14. starptautiskā konference 2012 - Latvijas Jūras akadēmija

Proceedings of 14th International conference „Maritime Transport and Infrastructure - 2012”APPLICATION OF A PARTIAL DERIVATIVEKsenija Maslova, Arturs Smirnovs, Mārtiņš Vanags*, Voldemārs Barkāns***Latvijas Zinātņu Akadēmija, Akadēmijas laukums 1, Rīga, LV-1050, Latvija; E-pasts: SF11053@gmail.com**Latvijas Jūras Akadēmija, Flotes ielā 5B, Rīga, LV-1016, Latvija; E-pasts: Voldemars.Barkans@inbox.lvAnnotationThe report covers the application of a partial derivative approximating the curve that isexperimentally obtained using the method of least squares.Key words: partial derivative, method of least squares.IntroductionWe continue a series of reports, that cover the various parts of application of Mathematics course thatwere initiated at the previous Latvian Maritime Academy conferences. The Mathematics course duringthe bachelor degree programs at technical high education institutions is required to get studentsacquainted with Mathematics apparatus that is necessary in comprehensive technical courses to dealwith practical tasks.TaskThe measurements (Table 1, t and y) were made and the experimental curve 2 (Fig. 1) wasobtained, experimenting with the new composition of fuel.To obtain an empirical formula for the analysis of the physical process, the results of theexperiment are approximated using the method of least squares [1], [2].The function for approximation is chosenftkt y a te(1)The function is converted by taking logarithm of both sides:ln y ln a ln t kt. (2)Designated: Y = ln y; X = t; b = ln a . Obtained:Y = kX+ lnX + b. (3)The difference (bias) i between the experimentally obtained Yiand theoretically establishedis designated by: kX ln X b Y. (4)iiiiThe sum is formed:s ni1nkXi ln Xi b Yi2 , (5)ii1275