Mathematical tools in physics

Completed courses Mathematics 1 and Linear algebra.

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.

1. I. Kuščer ... [et al.]: Fizika za srednje šole. 1.-3. del, Ljubljana : DZS, 1999-2000.
2. I. Kuščer, A. Kodre: Matematika v fiziki in tehniki, Ljubljana : DMFA - založništvo, 2006.
3. J. Strnad: Fizika. Del 1, Mehanika, toplota, Ljubljana : DMFA - založništvo, 2002, 2007.
4. J. Strnad: Fizika. Del 2, Elektrika, optika, Ljubljana : DMFA - založništvo, 1995, 2005.
5. J. Strnad: Fizika. Del 3, Posebna teorija relativnosti, kvantna fizika, atomi, 2. spremenjena izd., Ljubljana : DMFA - založništvo, 2002, 2009.

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

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.

Lectures, exercises, consultations

Two midterm exams instead of written exam, written exam,
Test and oral exam
Students get two grades: one from the written exam, the other from the theory and defense.
grading: 5 (fail), 6-10 (pass) (according to the Statute of UL)

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]