 
Abbreviation: B12A05  Load: 30(L)
+ 0(P)
+ 0(FE)
+ 0(LE)
+ 0(S)
+ 0(PEE)
+ 15(E)
+ 0(DE)

Lecturers in charge:  v. pred. mr. sc. Vida ZadeljMartić 
Lecturers:  
Course description:
Understanding the key topics and problems of Vector Analysis. Also it is necessary to develop many skills between abstract entities according to certain rules and apply it into Geodesy.
Learning outcomes at the level of the programme to which the course contributes
 Demonstrate competences in theoretical principles, procedures of computing and visualising the surveying data.
 Understand mathematical methods and physical laws applied in geodesy and geoinformatics.
 Apply knowledge of mathematics and physics for the purpose of recognizing, formulating and solving of problems in the field of geodesy and geoinformatics.
 Exercise appropriate judgements on the basis of performed calculation processing and interpretation of data obtained by means of surveying and its results.
 Take responsibility for continuing academic development in the field of geodesy and geoinformatics, or related disciplines, and for the development of interest in lifelong learning and further professional education.
Learning outcomes expected at the level of the course
 Define and implement the tasks of the term of the vector functions of one scalar variable
 Define and apply the concepts of tasks: line integral of the first and the second kind and their properties; determine the relationship between line integral of the first and the second kind, and define and apply Green formula
 Define and apply the concepts of tasks: double and triple integrals and their applications, with the introduction of the Jacobian for cylindrical and spherical coordinates
 Define and apply the concepts of tasks: surface integrals and vector surface integrals. Describe the flux of a vector field through a surface
 Define and apply the concepts of tasks: scalar and vector fields and directional derivatives
 Telling the GreenGaussOstrogradski theorem and Stokes' theorem and applying to the tasks
Course content broken down in detail by weekly class schedule (syllabus)
 Vector function and space curves; derivatives and integrals of vector functions
 Line integrals of the first kind and properties( Jordan curve, curve orientation, tangent vector to the curve, length of a curve, line integrals of the first kind, properties, line integral of the first kind using polar coordinates)
 Application of line integral of the first kind on tasks
 Line integrals of the second kind and properties
 Application of line integrals of the second kind on tasks; relationship between line integral of the first and the second kind
 Double and triple integrals and applications (double integral, replacing the order of integration, volume and surface area using double integrals, change of variables in a double integral, Jacobian, volume by the triple integrals, Jacobian for cylindrical and spherical coordinates)
 Green's formula
 Definition of parametric surfaces; Normal vectors and tangent planes; Area of a parametric surface
 Definition of the surface integral
 Oriented surfaces; The vector surface integral ; flux of a vector field through a surface
 The use of surface integrals on various types of tasks
 Scalar and vector fields (scalar fields, level surface and level curves of a scalar field, gradient of a scalar field, Hamilton's operator, Laplace operator, vector field, the curl of a vector field, divergence of a vector field, solenoidal field)
 Directional derivative
 GreenGaussOstrogradski theorem and Stokes' theorem
Screening student work
 Class attendance  1 ECTS
 Tests  (2 ECTS)
 Oral exam  1 ECTS
 Written exam  1 ECTS

Compulsory literature:    
Recommended literature:    
 