Mathematics 1

2022/2023
Programme:
Practical Mathematics
Year:
1 year
Semester:
first and second
Kind:
mandatory
ECTS:
16
Language:
slovenian
Hours per week – 1. semester:
Lectures
4
Seminar
0
Tutorial
4
Lab
0
Hours per week – 2. semester:
Lectures
4
Seminar
0
Tutorial
4
Lab
0
Content (Syllabus outline)

Basic concepts of sets and mappings.
Fundamentals of mathematical logic: and, or.
Real and complex numbers.
Number sequences and series.
Basic properties of real functions.
Overview of elementary functions.
Differentiation of functions. Rolle's and Lagrange's theorem.
Higher derivatives. Applications of the derivative.
Indefinite integral.
Definite integral. Properties of the definite integral. The relationship between definite and indefinite integral.
Applications of the integral.
Improper integral.
Taylor formula and series.
Sequences and series of functions.

Readings

J. Globevnik, M. Brojan: Analiza 1, DMFA založništvo, Ljubljana, 2010.
R. Jamnik: Matematika, DMFA založništvo, Ljubljana, 1994.
I. Vidav: Višja matematika I, DZS, Ljubljana, 1981.
M.H. Protter, C.B. Morrez: Intermediate Calculus, Springer-Verlag, New York, 1985.
E. Krezsyig: Advanced Engineering Mathematics, Wiley, New York, 1988.
P. Mizori-Oblak, Matematika za študente tehnike in naravoslovja, 1. del, Fakulteta za strojništvo, 2001.
A. Turnšek: Tehniška matematika, Fakulteta za strojništvo, Ljubljana, 2007.

Objectives and competences

Students acquire the basic knowledge of set theory, mathematical logic, mappings, sets of numbers, sequences and series, real functions, differentiable calculus and integration.
They will have a very good understanding and the ability to use elementary functions. They will acquire the basic skills needed in the mathematical analysis.

Intended learning outcomes

Knowledge and understanding:
Knowing and understanding the basic concepts needed in the mathematical analysis. Using the obtained knowledge in other fields of mathematics and other sciences.
Application:
Mastering the basic concepts of mathematical analysis is needed in almost all fields of applied mathematics. Mathematical analysis is fundamental in almost all branches of applied mathematics.
Reflection:
Combining theory and computational procedures to solve the simplest problems in applied mathematics.
Transferable skills:
The ability of a correct formulation of a problem, selecting the appropriate method, solving problems independently, the ability to analyze the results obtained.

Learning and teaching methods

Lectures, exercises, homeworks, consultations, extra hours of studying with the help of teaching assistants and tutors, virtual classroom (chatrooms, forums, etc.)

Assessment

Type (examination, oral, coursework, project):
written exam or 4 midterm exams instead of the written exam,
oral exam or theoretical test,
homework (optional).
Grading: 1-5 (fail), 6-10 (pass) (according to the Statute of UL)

Lecturer's references

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. Generalized Ahlfors functions. Transactions of the American Mathematical Society, ISSN 0002-9947, 2007, vol. 359, no. 2, str. 671-686. [COBISS-SI-ID 14227801]
ČERNE, Miran, FLORES, Manuel. Quasilinear [overline{partial}]-equation on bordered Riemann surfaces. Mathematische Annalen, ISSN 0025-5831, 2006, vol. 335, no. 2, str. 379-403. [COBISS-SI-ID 13970777]
Barbara Drinovec Drnovšek:
DRINOVEC-DRNOVŠEK, Barbara, FORSTNERIČ, Franc. Holomorphic curves in complex spaces. Duke mathematical journal, ISSN 0012-7094, 2007, vol. 139, no. 2, str. 203-254. [COBISS-SI-ID 14351705]
DRINOVEC-DRNOVŠEK, Barbara, FORSTNERIČ, Franc. The Poletsky-Rosay theorem on singular complex spaces. Indiana University mathematics journal, ISSN 0022-2518, 2012, vol. 61, no. 4, str. 1407-1423. [COBISS-SI-ID 16679257]
DRINOVEC-DRNOVŠEK, Barbara, FORSTNERIČ, Franc. Disc functionals and Siciak-Zaharyuta extremal functions on singular varieties. V: Proceedings of Conference on Several Complex Variables on the occasion of Professor Józef Siciak's 80th birthday : July 4-8, 2011, Kraków, Poland, (Annales Polonici Mathematici, ISSN 0066-2216, Vol. 106). Warsaw: Institute of Mathematics, Polish Academy of Sciences, 2012, str. 171-191. [COBISS-SI-ID 16436057]
Jaka Smrekar:
SMREKAR, Jaka. Homotopy type of mapping spaces and existence of geometric exponents. Forum mathematicum, ISSN 0933-7741, 2010, vol. 22, no. 3, str. 433-456. [COBISS-SI-ID 15638105]
SMREKAR, Jaka, YAMASHITA, Atsushi. Function spaces of CW homotopy type are Hilbert manifolds. Proceedings of the American Mathematical Society, ISSN 0002-9939, 2009, vol. 137, no. 2, str. 751-759. [COBISS-SI-ID 14965849]
SMREKAR, Jaka. Periodic homotopy and conjugacy idempotents. Proceedings of the American Mathematical Society, ISSN 0002-9939, 2007, vol. 135, no. 12, str. 4045-4055. [COBISS-SI-ID 14382681]
Peter Šemrl:
ŠEMRL, Peter. Comparability preserving maps on Hilbert space effect algebras. Communications in Mathematical Physics, ISSN 0010-3616, 2012, vol. 313, iss. 2, str. 375-384. [COBISS-SI-ID 16568409]
ŠEMRL, Peter. Symmetries on bounded observables: a unified approach based on adjacency preserving maps. Integral equations and operator theory, ISSN 0378-620X, 2012, vol. 72, iss. 1, str. 7-66. [COBISS-SI-ID 16568665]
MOLNÁR, Lajos, ŠEMRL, Peter. Transformations of the unitary group on a Hilbert space. Journal of mathematical analysis and applications, ISSN 0022-247X. [Print ed.], 2012, vol. 388, iss. 2, str. 1205-1217. [COBISS-SI-ID 16568153]