1. OPĆE INFORMACIJE

1.1. Nositelj predmeta

Jelka Beban Brkić

1.6. Godina studija

Prva, I semestar

1.2. Naziv predmeta

Analitička geometrija i linearna algebra

1.7. Bodovna vrijednost (ECTS)

5

1.3. Suradnici

Željka Tutek

1.8. Način izvođenja nastave (broj sati P+V+S+e-učenje)

30(P)+30(V)+e-učenje

1.4. Studijski program (preddiplomski, diplomski, integrirani)

preddiplomski

1.9. Očekivani broj studenata na predmetu

90

1.5. Status predmeta

obvezan

1.10. Razina primjene e-učenja (1, 2, 3 razina), postotak izvođenja predmeta on line (maks. 20%)

Razina e-učenja: 2

2. OPIS PREDMETA

2.1. Ciljevi predmeta

Prepoznati stečene matematičko‐numeričke vještine analitičke geometrije i linearne algebre u području studiranja.

Upotrijebiti stečene matematičko‐numeričke vještine analitičke geometrije i linearne algebre na rješavanje problema u području studiranja.

2.2. Uvjeti za upis predmeta i ulazne kompetencije potrebne za predmet

Uvjeti za upis: Položena Državna matura. Upisan Fakultet.

Kompetencije: poznavanje srednjoškolskog matematičkog gradiva

2.3. Ishodi učenja na razini programa kojima predmet pridonosi

  • Poznavati teorijska načela, postupke računske obrade i vizualizacije podataka geodetskih izmjera.
  • Razumjeti matematičke metode i fizikalne zakone koji se primjenjuju u geodeziji i geoinformatici.
  • Primijeniti znanja matematike i fizike u prepoznavanju, formuliranju i rješavanju inženjerskih zadataka.
  • Donositi zaključke na temelju obavljene računske obrade i interpretacije podataka geodetskih izmjera i dobivenih rezultata.
  • Planirati nastavak akademskog obrazovanja u području geodezije i geoinformatike ili srodnih disciplina, te razviti kulturu cijeloživotnog i stručnog obrazovanja.

2.4. Očekivani ishodi učenja na razini predmeta (4-10 ishoda učenja)

  • reproducirati temeljne pojmove vektorske algebre i analitičke geometrije prostora te ih primijeniti u rješavanju zadataka;
  • prepoznati i razlikovati vrste ploha drugog reda;
  • objasniti pojmove matrice i determinante, nabrojiti njihova svojstva te ih koristiti u računu matrica i determinanti;
  • razlikovati metode rješavanja sustava linearnih jednadžbi i primijeniti odgovarajuću metodu u rješavanju konkretnog sustava;
  • opisati metodu najmanjih kvadrata i argumentirati njenu primjenu u rješavanju zadataka;
  • definirati pojmove svojstvenih vrijednosti i svojstvenih vektora te poznavati njihove karakteristične primjene;
  • opisati pojmove dijagonalizacije i ortogonalne dijagonalizacije matrica te ih provesti na konkretno zadanim matricama;
  • koristiti sustav za e-učenje.

2.5. Sadržaj predmeta detaljno razrađen prema satnici nastave

Algebra vektorska. 3h

Analitika prostora. 3h

Jednadžba, skica i prepoznavanje ploha drugog reda. 1h

Algebra matrica. 2h

Elementarne transformacije i elementarne matrice. 1h

Ponavljanje gradiva. 1h

1. kolokvij 1h

Reducirani oblik matrice i inverz matrice. 2h

Rješavanje linearnih sustava Gauss-Jordanovom redukcijom. Homogeni sustavi. Kronecker-Capellijev teorem. 2h

Pojam i izračunavanje determinanti. Cramerovo pravilo. 2h

Metoda najmanjih kvadrata. 1h

Ponavljanje gradiva. 1h

2. kolokvij 1h

Pojam vektorskog prostora. Linearna zavisnost i linearna nezavisnost vektora. 2h

Koordinate i promjena baze. Svojstvene vrijednosti i svojstveni vektori. 2h

Linearne transformacije. Dijagonalizacija matrice. 2h

Kvadratne forme konike, kvadrike. Dijagonalizacija kvadratne forme. 2h

Završna provjera znanja. 1h

2.6. Vrste izvođenja nastave:

predavanja

seminari i radionice

vježbe

on line u cijelosti

mješovito e-učenje

terenska nastava

samostalni zadaci

multimedija i mreža

laboratorij

mentorski rad

(ostalo upisati)

2.7. Komentari:

2.8. Obveze studenata

Redovito pohađanje nastave.

Praćenje sustava za e-učenje.

Pisanje zadaća.

Dolazak na konzultacije (nastavnik/demonstrator)

2.9. Praćenje rada studenata (upisati udio u ECTS bodovima za svaku aktivnost tako da ukupni broj ECTS bodova odgovara bodovnoj vrijednosti predmeta):

Pohađanje nastave

Istraživanje

Praktični rad

Eksperimentalni rad

Referat

Samostalni zadaci

4%

Esej

Seminarski rad

Interaktivni zadaci

4%

Kolokviji

92%

Usmeni ispit

(Ostalo upisati)

Pismeni ispit

100%

Projekt

(Ostalo upisati)

2.1. Ocjenjivanje i vrjednovanje rada studenata tijekom nastave i na završnom ispitu

Prema bodovnoj tablici:

50-61 bodova

dovoljan (2)

62-74 bodova

dobar (3)

75-87 bodova

vrlo dobar (4)

88-100 bodova

odličan (5)

2.2. Obvezna literatura (dostupna u knjižnici i putem ostalih medija)

Naslov

Broj primjeraka u knjižnici

Dostupnost putem ostalih medija

Beban Brkic, J., Tutek, Ž.: Analitička geometrija i linearna algebra, Skripta Geodetskog fakulteta, Zagreb, 2012.

desetak

Beban Brkic, J.: Analitička geometrija i linearna algebra, Nastavni materijal za studente (na web-u),Geodetski fakultet

Moodle / e-učenje

Elezović, N.: Linearna algebra, Element, Zagreb (više izdanja)

desetak

Elezović, N., Aglić, A.: Linearna algebra, Zbirka zadataka, Element, Zagreb (više izdanja)

desetak

2.12.Dopunska literatura (u trenutku prijave prijedloga studijskoga programa)

Anton, H., Rorres, C.: Elementary Linear Algebra, John Wiley & Sons, N.Y.2000.

Slapničar I.: Matematika 1, www.fesb.hr/~mat1

2.13.Načini praćenja kvalitete koji osiguravaju stjecanje izlaznih kompetencija

Pri ponavljanju gradiva na predavanjima. Samostalno rješavanje zadataka tijekom vježbi. Aktivnost na sustavu za e-učenje. Samostalni zadaci. Interaktivni zadaci. Prisutnost na konzultacijama. Kolokviji. Ispiti.

Provedba jedinstvene sveučilišne ankete među studentima za ocjenjivanje nastavnika koju utvrđuje Senat Sveučilišta.

2.14.Ostalo (prema mišljenju

predlagatelja)

1. GENERAL INFORMATION

1.1. Course teacher

Jelka Beban Brkić

1.6. Year of the study programme

First, 1st semester

1.2. Name of the course

Analytical Geometry and Linear Algebra

1.7. Credits (ECTS)

5

1.3. Associate teachers

Željka Tutek

1.8. Type of instruction (number of hours L + S + E + e-learning)

30 (L) + 30 (E)

1.4. Study programme (undergraduate, graduate, integrated)

Bachelor Study

1.9. Expected enrolment in the course

90

1.5. Status of the course

compulsory

1.10. Level of application of e-learning (level 1, 2, 3), percentage of online instruction (max. 20%)

e-learning level: 2

2. COUSE DESCRIPTION

2.1. Course objectives

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.

2.2. Course enrolment requirements and entry competences required for the course

Admission requirements: High school graduation. Faculty enrolled.
Competencies: knowledge of high school mathematics curriculum.

2.3. 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.

2.4. Learning outcomes expected at the level of the course (4 to 10 learning outcomes)

  • Master the fundamental vector algebra and analytic geometry concepts and apply them in solving tasks;
  • Identify and differentiate between types of second order surfaces;
  • Explain the concepts of matrices and determinants, list their properties and use them in computations with matrices and determinants;
  • Distinguish methods for solving systems of linear equations and apply the appropriate method to solve a given system;
  • Describe the method of least squares and argue its application in solving tasks;
  • Define the terms of eigenvalues and eigenvectors and know their typical applications;
  • Describe and implement the concepts of diagonalization and orthogonal diagonalization of a matrix.
  • Use the system for e-learning.

2.5. Course content broken down in detail by weekly class schedule (syllabus)

Vector algebra. 3h

Analytical geometry. 3h

Equation, sketch and recognition of surfaces of the second order. 1h

Matrix algebra. 2h

Elementary transformations and elementary matrices. 1h

Review of previous work. 1h

1st preliminary exam 1h

Reduced form of the matrix, inverse matrix. 2h

Solving linear systems using the Gauss-Jordan reduction. Homogeneous linear systems. The Kronecker-Capelli theorem. 2h

The concept and calculation of determinants. Cramer's rule. 2h
Least squares method. 1h

Review of previous work. 1h

2nd preliminary exam 1h

Vector space. Linear independence. 2h

Coordinates and change of basis. Eigenvalues and eigenvectors. 2h

Linear transformations. Matrix diagonalization. 2h

Quadratic forms. Diagonalization of quadratic forms. 2h
The final exam. 1h

2.6. Format of instruction:

lectures

seminars and workshops

exercises

on line in entirety

partial e-learning

field work

independent assignments

multimedia and the internet

laboratory

work with mentor

(other)

2.7. Comments:

2.8. Student responsibilities

Regular school attendance. Monitoring of e-learning. Writing tasks. Consultations (teacher / student assistant)

2.9. Screening student work (name the proportion of ECTS credits for each activity so that the total number of ECTS credits is equal to the ECTS value of the course )

Class attendance

Requirement for the signature

Research

Practical training

Experimental work

Report

independent assignments

4%

Essay

Seminar essay

interactive tasks

4%

Tests

92%

Oral exam

optional

(other)

Written exam

100%

Project

(other)

2.10. Grading and evaluating student work in class and at the final exam

50-61 credits

sufficient (2)

62-74 credits

good (3)

75-87 credits

very good (4)

88-100 credits

excellent (5)

2.11. Required literature (available in the library and via other media)

Title

Number of copies in the library

Availability via other media

Beban Brkic, J., Tutek, Ž.: Analytical Geometry and Linear Algebra, Textbook for students, Faculty of Geodesy, Zagreb 2012

in preparation

Beban Brkic, J.: Analitička geometrija i linearna algebra, Textbook for students (on the web), Faculty of Geodesy

http://e-ucenje.geof.unizg.hr/

Elezović, N.: Linear Algebra, Element, Zagreb, 1995 (multiple editions)

some ten

Elezović, N., Aglić, A.: Linear Algebra Workbook, Element, Zagreb, 1995 (multiple editions)

some ten

2.12.Optional literature (at the time of submission of study programme proposal)

Anton, H., Rorres, C.: Elementary Linear Algebra, John Wiley & Sons, N.Y.2000.

Slapničar I.: Matematika 1, www.fesb.hr/~mat1

2.13.Quality assurance methods that ensure the acquisition of exit competences

Class attendance. In revising during lectures. Problem solving during exercises. Activity on the system for e-learning. Individual assignment. Interactive tasks. Consultations attendance. Preliminary exams. Exams.

The implementation of a single university Questionnaire for evaluating teachers prescribed by the Senate.

2.14.Other (as the proposer wishes to add)