Enrollment into the program

# Mathematics 1

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.

• 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.

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.

Knowledge and understanding:

Knowing and understanding the basic concepts needed in the mathematical analysis. Using the obtained knowledge in physics.

Application:

Mastering the basic concepts of mathematical analysis is needed in almost all fields of physics.

Reflection:

Combining theory and computational procedures to solve the simplest mathematical problems in physics.

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.

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

Written exam or 4 midterm exams instead of the written exam

oral exam or theoretical test

Homework (optional)

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

[1] M. Černe, M. Zajec, Boundary differential relations for holomorphic functions on the disc. Proc.

Am. Math. Soc. 139 (2011), 473-484.

[2] M. Černe, M. Flores, Generalized Ahlfors functions. Trans. Am. Math. Soc. 359 (2007), 671-686.

[3] M. Černe, M. Flores, Quasilinear -equation on bordered Riemann surfaces. Math. Ann. 335

(2006), 379-403.

[4] B. Drinovec Drnovšek, F. Forstnerič, Holomorphic curves in complex spaces, Duke Math. J. 139

(2007), 203-253.

[5] B. Drinovec Drnovšek, F. Forstnerič, The Poletsky-Rosay theorem on singular complex spaces,

Indiana Univ. math. j. 61 (2012), 1407-1423.

[6] B. Drinovec Drnovšek, F. Forstnerič, Disc functionals and Siciak-Zaharyuta extremal functions on

singular varieties, Ann. Polon. Math. 106 (2012), 171-191.

[7] J. Smrekar, Homotopy type of mapping spaces and existence of geometric exponents, Forum

Math. 22 (2010), 433-456.

[8] J. Smrekar, A. Yamashita, Function spaces of CW homotopy type are Hilbert manifolds, Proc.

Amer. Math. Soc. 137 (2009), 751-759.

[9] J. Smrekar, Periodic homotopy and conjugacy idempotents, Proc. Amer. Math. Soc. 135 (2007),

4045-4055.

[10] P. Šemrl, Comparability preserving maps on Hilbert space effect algebras, Comm. Math. Phys.

313 (2012), no. 2, 375–384.

[11] P. Šemrl, Symmetries on bounded observables: a unified approach based on adjacency

preserving maps, Integral Equations Operator Theory 72 (2012), no. 1, 7–66.

[12] L. Molnár, P. Šemrl, Transformations of the unitary group on a Hilbert space, J. Math. Anal. Appl.

388 (2012), no. 2, 1205–1217.