Enrollment into the program
Mathematics I
2025/2026
Programme:
Applied Physics, First Cycle
Year:
1 year
Semester:
first and second
Kind:
mandatory
ECTS:
16
Language:
slovenian
Course director:
Lecturer (contact person):
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 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.
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
Written exam or 4 midterm exams instead of the written exam
oral exam or theoretical test
Homework (optional)
5 - 10, a student passes the exam if he is graded from 6 to 10
Lecturer's references
Pavle Saksida:
[1] SAKSIDA, Pavle. Discrete nonlinear Fourier transforms and their inverses. Inverse problems, ISSN 0266-5611. - Vol. 38, no. 8, art 085003 (22 str.) [COBISS-SI-ID 123592195]
[2] SAKSIDA, Pavle. Nonlinear Fourier transform - towards the construction of nonlinear Fourier modes. Journal of Physics A, Mathematical and theoretical, ISSN 1751-8113. - Vol. 51, no. 1, 015205 (31 str.) [COBISS-SI-ID 18191449]
[3] SAKSIDA, Pavle. Lattices of Neumann oscillators and Maxwell/Bloch equations. Nonlinearity, ISSN 1751-8113. - Vol. 44, no. 8, 085203 (19 str.) [COBISS-SI-ID 15909465]
