a problem mathematical language, the ability to select an appropriate method. The ability to accurately solve the problem and analize the obtained results.
Lectures, exercises, homeworks, consultations
2 midterm exams instead of written exam, written exam
Oral exam
grading: 5 (fail), 6-10 (pass) (according to the Statute of UL)
Miran Černe:
ČERNE, Miran, ZAJEC, Matej. Boundary differential relations for holomorphic functions on the disc. Proceedings of the American Mathematical Society, ISSN 0002-9939, 2011, vol. 139, no. 2, str. 473-484. [COBISS-SI-ID 15710553]
ČERNE, Miran, FLORES, Manuel. Some remarks on Hartogs' extension lemma. Proceedings of the American Mathematical Society, ISSN 0002-9939, 2010, vol. 138, no. 10, str. 3603-3609. [COBISS-SI-ID 15696473]
ČERNE, Miran, FLORES, Manuel. Boundary value problems for holomorphic functions on the upper half-plane. The Asian journal of mathematics, ISSN 1093-6106, 2007, vol. 11, no. 4, str. 609-620. [COBISS-SI-ID 14762073]
ČERNE, Miran. Matematika 2, (Matematični rokopisi, 24). Ljubljana: Društvo matematikov, fizikov in astronomov Slovenije: DMFA - založništvo, 1999. 127 str., ilustr. ISBN 961-212-096-X. [COBISS-SI-ID 103971072]
Oliver Dragičević:
DRAGIČEVIĆ, Oliver, VOLBERG, Alexander. Linear dimension-free estimates in the embedding theorem for Schrödinger operators. Journal of the London Mathematical Society, ISSN 0024-6107, 2012, vol. 85, p. 1, str. 191-222. [COBISS-SI-ID 16214873]
DRAGIČEVIĆ, Oliver. Some remarks on the L [sup] p estimates for powers of the Ahlfors-Beurling operator. Archiv der Mathematik, ISSN 0003-889X, 2011, vol. 96, no. 5, str. 463-471. [COBISS-SI-ID 16090713]
DRAGIČEVIĆ, Oliver. Weighted estimates for powers of the Ahlfors-Beurling operator. Proceedings of the American Mathematical Society, ISSN 0002-9939, 2011, vol. 139, no. 6, str. 2113-2120. [COBISS-SI-ID 15876697]
Peter Šemrl:
ŠEMRL, Peter. A characterization of normed spaces among metric spaces. Rocky Mountain journal of mathematics, ISSN 0035-7596, 2011, vol. 41, no. 1, str. 293-298. [COBISS-SI-ID 15865177]
ŠEMRL, Peter. Applying projective geometry to transformations on rank one idempotents. Journal of functional analysis, ISSN 0022-1236, 2004, vol. 210, no. , str. 248-257. [COBISS-SI-ID 13012825]
ŠEMRL, Peter. Comparability preserving maps on bounded observables. Integral equations and operator theory, ISSN 0378-620X, 2008, vol. 62, no. 3, str. 441-454. [COBISS-SI-ID 15005273]
ŠEMRL, Peter. Osnove višje matematike I, (Izbrana poglavja iz matematike in računalništva, 45). Ljubljana: DMFA - založništvo, 2009. 275 str., ilustr. ISBN 978-961-212-214-0. [COBISS-SI-ID 245381632]
