Course content

Vector Analysis

Code:

144611

Abbreviation:

B12A05

Higher education institution:

Faculty of Geodesy

ECTS credits:

3.0

Load:

15(E) + 30(L)

Issuing teachers:

Assistant Professor Sonja Žunar Kožić, PhD

Course contractors:

Assistant Professor Sonja Žunar Kožić, PhD (E, L)

Course description:

By completing this course, the students will master the key concepts and techniques of Vector Analysis and their applications to concrete problems. Learning outcomes at the level of the program to which the course contributes: 1) Understanding theoretical principles, computation, and visualization of the surveying data 2) Understanding mathematical methods and physical laws with applications in geodesy and geoinformatics 3) Applying knowledge of mathematics and physics to recognize, formulate and solve problems in the field of geodesy and geoinformatics 4) Exercise appropriate judgments based on computations and interpretation of surveying data 5) Taking responsibility for continuing academic development in the field of geodesy and geoinformatics, or related disciplines, and developing an interest in lifelong learning and further professional education. Learning outcomes at the level of the course: 1) Defining and applying vector functions of one scalar variable 2) Defining and applying the line integral of the first kind and the line integral of the second kind; determining the relationship between the line integral of the first kind and the line integral of the second kind; stating and applying Green's formula 3) Defining and applying double and triple integrals, introducing the Jacobian for cylindrical and spherical coordinates 4) Defining and applying surface integrals and vector surface integrals 5) Describing the flux of a vector field through a surface 6) Defining and applying scalar and vector fields and directional derivatives 7) Stating and applying the Green-Gauss theorem and Stokes's theorem. Course content by weekly class schedule (syllabus) 1) Derivatives and integrals (review) (Lec. 2h + Tut. 1h) 2) Vector functions; space curves, tangent vector of a curve, regular curve, orientiation of a curve, arc length, tangent line to a curve (Lec. 2h + Tut. 1h) 3) Line integrals of the first kind, its properties, and applications; line integral of the first kind in polar coordinates (Lec. 2h + Tut. 1h) 4) Line integral of the second kind, its properties and applications; relationship between the line integral of the first kind and the line integral of the second kind, circulation of a vector field around a closed curve (Lec. 2h + Tut. 1h) 5) Double and triple integrals and applications (double integral, changing the order of integration, volume and surface area using double integrals, change of variables in a double integral, Jacobian, volume using triple integrals, Jacobian for cylindrical and spherical coordinates) (Lec. 4h + Tut. 2h) 6) Green's formula; area of a plane surface bounded by a closed curve (Lec. 2h + Tut. 1h) 7) 1st midterm (2h) 8) Surface area; normal vectors, area between two parallels and two meridians on a sphere (Lec. 2h + Tut. 2h) 9) Surface integral of the first kind and applications (Lec. 2h + Tut. 1h) 10) Surface integral of the second kind and applications; flux of a vector field through a surface (Lec. 4h + Tut. 2h) 12) 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) (Lec. 2h + Tut. 1h) 13) Directional derivative; Green-Gauss theorem and Stokes's theorem (Lec. 2h + Tut. 2h) 14) 2nd midterm (2h) Screening student work: Class attendance - 1 ECTS Short tests and midterms - 1 ECTS Written and oral exam - 1 ECTS.

Mandatory literature:

Javor, P. (2002): Matematička analiza 2

Lapaine, M. (1997): Vektorska analiza. Zbirka riješenih zadataka

Recommended literature:

Demidovič, B. P. (2003): Zadaci i riješeni primjeri iz Matematičke analize za Tehničke fakultete

Learning outcomes:

1. Defining and applying vector functions of a scalar argument

2. Defining and applying the line integral of the first kind and the line integral of the second kind; determining the relationship between the line integral of the first kind and the line integral of the second kind; stating and applying Green's formula

3. Defining and applying double and triple integrals, introducing the Jacobian for cylindrical and spherical coordinates

4. Defining and applying surface integrals and vector surface integrals

5. Describing the flux of a vector field through a surface

6. Defining and applying scalar and vector fields and directional derivatives

7. Stating and applying the Green-Gauss theorem and Stokes's theorem

Course in study programme:

Code	Name of study	Level of study	Semester	Required/Elective
71	Geodesy and Geoinformatics	undergraduate	2	required

* the course is not taught in that semester

Legend

E - Exercises

L - Lectures