Course content

Analytical Geometry and Linear Algebra

Code:

33487

Abbreviation:

B11A01

Higher education institution:

Faculty of Geodesy

ECTS credits:

5.0

Load:

30(E) + 30(L)

Issuing teachers:

Assistant Professor Iva Kodrnja, PhD

Course contractors:

Assistant Professor Iva Kodrnja, PhD (E, L)

Senior Lecturer Željka Tutek, MSc (E)

Course description:

Recognize the acquired mathematical and numerical skills of analytical geometry and linear algebra in the field of study. Use of acquired mathematical and numerical skills of analytical geometry and linear algebra to solve problems in the field of study. Learning outcomes at the level of the programme to which the course contributes <ul><li>Demonstrate competences in theoretical principles, procedures of computing and visualising the surveying data. <li>Understand mathematical methods and physical laws applied in geodesy and geoinformatics. <li>Apply knowledge of mathematics and physics for the purpose of recognizing, formulating and solving of problems in the field of geodesy and geoinformatics. <li>Exercise appropriate judgements on the basis of performed calculation processing and interpretation of data obtained by means of surveying and its results. <li>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.</ul> Learning outcomes expected at the level of the course <ul><li>Master the fundamental vector algebra and analytic geometry concepts and apply them in solving tasks; <li>Identify and differentiate between types of second order surfaces; <li>Explain the concepts of matrices and determinants, list their properties and use them in computations with matrices and determinants; <li>Distinguish methods for solving systems of linear equations and apply the appropriate method to solve a given system; <li>Describe the method of least squares and argue its application in solving tasks; <li>Define the terms of eigenvalues and eigenvectors and know their typical applications; <li>Describe and implement the concepts of diagonalization and orthogonal diagonalization of a matrix. <li>Use the system for e-learning.</ul> Course content broken down in detail by weekly class schedule (syllabus) <ul><li>Vector algebra. 3h <li>Analytical geometry. 3h <li>Equation, sketch and recognition of surfaces of the second order. 1h <li>Matrix algebra. 2h <li>Elementary transformations and elementary matrices. 1h <li>Review of previous work. 1h <li>1st preliminary exam 1h <li>Reduced form of the matrix, inverse matrix. 2h <li>Solving linear systems using the Gauss-Jordan reduction. Homogeneous linear systems. The Kronecker-Capelli theorem. 2h <li>The concept and calculation of determinants. Cramer's rule. 2h <li>Least squares method. 1h <li>Review of previous work. 1h <li>2nd preliminary exam 1h <li>Vector space. Linear independence. 2h <li>Coordinates and change of basis. Eigenvalues and eigenvectors. 2h <li>Linear transformations. Matrix diagonalization. 2h <li>Quadratic forms. Diagonalization of quadratic forms. 2h <li>The final exam. 1h</ul> Screening student work <ul><li>Class attendance - Requirement for the signature <li>independent assignments - 4% <li>interactive tasks - 4% <li>Tests - 92% <li>Oral exam - optional <li>Written exam - 100%</ul>

Course languages:

Engleski

Hrvatski

Mandatory literature:

1. Beban Brkić, J., Tutek, Ž.: Analitička geometrija i linearna algebra, Interna skripta, dostupna na e-učenju Elezović, N.: Linearna algebra, Element, Zagreb 2003. Elezović, N., Aglić, A.: Linearna algebra, Zbirka zadataka, Element, Zagreb 2003.

Recommended literature:

2. Anton, H., Rorres, C.: Elementary Linear Algebra, John Wiley & Sons, Inc., N. Y. 2000. Internetske aplikacije za vježbu.

Course in study programme:

Code	Name of study	Level of study	Semester	Required/Elective
71	Geodesy and Geoinformatics	undergraduate	1	required

* the course is not taught in that semester

Legend

E - Exercises

L - Lectures