|Abbreviation: B12A05||Load: 30(L)
|Lecturers in charge: ||v. pred. mr. sc. Vida Zadelj-Martić
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 Green-Gauss-Ostrogradski 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
- Green-Gauss-Ostrogradski 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: - - -