Mathematical tools in physics

2022/2023
Programme:
Practical Mathematics
Year:
2 year
Semester:
second
Kind:
mandatory
ECTS:
5
Language:
slovenian
Hours per week – 2. semester:
Lectures
3
Seminar
0
Tutorial
0
Lab
3
Content (Syllabus outline)

Scalars and vectors:
scalars and vectors in mathematics, the dot and the cross products of vectors, translations, rotations and inversions, two examples of scalars in physics: mass and electric charge, an example of a vector in physics: position vector.
Derivative:
velocity and acceleration, projectile motion, circular motion, electric current.
Scalars in physics:
Galilean and Lorentz transformations, distance between two points, speed of light, kinetic energy.
Vectors in physics:
force, momentum, electric force and electric field, torque, angular momentum of a pointlike particle, angular velocity, magnetic force and flux density, torque of magnetic forces.
Integral:
impulse, work, electric work and voltage, magnetic flux.
Mixed (or scalar triple) product:
induction.
Scalars and pseudoscalars, vectors and axial vectors.
Tensors:
inertia tensor.
Calculus of variations:
Fermat’s principle of refraction.
Matrices:
systems of linear equations in electric circuits, matrix geometric optics.
Differential equations:
resistors, capacitors and coils in alternating current circuits, charging and discharging of capacitors and coils, electrical and mechanical oscillations, transformer.
Probability calculus:
radioactive decay, kinetic theory of gasses, quantum mechanics.

Readings

Kuščer, A. Moljk, T. Kranjc, J. Peternelj: Fizika za srednje šole – 1. del, DZS, Ljubljana, 1999.
Kuščer, A. Moljk, T. Kranjc, J. Peternelj: Fizika za srednje šole – 2. del, DZS, Ljubljana, 2000.
I. Kuščer, A. Moljk, T. Kranjc, J. Peternelj, M. Rosina, J. Strnad: Fizika za srednje šole – 3. del, DZS, Ljubljana, 2002.
J. Strnad, Fizika – 1.del, DMFA založništvo, Ljubljana, 1984.
J. Strnad, Fizika – 2.del, DMFA založništvo, Ljubljana, 1985.
J. Strnad, Fizika – 3.del, DMFA založništvo, Ljubljana, 1982.
I. Kuščer, A. Kodre: Matematika v fiziki in tehniki. DMFA založništvo, Ljubljana, 2006.

Objectives and competences

Lectures possibilities to apply mathematical tools in physics. At tutorials and with individual practice, students develop skills of independent modelling and applying these tools.

Intended learning outcomes

Knowledge and understanding:
Topics, encountered first at Introduction to physics, are now covered in greater depth by invoking knowledge and tools, acuired at mathematical courses.
Application:
Ability of independent solving of physics problems.
Reflection:
Insight into the interplay between mathematics and empirical science.
Transferable skills:
To approach and to solve problems in science by modelling.

Learning and teaching methods

Lectures, exercises, consultations

Assessment

Two midterm exams instead of written exam, written exam,
Test and oral exam

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

Lecturer's references

PODOBNIK, Tomaž, ŽIVKO, Tomi. On probabilistic parametric inference. Journal of statistical planning and inference, ISSN 0378-3758, 2014, vol. 142, no. 12, str. 3152-3166. [COBISS-SI-ID 27449383]
DELPHI Collaboration, ABREU, P., ERŽEN, Borut, GOLOB, Boštjan, KRIŽNIČ, Ervin, PODOBNIK, Tomaž, STANIČ, Samo, ZAVRTANIK, Danilo, et al. Measurement of [vertical]V[sub]cs[vertical] using W decays at LEP2. Physics letters. Section B, ISSN 0370-2693. [Print ed.], 1998, vol. 439, str. 209-224. [COBISS-SI-ID 35835]
ARGUS Collaboration, ALBRECHT, H., BRAČKO, Marko, KERNEL, Gabrijel, KRIŽAN, Peter, KRIŽNIČ, Ervin, MEDIN, Gordana, PODOBNIK, Tomaž, ŽIVKO, Tomi, et al. A partial wave analysis of the reaction [gamma][gamma] [to] [pi][sup]+[pi][sup]-[pi][sup]0. Zeitschrift für Physic C. Particles and fields, ISSN 0170-9739, 1997, vol. 74, str. 469-477. [COBISS-SI-ID 12892711]