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Cilj ovog rada je objasniti što je vektorska funkcija te je definirati i uvesti pojmove koji su bitni i vezani za to područje. Prvo je definirana vektorska funkcija uz pojmove limes vektorske funkcije, hodograf vektorske funkcije i svojstva neprekidnosti. Objašnjene su derivacije i integrali vektorskih funkcija. Nakon toga, uvedeni su i ostali koordinatni sustavi te je spomenut Gaussov i Stokeov teorem. Definirani su operatori vektorskog polja, a to su gradijent, rotacija i divergencija vektorskog polja. Na kraju se spominju primjene vektorskih polja u fizici, Maxwellove jednadžbe te riješeni primjeri zadataka The main goal of this paper is to explain what is vector function and to define and introduce concepts that are relevant and related to that area. Firstly, vector function is defined by the terms of limit of the vector function, the graph of vector function and continuous function properties. Also, derives and integral of vector functions are explained. Furthermore, other coordinate systems were introduced and Gaussian and Stokes theorem were mentioned. Vector field operators are defined which are gradient, curl and divergence of the vector field. In the end is pointed out the use of vector fields in physics. Maxwell's equations and solved examples of tasks are mentioned

U ovom diplomskom radu dali smo pregled linearnih (elastičnih) i nelinearnih (neelastičnih) optičkih raspršenja. Rayleighevo i Mieovo spadaju u linearna, dok Ramanovo i Brillouinovo spadaju u nelinearna raspršenja. Kod linearnog raspršenja, sva se energija redistribuira u druge optičke valove. Kod nelinearnog raspršenja dio energije utroši se za nastanak fonona, odnosno vibrirajućih ili rotirajućih molekula koje sadrže određenu količinu energije. Kod Ramanova raspršenja nastaju Stokesovi i anti-Stokesovi signali, nastali kao posljedica nelinearnog efekta. Opisali smo dvije metode distribuiranog optičkog senzorskog mjerenja. OTDR koristi kratki optički impuls koji odašiljemo u svjetlovod, a na povratku mjerimo snage reflektiranih signala, dok OFDR koristi prebrisavanje frekvencije u određenom frekvencijskom pojasu za distribuirano optičko mjerenje. Napravili smo distribuirani optički senzorski sustav kojim je moguće mjeriti temperaturu u sustavu. Koristili smo impulsni signal širine 348 ns, što daje rezoluciju od 72 metra. Mjereći snage povratnih signala možemo odrediti temperaturu na određenom mjestu u sustavu. Rayleigh and Mie scattering are the most common elastic scattering. In a linear collision process energy of scattered photon is not changed. Raman and Brillouin scattering are the most common inelastic scattering. In a nonlinear collision process energy of scattered photon is changed due to occurrence of the phonon, vibrating or rotating molecule. Stokes and anti-Stokes signals occurre in Raman scattering. Stokes has 13,2 THz lower frequency than incident photon and anti-Stokes has higher frequency components. We describe two methods of distributed optical measurement. In the OTDR, high-power optical pulses are launched into a fiber, which is being inspected, or is used as a distributed sensor, the pulses are scattered back along with propagation in the fiber, and their intensity decays due to the fiber loss. The return signal is thus a declined curve displayed in an oscilloscope. The OFDR uses the frequency-modulated continuous wave (FMCW) ranging technique, referring to the radar technology. In the system, a cw optical carrier with a periodic linear frequency sweep is employed. We made an distributed optical sensor system that can measure increment of temperature in specific place of system, depending of resolution. Pulse width was 348 ns and resolution of system was 72 meters. Measurements of reflected signals can give us an information of temperature at specific place in system.