Višja matematika v fiziki

Higher Mathematics in Physics. In physics all the laws and theorems connected with the physical quantities which vary in space and time, can be written with differential equations. These can be ordinary or partial, scalar or vector, but in several cases there is a system of a few or many coupled differential equations, depending on the dimension and complexity of the physical problem. While the differential equations are the local form of writing physical laws, the integral equations contain the whole space or time, or a definite space and time area. A typical example of writing equations in both forms is a set of Maxwell equations in electromagnetism or variational calculus connected with the minimization of the free energy. By setting and solving (analytically or numerically) these equation we can capture all the areas of physics, from mechanics and movement of point-like bodies, where the special physical branch called analytical mechanics introduces the concepts of generalized coordinates and impulses, Lagrangian and Hamiltonian, up to treatment of scalar and vector fields in electromagnetism and wave optics, quantum physics, thermodynamics, physics of fluids, probability theory etc.