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# Vector Function in Three Dimensional Space with Application to Partial Derivative

 dc.contributor.author Alawad, Sahar Mohammed Ahmed dc.date.accessioned 2018-08-30T07:07:37Z dc.date.available 2018-08-30T07:07:37Z dc.date.issued 2017-08-10 dc.identifier.uri http://repo.uofg.edu.sd/handle/123456789/1385 dc.description A Dissertation Submitted to the University of Gezira in Partial Fulfillment of the Requirements for the Award of the Degree of Master of Science in Mathematics, Department of Mathematics and Physics , Faculty of Education - Hantoub, August - 2017 en_US dc.description.abstract When using and applying function oriented towards the three dimensional space (R3) there was a difference between them and those function in the mono-space (R) and two-dimensional space (R2) sp that when stating the straight line equation in R which is a point on a horizontal line in R2 it is a relationship between a number that represent the slope and two axises. But in R3 the slope is not a simple number or an ordinary one, we need a vector as in the straight line equation in the three dimensional space which is the base of educational of functions directed towards the three dimensional space (R3). The study aimed to find out the functions oriented towards the three dimensional space (R3). And their role in calculating and describing the areas and dimensional in an easy accurate way. It also aimed to clarify the differences between the spaces R – R2 – R3 by representing and drawing the same equation on the three spaces, this shows the completion and clarity of the figure in R3 and to shows the all types of coordinates: rectangular, cylindrical and spherical and the way to transform from one type into another. The study adopted the descriptive inductive method. The most important result: clarifying integration of oriented functions and understanding the concept of bending method of finding it out and its application by partial differential where finding tangent plane and studying linear approximation of the function and the absolute and extreme values of the functions by using Lagrange. It also revealed that the straight line equation in R3 is the best example for the vector function. Lagrange method can be used in making feasibility studies in the economic field where it gives the highest and lowest rate of profil and loss. It is not necessary that every drawing of the functions directed towards the three dimensional line whereas a curve can be drawn, so sometimes this space is called space of the curve. The study recommends using Lagrange method and its extension in the economic field to make the feasibility studies. The study recommends investigating this topic in the general space Rn¬ as an extension to this study. en_US dc.description.sponsorship Abdelrahim Basheir Hamid Basheir (Main - Supervisor) en_US Altyip Abdalgader Abdalmajed Ebrahim (Co - Supervisor) dc.language.iso en en_US dc.publisher University of Gezira en_US dc.subject partial differential en_US dc.subject Mathematics en_US dc.title Vector Function in Three Dimensional Space with Application to Partial Derivative en_US dc.type Thesis en_US
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